Student Handbook

Data File Architecture ...... 644 Earth Science ...... 646 Economics ...... 648 Health & Fitness ...... 650 Sports ...... 652

Prerequisite Skills ...... 654

Extra Practice ...... 662

Preparing for Standardized Tests ...... 709

Technology Reference Guide ...... 725

English-Spanish Glossary ...... 729

Selected Answers...... 752

Photo Credits...... 782

Index ...... 783

643 Data File 644 Data File Sydney HarborBridge ako hn oe ogKn 987 6 1209 368 1483 72 452 1988 88 Chicago HongKong John HancockCenter 1998 Amoco Building NewYork Bank ofChinaTower KualaLumpur Central Plaza Empire StateBuilding Sears Tower Petronas Tower II Petronas Tower I Brooklyn Bridge,NewYork 213 Garabit Viaduct, France Tunkhannock Viaduct, Pennsylvania Sydney HarborBridge,Australia Verrazano-Narrows Bridge,NewYork Firth ofForthBridge,Scotland Architecture Data File Building Bridges oftheWorld Notable Tall BuildingsoftheWorld Bridge Height(feet) ogKn 927 7 1227 374 1483 78 452 1992 Chicago 88 Hong Kong 1998 Chicago Kuala Lumpur City Completed 938 4 1136 346 1454 80 443 1973 110 1974 9810341127 344 1250 100 381 1968 102 1931 Year 135 240 171 148 480 Stories (meters) Height Fan-Fink Types ofStructuralSupports(Trusses) King-Post Fink Scissors Used inArchitecture Height (feet) apex Petronas Towers IandII Queen-Post Data File 645 Parthenon Architecture West Vacant South Midwest Occupied Year-Round Units Year-Round Northeast Owner Renter Length Width Length (meters) (meters)

Total GreeceMexicoEgyptEgypt 69.5 96EgyptEngland* 30.9 230.6Middle East 125 11 230.6 290 62 2.4Japan 109 Japan 280 Japan 43 2.3 Cambodia 10.9Cambodia 14.5 70Thailand 10.9 21 103Japan 17.9 23 70 122 20.7 67 23 27 Sea- sonal Total 5,1344,5583,530 73 99 4,372 146 3,760 2,913 344 261 4,029 287 3,500 2,627 903 818 904 967 766 1,408 603 1,360 1,094 651 689 817 756 699 470 Units 99,931 3,182 88,425 56,145 32,280 18,729 22,142 30,064 17,490 8,324 11,655 134 10,217 1,996 8,221 3,324 2,515 2,426 1,952 1,304 Housing *Gift to England from Egypt by Tenure and Region: One Recent Year and Region: One by Tenure (In thousands of units, except as indicated. Based on the American Housing Survey) (In thousands of units, except as indicated. Based on the American Housing Structure Country Structure Noted Rectangular Structures Rectangular Noted Housing Units-Summary of Characteristics and Equipment, Housing Units-Summary Item Total units Total Percent distributionUnits in structure: 100.0Single family detached 60,607 3.2Single family attached 1,8342–4 units 4,514 55,076 88.55–9 units 46,70310–19 units 56.2 64 8,37320–49 units 4,102 32.3 9,36850 or more units 2,211Mobile home or trailer 14,958 21.2 1,890 6,094 19,984 10,766 3,839 1,431 698 3,697 25.0 4,754 135 34.0 814 3,230 3,906 1,212 19.8 848 438 645 8.3 2,792 440 349 1,540 860 661 2,440 1,014 583 642 446 474 Palace of the Governors Palace of Great Pyramid of Cheops Step Pyramid of Zosar of Hathor Temple (base) Cleopatra's Needle Ziggurat of Ur (base) Dule MonasteryGuanyin Pavilion of Izumo Shrine ChinaKibitsu Shrine (main) Kongorinjo Hondo Roluos Bakong Temple, 20 Keo Temple Ta Lampun Temple, Kukut Wat Hotel Tsukiji 14 Parthenon Data File Rivers oftheWorld 646 Some Principal abz 1700 236 Zambezi Volga Tiber Thames 800 Snake 1900 St. Lawrence Rio Grande 1584 1600 Rhine Red Paraguay Orinoco 2540 Ohio 2340 Nile 2635 Missouri 1560 Mississippi 1776 Mackenzie Indus 1243 Ganges 1459 Danube 4000 Columbia Arkansas Amazon River Earth Science Data File Length (miles) 2194 1038 1290 1310 4160 1800 252 820 September November December February October January August March April June May July Average DailyTemperatures (ºF) 10° 20° 30° 40° Size andDepthoftheOceans 50° rtc5400017,881 24,441 5,400,000 30,249 28,900,000 36,161 Arctic 31,800,000 63,800,000 Indian Atlantic Pacific Ocean 60° Square Miles 70° 80° San Diego,CA Milwaukee, WI 90° Depth (feet) Greatest San Diego,CA Data File 647 – 92 Richter Scale 512 Sea Level Feet Below Mount McKinley, Alaska Mount McKinley, Earth Science Lowest Point (feet) 29,028 Dead Sea, Israel-Jordan20,32019,340 California Death Valley, Lake Assai, Djibouti 1,312 282 18,510 Caspian Sea, Russia 16,864 Unknown Elevation represents the change , where x represents the change x and 30 x Highest Point Mount Everest, Nepal-Tibet Kilmanjaro, Tanzania Mount El'brus, Russia Highest and Lowest Continental Altitudes Measuring Earthquakes Measuring Continent Asia South AmericaNorth America Mount Aconcagua, ArgentinaAfrica Alaska Mount McKinley, 22,834 Peninsula, Argentina Valdes 131 Europe Australia Kosciusko, New South Wales Mount 7,310 Lake Eyre, South Australia 52 Antarctica Massif Vinson Richter scale 2.5 3.5 4.5 6.0 Generally not felt, but recorded on seismometers. 7.0 Felt by many people. 8.0 and above Some local damage may occur. these occur once every five to ten years. Great earthquakes; A destructive earthquake that causes significant damage. A major earthquake; about ten occur each year. The energy of an earthquake is generally reported using the Richter scale, a system is generally reported using the Richter The energy of an earthquake on measuring the geologist Charles Richter in 1935, based developed by American on a seismograph. heights of wave measurements times more ground each single-integer increase represents 10 On the Richter scale, between more energy released. The change in magnitude movement and 30 times can be represented by 10 numbers on the scale in the Richter scale measure. Therefore, a 3.0 earthquake has 100 times more ground Therefore, a 3.0 earthquake has 100 in the Richter scale measure. than a 1.0 earthquake. movement and 900 times more energy released Data File 648 Economics Data File units forthecountrieslistedabove. One dollar-100pennies.Unlessnotedotherwise,thebasicmonetaryunitequalschieffractional In theUnitedStatesbasicmonetaryunitisdollarandchieffractionalpenny. Sudan Mexico Japan India France Canada Australia Country yen dnrpatr259.502 piaster dinar euro peso dla cent dollar Money Around theWorld dla cent dollar Basic Monetary ue paise rupee Unit Chief Fractional cent etv 11.5511 centavo (not used) 100 sen 108.9 Unit eeul ,4 ,3 31315,094 134,616 121,429 13,173 28,240 74,297 115,187 4,430 18,646 97,470 51,449 209,088 19,016 4,749 56,791 155,893 67,607 Venezuela 14,455 160,923 Mexico 134,210 Japan France Canada Country Exchange Rate 1 USdollar 45.9797 0.821272 1.44055 1.34255 United StatesForeign Trade 19962004 2004 U.S.exportsimports (millions ofdollars) Data File 649 Economics of the Dollar 5 lb 1 lb 1 qt 10 lb flour steak round milk potatoes The Shrinking Value The Shrinking Value 6 6.25 4.75 Rate Percent Year 1890 $0.15 1910 0.18 $0.12 $0.07 $0.16 1930 0.23 0.17 0.08 0.17 1950 0.49 0.43 0.14 0.36 1970 0.59 0.94 0.21 0.46 1975 0.98 1.30 0.33 0.90 1995 1.20 1.89 0.45 0.99 1999 1.70 3.20 0.74 3.80 2003 1.56 2.93 0.83 2.82 3.84 0.69 4.59 State Rate 5 Pennsylvania 6 6.5 Virginia 4.5 Percent State North Dakota 5 Rate 5.75 Minnesota6 6.5 Tennessee Nevada 5 7 New York 4.25 Wisconsin 5 Percent State General Sales and Use Taxes, 2004 Taxes, and Use General Sales State State AlabamaArizonaArkansas 4CaliforniaColorado 5.6 5.125Connecticut 7.25 KentuckyD.C. Maine Louisiana 2.9 6Florida MarylandGeorgia 6 MassachusettsHawaii 4 MichiganIdaho 5 5 6Illinois 4 Ohio Indiana Oklahoma 4 6Iowa Island Rhode South Carolina Mississippi MissouriKansas 5 6.25 7 4.5 6 Nebraska South Dakota 7 New Jersey 4 5.3 4.225 New Mexico 5.5 Utah Texas 6 North Carolina 5 Vermont 4.5 Washington Virginia West Wyoming 6.5 6 6 4 NOTE: Alaska, Delaware, Montana, New Hampshire, and Oregon have no statewide sales and use taxes. NOTE: Alaska, Delaware, Montana, New Hampshire, and Health & Fitness

Calorie Count of Selected Dairy Products, Breads, Pastas, Snacks, Fruits, and Juices

Approximate Food Energy Food Amount (kcal) Apple, raw 1 80 Apple juice 1 cup 120 Banana 1 100 Bread, white 1 slice 70 Butter or margarine 1 tbsp 100

Data File Cheese, American 1 oz 105 Cheese, cottage 1 cup 235 Corn flakes 1 cup 95 Crackers, saltine 4 50 Lemonade 1 cup 105 Macaroni with cheese 1 cup 430 Milk, skim 1 cup 85 Milk, whole 1 cup 150 Oatmeal 1 cup 130 Orange 1 65 Orange juice 1 cup 120 Pizza, cheese 1 medium slice 145 Raisins 1/2 oz package 40 Sherbert 1 cup 270 Spaghetti with meatballs 1 cup 330

Height and Weight Tables Men Women Height Small Medium Large Height Small Medium Large ft in. Frame Frame Frame ft in. Frame Frame Frame 5 2 128-134 131-141 138-150 4 10 102-111 109-121 118-131 5 3 130-136 133-143 140-153 4 11 103-113 111-123 120-134 5 4 132-138 135-145 142-156 5 0 104-115 113-126 122-137 5 5 134-140 137-148 144-160 5 1 106-118 115-129 125-140 5 6 136-142 139-151 146-164 5 2 108-121 118-132 128-143 5 7 138-145 142-154 149-168 5 3 111-124 121-135 131-147 5 8 140-148 145-157 152-172 5 4 114-127 124-138 134-152 5 9 142-151 148-160 155-176 5 5 117-130 127-141 137-155 5 10 144-154 151-163 158-180 5 6 120-133 130-144 140-159 5 11 146-157 154-166 161-184 5 7 123-136 133-147 143-163 6 0 149-160 157-170 164-188 5 8 126-139 136-150 146-167 6 1 152-164 160-174 168-192 5 9 129-142 139-153 149-170 6 2 155-168 164-178 172-197 5 10 132-145 142-156 152-173 6 3 158-172 167-182 176-202 5 11 135-148 145-159 155-176 6 4 162-176 171-187 181-207 6 0 138-151 148-162 158-179

650 Data File Data File 651 P.M. 6 P.M. Sleep period Noon 3 Health & Fitness A.M. 9 A.M. 6 Time of day A.M. 3 Midnight Patternsof Sleep P.M. 9 P.M. 6 Waking period Waking 4 1 10 year Birth years years Adult 620610 790 775465 960 550 945 515 595 700 655 720 515 850 515 795 350 655435 655235 445 795 145 555 795 435 300 540 350 185 675 355 555 365 355 445 225 235 450 675 335 450 540 300 550 275 425 550 275 365 350 520 350 425 425 Calories Burned Per Hour 110 lb 154 lb 198 lb Exercise 12-min mile crawl, 30 yd/min moderate 3303 mi/h 4202 mi/h moderate 510 People of Different Body Weights People of Different Racquetball (2 people) Basketball (full-court game)Skiing–cross country (5 mi/h) downhill Running–8-min mile 585 550Swimming–crawl, 45 yd/min 750 700Stationary bicycle–15 mi/h Aerobic dancing–intense 910 540 850 Walking–5 mi/h 690Calisthenics–intense 835 Scuba diving Hiking–20-lb pack, 4 mi/h 20-lb pack, 2 mi/h recreational Tennis–singles, doubles, recreationalIce skating Roller skating 235 300 365 Martial arts Number of Calories Burned by Per Hour Data File 652 Sports Data File er16 9217 9018 9819 9620 2004 2000 1996 1992 1964 1988 1960 4:05.34 3:43.10 4:05.80 1984 3:40.59 4:43.3 4:07.25 4:12.2 3:47.97 1956 4:07.18 4:50.6 3:45.00 4:18.3 4:03.85 1980 3:46.95 4:07.10 1952 4:54.6 3:51.23 4:27.3 4:08.76 3:51.31 1976 4:09.89 5:12.1 3:51.93 4:30.7 1948 4:19.44 4:00.27 5:17.8 1972 4:41.0 4:31.8 4:09.0 1936 5:26.4 Female 4:44.5 1968 5:28.5 Male 4:48.4 1932 5:42.8 Year 5:01.6 1928 6:02.2 5:04.2 Female 1924 Male Year Olympic GoldMedalWinningTimes for 400-m Freestyle Swimming,inMinutes All-American GirlsProfessional Baseball 94Jan evr otWye33.429 .346 .344 333 410 .368 314 .346 JoanneWeaver, FortWayne 342 JoanneWeaver. FortWayne 361 .306 JoanneWeaver,1954 FortWayne .316 .299 BettyWeaver Foss,FortWayne 1953 BettyWeaver Foss,FortWayne 1952 366 DorisSams,Muskegon 1951 408 408 1950 AudreyWagner, Kenosha 1949 DorothyKamenshek,Rockford DorothyKamenshek,Rockford 1948* HelenCallahan,FortWayne 1947 BetsyJochum,SouthBend 1946 GladysDavis,Rockford 1945 1944 1943 Year League BattingChampions,1943-1954 Source: AWholeNewBallgame,SueMacy, HenryHoltandCompany, NewYork, 1993. *First yearoverhandpitchingwasallowed. Player, Team tBt Average At-Bats 0 .279 .312 408 417 .296 .332 433 349 Data File 653 2 46 65 57 Sports 160 145 596 340 425 279 187 256 Average Average Weight (grams) 7.6 8.6 4.3 4.8 6.5 24.0 22.0 21.9 Diameter (centimeters) Type Carr Used in Various Sports Used in Various Lato Sizes and Weights of Balls of Sizes and Weights Baseball Basketball Croquet ball Field hockey ballGolf ball 7.6 Handball Soccer ball Volleyball Softball, largeSoftball, small tennis ballTable ball Tennis 13.0 9.8 3.7 18 yd Kasperczak Deyna Cruz 20 yd Gordon Correa Tomaszewski Soccer Playboard Cheng Neyome Young Prerequisite Skills

1 Place Value and Order Example 1

Write 2,345,678.9123 in words. Solution The place value chart shows the value of each digit. The value of each place is ten times the place to the right. mhttth to. t h t tt iuhehuen euheh l nononne nnono ldu udss tdu u i rstsr hr s s oeahae sea a n dnond d n n sduds tdd sss ht t ashh nss d s 2 3 45678.912 3

The number shown is two million, three hundred forty-five thousand, six hundred seventy-eight and nine thousand one hundred twenty-three ten-thousandths.

Example 2

Use b or a to make this sentence true. 6 2 Prerequisite Skills Solution Remember, means “less than” and means “greater than.” So, 6 2.

EXTRA PRACTICE EXERCISES Write each number in words. six million, four thousand, three hundred and two thousandths 1. 3647 three thousand, 2. 6,004,300.002 3. 0.9001 six hundred forty-seven nine thousand one Write each of the following as a number. ten-thousandths 4. two million, one hundred fifty thousand, four hundred seventeen 2,150,417 5. five thousand, one hundred twenty and five hundred two thousandths 5120.502 6. nine million, ninety thousand, nine hundred and ninety-nine ten-thousandths 9,090,900.0099 Use or to make each sentence true. 7. 9 8 8. 164 246 9. 63,475 6,435 10. 52 50 11. 5.39 9.02 12. 43.94 53.69 654 Prerequisite Skills 2 Multiply Whole Numbers and Decimals

To multiply whole numbers, find each partial product and then add. When multiplying decimals, locate the decimal point in the product so that there are as many decimal places in the product as the total number of decimal places in the factors.

Example 1

Multiply 2.6394 by 3000.

Solution 2.6394 3000 7918.2000 or 7918.2 Zeros after the decimal point can be dropped because they are not significant digits.

Example 2 Prerequisite Skills Multiply 3.92 by 0.023.

Solution 3.92 2 decimal places 0.023 3 decimal places 1176 7840 0.09016 5 decimal places The zero is added before the nine so that the product will have five decimal places.

EXTRA PRACTICE EXERCISES

Multiply. 1. 36 45 1620 2. 500 30 15,000 3. 17,000 230 3,910,000 4. 6.2 8 49.6 5. 950 1.6 1520 6. 3.652 20 73.04 7. 179 83 14,857 8. 257 320 82,240 9. 8560 275 2,354,000 10. 467 0.3 140.1 11. 2.63 183 481.29 12. 0.758 321.8 243.9244 13. 49.3 1.6 78.88 14. 6.859 7.9 54.1861 15. 794.4 321.8 255,637.9181 16. 0.08 4 0.32 17. 0.062 0.5 0.031 18. 0.0135 0.003 0.0000405 19. 21.6 3.1 66.96 20. 8.76 0.005 0.0438 21. 5.521 3.642 20.107482 22. 5.749 3.008 17.292992 23. 8.09 0.18 1.4562 24. 89,946 2.85 256,346.1 25. 6.31 908 5729.48 26. 391.05 25 9776.25 27. 35,021 76.34 2,673,503.14 Prerequisite Skills 655 3 Divide Whole Numbers and Decimals

Dividing whole numbers and 34 quotient decimals involves a repetitive divisor 7239 dividend process of estimating a quotient, 21 3 7 multiplying and subtracting. 29 Subtract. Bring down the 9. 28 4 7 1 remainder Example 1

Find: 283.86 5.7

Solution When dividing decimals, move the 49.8 decimal point in the divisor to the right 5.7.283.8.6 572838.6 until it is a whole number. Move the 228 decimal point the same number of places 558 in the dividend. Then place the decimal 513 point in the answer directly above the 45 6 new location of the decimal point in the 45 6 dividend. 0 If answers do not have a remainder of 0, you can add 0s after the last digit of the dividend and continue dividing.

EXTRA PRACTICE EXERCISES

Prerequisite Skills Divide. 1. 72 6 12 2. 6000 20 300 3. 26,568 8 3321 4. 5.6 7 0.8 5. 120 0.4 300 6. 936 12 78 7. 3.28 4 0.82 8. 0.1960 5 0.0392 9. 1968 0.08 24,600 10. 16 0.04 400 11. 1525 0.05 30,500 12. 109.94 0.23 478 13. 0.6 24 0.025 14. 7.924 0.28 28.3 15. 32.6417 9.1 3.587 16. 24 0.6 40 17. 1784.75 29.5 60.5 18. 0.01998 0.37 0.054 19. 7.8 0.3 26 20. 12,000 0.04 300,000 21. 820.94 0.02 41,047 22. 89,946 28.5 3156 23. 15 0.75 20 24. 7.56 2.25 3.36 25. 0.19176 68 0.00282 26. 0.168 0.48 0.35 27. 5.1 0.006 850 28. 55,673 0.05 1,113,460 29. 84.536 4 21.134 30. 261.18 10 26.118 31. 134,554 0.14 961,100 32. 90,294 7.85 11,502.42038 33. 59,368 47.3 1255.137421 34. 11,633.5 439 26.5 35. 28.098 14 2.007 36. 16.309 0.09 181.21 37. 55.26 1.8 30.7 38. 8276 0.627 13,199.36204 39. 10,693 92.8 115.2262931 40. 48.8 1.6 30.5 41. 27,268 34 802 42. 546.702 0.078 7009 656 Prerequisite Skills 4 Multiply and Divide Fractions

To multiply fractions, multiply the numerators and then multiply the denominators. Write the answer in simplest form.

Example 1 2 7 Multiply and . 5 8

Solution 2 7 2 7 14 7 5 8 5 8 40 20

To divide by a fraction, multiply by the reciprocal of that fraction. To find the reciprocal of a fraction, invert the fraction (turn it upside down). The product of a fraction and its reciprocal is 1. Since 2 3 = 6 or 1, 2 and 3 3 2 6 3 2 are reciprocals of each other.

Example 2 Prerequisite Skills 1 2 Divide 1 by . 5 3

Solution 1 2 6 2 6 3 6 3 18 4 1 , or 1 5 3 5 3 5 2 5 2 10 5

EXTRA PRACTICE EXERCISES

Multiply or divide. Write each answer in simplest form. 2 5 4 3 10 1 5 1 1 1. 2. 3. 2 3 6 5 5 12 2 8 4 2 1 2 1 2 1 1 3 5 4. 5. 6. 15 2 3 3 3 2 3 4 8 32 1 2 3 2 1 1 3 5 1 7. 8. 1 9. 1 2 3 4 3 2 3 4 8 5 2 3 2 1 1 7 1 1 2 10. 2 1 1 11. 1 2 2 12. 3 1 3 3 5 3 5 4 10 3 10 3 2 4 1 4 2 10 4 2 31 13. 5 2 2 14. 2 5 15. 2 5 13 5 7 10 7 5 21 7 5 35 7 7 3 2 5 2 1 1 1 1 16. 1 1 1 17. 1 2 2 18. 7 2 3 8 8 4 3 8 3 6 2 4 3 2 1 3 1 5 1 8 25 5 1 19. 6 4 5 161 20. 11 6 70 21. 2 3 2 8 4 9 12 27 42 21 2 13 8 13 3 11 16 1 51 17 2 22. 23. 24. 1 18 9 16 8 12 33 6 56 24 7

Prerequisite Skills 657 5 Add and Subtract Fractions

To add and subtract fractions, you need to find a common denominator and then add or subtract, renaming as necessary.

Example 1 3 5 Add and . 4 6 Solution 3 3 3 9 4 4 3 12 5 5 2 10 6 6 2 12 19 Add the numerators and use the common denominator. 12 19 7 Then simplify. 1 12 12

Example 2 3 1 Subtract 1 from 5. 5 2 Solution 1 5 15 5 5 4 2 10 10 3 6 6 6 5 Prerequisite Skills 1 1 1 You cannot subtract from , so rename again. 5 10 10 10 10 9 3 10

EXTRA PRACTICE EXERCISES

Add or subtract. 1 1 3 2 1 5 3 3 1. 2. 1 3. 1 5 10 10 3 3 8 4 8 6 2 4 3 1 5 5 1 3 4. 5. 6. 7 7 7 4 3 12 8 4 8 1 1 5 7 1 2 1 1 7. 2 3 6 8. 6 3 10 9. 3 4 8 2 2 8 8 2 3 2 6 3 1 1 1 7 1 1 2 2 10. 2 1 1 11. 5 3 1 12. 1 4 4 2 8 8 4 3 3 3 1 7 5 2 1 11 2 1 13 13. 6 5 12 14. 9 1 8 15. 7 6 13 2 9 18 5 8 40 3 5 15 1 2 13 1 3 9 5 3 7 16. 8 5 2 17. 6 5 18. 10 9 10 3 30 2 5 10 8 4 8 1 1 1 47 2 3 1 23 7 3 1 5 3 19. 1 2 5 8 20. 9 4 6 20 21. 10 3 6 2 23 5 3 4 60 3 5 2 30 8 4 2 8 4 658 Prerequisite Skills 6 Fractions, Decimals and Percents

Percent means per hundred. Therefore, 35% means 35 out of 100. Percents can be written as equivalent decimals and fractions. 35% 0.35 Move the decimal point two places to the left. 35 35% Write the fraction with a 100 denominator of 100. 7 Then simplify. 20

Example 1 3 Write as a decimal and as a percent. 8 Solution 3 0.375 Divide to change a fraction to a decimal. 8

0.375 = 37.5% To change a decimal to a percent move the decimal point two Prerequisite Skills places to the right and insert the percent symbol.

Percents greater than 100% represent whole numbers or mixed numbers. 1 200% 2 or 2.00 350% 3.5 or 3 2

EXTRA PRACTICE EXERCISES

Write each fraction or mixed number as a decimal and as a percent. 1 1 3 1. 0.5; 50% 2. 0.25; 25% 3. 0.75; 75% 2 4 4 9 3 1 4. 0.9; 90% 5. 0.3; 30% 6. 0.04; 4% 10 10 25 7 1 13 7. 3 3.875; 387.5% 8. 1 1.2; 120% 9. 0.52; 52% 8 5 25

Write each decimal or mixed number as a fraction and as a percent. 63 3 2 10. 0.63 ; 63% 11. 0.15 ; 15% 12. 0.4 ; 40% 100 20 5 7 1 5 13. 2.35 2; 235% 14. 10.125 10; 1012.5% 15. 0.625 ; 62.5% 20 8 8 1 1 5 16. 0.05 ;5% 17. 0.125 ; 12.5% 18. 0.3125 ; 31.25% 20 8 16 Write each percent as a decimal and as a fraction or mixed number. 1 3 19. 10% 0.10; 20. 12% 0.12; 21. 100% 1; 1 10 25 1 3 3 22. 150% 1.5; 1 23. 160% 1.6; 1 24. 75% 0.75; 2 5 4 2 7 7 25. 8% 0.08; 26. 87.5% 0.875; 27. 0.35% 0.0035; 25 8 2000 Prerequisite Skills 659 7 Multiply and Divide by Powers of Ten

To multiply a number by a power of 10, move the decimal point to the right. To multiply by 100 means to multiply by 10 two times. Each multiplication by 10 moves the decimal point one place to the right. To divide a number by a power of 10, move the decimal point to the left. To divide by 1000 means to divide by 10 three times. Each division by 10 moves the decimal point one place to the right.

Example 1

Multiply 21 by 10,000.

Solution 21 10,000 210,000 The decimal point moves four places to the right.

Example 2

Find 145 500.

Solution 145 500 145 5 100 29 100 0.29 The decimal point moves two places to the left. Prerequisite Skills EXTRA PRACTICE EXERCISES

Multiply or divide. 1. 15 100 1500 2. 96 10,000 960,000 3. 1296 100 12.96 4. 9687.03 1000 9.68703 5. 36 20,000 720,000 6. 7500 3000 2.5 7. 9 30 270 8. 94 6000 564,000 9. 561 30 18.7 10. 1505 500 3.01 11. 71 90,000 6,390,000 12. 9 120,000 1,080,000 13. 3159 10,000 0.3159 14. 1,000,000 0.79 790,000 15. 601 30,000 18,030,000 16. 75 300 0.25 17. 4000 12 48,000 18. 14 7,000,000 98,000,000 19. 49,000 7000 7 20. 980 10,000 0.098 21. 216 2000 0.108 22. 108,000 900 120 23. 72 10,000,000 720,000,000 24. 953.16 10,000 0.095316 25. 1472 8000 0.184 26. 490,000 700 700 27. 80 90,000 7,200,000 28. 8001 90 88.9 29. 50 6000 300,000 30. 950,000 50,000 19 31. 81,000 5 405,000 32. 1458 30,000 43,740,000 33. 452.3 10 45.23 34. 986,856.008 10,000 35. 316 70,000 22,120,000 36. 60 1200 0.05 98.6856008 660 Prerequisite Skills 8 Round and Order Decimals

To round a number, follow these rules: 1. Underline the digit in the specified place. This is the place digit. The digit to the immediate right of the place digit is the test digit. 2. If the test digit is 5 or larger, add 1 to the place digit and substitute zeros for all digits to its right. 3. If the test digit is less than 5, substitute zeros for it and all digits to the right.

Example 1

Round 4826 to the nearest hundred.

Solution 4826 Underline the place digit. 4800 Since the test digit is 2 and 2 is less than 5, substitute zeros for 2 and all digits to the right.

To place decimals in ascending order, write them in order from least to greatest. Prerequisite Skills

Example 2

Place in ascending order: 0.34, 0.33, 0.39.

Solution Compare the first decimal place, then compare the second decimal place. 0.33 (least), 0.34, 0.39 (greatest)

EXTRA PRACTICE EXERCISES

Round each number to the place indicated. 1. 367 to the nearest ten 370 2. 961 to the nearest ten 960 3. 7200 to the nearest thousand 7000 4. 3070 to the nearest hundred 3100 5. 41,440 to the nearest hundred 41,400 6. 34,254 to the nearest thousand 34,000 7. 208,395 to the nearest thousand 208,000 8. 654,837 to the nearest ten thousand 650,000

Write the decimals in ascending order. 9. 0.29, 0.82, 0.35 0.29, 0.35, 0.82 10. 1.8, 1.4, 1.5 1.4, 1.5, 1.8 11. 0.567, 0.579, 0.505, 0.542 12. 0.54, 0.45, 4.5, 5.4 0.45, 0.54, 4.5, 5.4 0.505, 0.542, 0.567, 0.579 13. 0.0802, 0.0822, 0.00222 14. 6.204, 6.206, 6.205, 6.203 0.00222, 0.0802, 0.0822 6.203, 6.204, 6.205, 6.206 15. 88.2, 88.1, 8.80, 8.82 16. 0.007, 7.0, 0.7, 0.07 0.007, 0.07, 0.7, 7.0 8.80, 8.82, 88.1, 88.2 Prerequisite Skills 661 Extra Practice

Chapter 1 Extra Practice 1–1 • The Language of Mathematics • pages 6–9 Name each set using roster notation. See additional 1. odd natural numbers greater than 6 2. months having 31 days answers. {7, 9, 11, . . .} 3. integers between 2 and 3 4. days beginning with the letter S See additional answers. Determine whether each statement is true or false. 5. 7 {xx is a negative integer} false 6. 15 {3, 0, 3, 6, . . .} true 7. {a, h, t} {m, a, t, h} true 8. {4} {natural numbers} false

Write all the subsets of each set. 9. {p} {p}, 10. {h, t} {h, t}, {h}, {t}, 11. {o, n, e} See additional answers. Which of the given values is a solution of the equation? 12. n 8 3; 5, 5 5 13. d 2 2; 4, 4 4 14. 3a 5 8; 1, 0, 1 1 4c 15. 4; 12, 3, 12 3 16. k 5 5; 0, 5, 10 17. c 7 10; 17, 3, 3 3 10 3 Use mental math to solve each equation. 18. x 7 4 3 19. n 6 3 9 20. 7q 28 4 c 1 3 1 21. 6 36 22. n 5 5 0 23. d 6 4 4 2 24. Henry saved $36 less than Alan. Henry saved $57. Use the equation 57 A 36 and the values {91, 93, 99} for A. Find A, the amount of money Alan saved. $93

Extra Practice 1–2 • Real Numbers • pages 10–13 Determine whether each statement is true or false. 1. 3.16 is a rational number. true 2. 0.121212. . . is an irrational number. false 3. 8 is a real number. true 4. 16 is an integer. true 5 15 5. 5 is not a real number. false 6. is a rational number. true 8 16 Graph each set of numbers on a number line. 7Ð14. See additional answers. 1 7. {3, 1, 1.5, 2} 8. 1.5, , 0, 9 Extra Practice 2 3 1 3 3 9. 3, 0.3, 1, 2 10. 2, 1, 0.6, 6 4 3 4 4 11. whole numbers less than 1 12. real numbers less than 3 13. real numbers from 3 to 2 inclusive. 14. real numbers greater than or equal to 2

662 Extra Practice Extra Practice 1–3 • Union and Intersection of Sets • pages 16–19

Refer to the diagram. Find the sets by listing the members. U 12 L J c e f 1. J K {a, b, c, d, 2, 4, 6, 8} 2. J L a 10 {a, c, d, e, f, d b {e, f, 4, 6, 8, 10, 12} 2 K 3. J 4. K 10, 12} 4 6 5. (J K) See additional answers. 6. (J K) {e, f, 10, 12} 8 7. K L 8. K L {b, e, f, 2, 4, 6, 8, 10}

Let U {g, r,a, p, h}, B {g, r,a, p}, and C {r, a, p}. Find each set, union, or intersection. 9. C {g, h} 10. B C {g, r, a, p} 11. B C {r, a, p} 12. B {h} 13. (B C) {h} 14. (B C) {g, h} 15. B C {r, a, p, h} 16. B C {h} 17. Let X {l, i, g, h, t} and Y {t, r, o, u, g, h}. Find X Y. {g, h, t} 18. Let R {4, 2, 0, 2, 4} and S {2, 4, 10}. Find R S. {4, 2, 0, 2, 4, 10} 19. Let P {0, 6, 12} and Q {0, 3, 6, 9, 12}. Find P Q. {0, 6, 12}

Use the set of real numbers as the replacement set. Graph the solution set of each compound inequality. 20Ð26. See additional answers. 20. x 0 or x 1 21. x 1 and x 1 22. x 4 and x 1 23. x 0 and x 2 24. x 4 or x 1 25. x 3 or x 1 26. Tondra’s car stays in first gear until it reaches a speed of 12 mi/h. Graph the speeds at which her car is in first gear.

Extra Practice 1–4 • Addition, Subtraction and Estimation • pages 20–23 Add or subtract. 1. 8 (37) 45 2. 46 17 29 3. 22 23 45 4. 18 (18) 36 5. 16.4 9.3 7.16. 68.9 70 1.1 7. 2.1 (16.2) 18.3 8. 4.3 5.7 10

7 3 1 1 3 1 5 1 19 2 1 5 9. 2 1 4 10. 6 5 11. 3 2 5 12. 7 3 4 8 8 4 4 4 2 8 6 24 3 4 12 13. 9.5 (11.7) 8.6 0.4 12.2 14. 19 21 16 (24) 6 Extra Practice 4 7 1 7 15. 8 6 3 18 16. 42 29 (16) 39 10 5 10 5 10 Evaluate each expression when x 24 and y 18. 17. x y 6 18. x y 42 19. y x 42 20. x y 42

Evaluate each expression when a 3 and b 1.8. 21. a b 4.8 22. a b 1.2 23. a b 4.8 24. a b 1.2 25. Alfonse makes the following transactions to his savings account. Previous balance, $564.82; Withdrawal, $125; Deposit, $152.68; Deposit, $38.95; Withdrawal, $75. What is his new balance? $556.45

Extra Practice 663 Extra Practice 1–5 • Multiplication and Division • pages 26–29 Perform the indicated operations. 1 1 1 1 1 3 1. 6.7(2.8)18.76 2. (3.2)(1.4) 4.48 3. 32 8 4. 61 9 2 3 6 4 2 8 2 4 1 2 5. 2 6 6. 3 2 1 7. (1.05) (0.35) 3 8. (2.25) (15) 3 9 3 3 0.15 7 1 5 11 9. 3 (5)(6) 26 10. 4 (3)(4) 7 11. 7.6 1.9 4.1 0.1 8 8 16 16 1 2 1 5 12. (9.1) (7) 1.3 0 13. 5 (4) 6 4 14. 3 1 6 3 3 8 8 1 1 2 15. 75 (10) 2 5 16. 17 (2) 2 6 17. (64) (96) 0 2 2 3 4 Evaluate each expression when r 3, s 1.5, and t . 5 1 4 18. r s 4.5 19. r t 2 20. r s 1.5 21. r t 3 5 5 22. rs 4.5 23. t(r s) 1.2 24. r st 1.8 25. (r s) t 1.875 26. Nat earns $6.40 per hour for each hour in his 32-h work week. For each hour over 32 h, he earns 11 times his hourly pay. How much will he earn if he works 42 h in 2 one week? $300.80 27. Gloria earns $7.50 per hour and 11 times that amount for each hour she works 2 over 32 h in week. One week she earned $273.75. How many hours of overtime did she work? 3 h

Extra Practice 1–7 • Distributive Properties and Properties of Exponents • pages 34–37 Use the distributive property to find each product. 1. 6.8 7 6.8 93 680 2. 2.7 8 2.7 12 54 3. 23 16 23 6 230 3 1 4. 101 27 2727 5. 352 85 6. 2420 483 7 8 Evaluate each expression when m 2 and n 5. 7. m 2 4 8. m 2 n 2 21 9. n 3 125 10. mn 2 50 11. m 3 8 12. 2mn 2 100 13. 2m 2n 40 14. (m n)2 49 15. (n m)2 49 16. (m 2 1)3 27 17. (2mn)2 400 18. 2mn 2 100

Simplify. x 7 8 6 214 x 3 3 3 y 6 3 3 y 9 19. 2 2 20. x 4 21. y y 22. (y )

8 1 1 10 15 3 4 5 2 2 5 23. 24. m m m 25 25. (x )(x )(x ) x 12 26. (x)(x )(x ) x n n 8 Extra Practice Evaluate mentally each sum or product when j 4.5, k 2, and l 0. 27. 10jk 90 28. 67j 2l 0 29. 5jk 45 30. (5.5 j)(11k) 22 31. (2j l)k 2 36 32. (j 0.5)(k 2) 20 33. (jk)2 80 1 34. (3.5 k)(j 5.5) 5.5 35. jk 3(2j 9) 0 664 Extra Practice Extra Practice 1–8 • Exponents and Scientific Notation • pages 38–41 Simplify. 1. (1)4 (1)5 0 2. (1)4 (1)6 2 3. c 18 c 6 c 12 4. n 4 n 3 n 1 5. x 4 x 3 x 7 6. y 3 y 3 y 6 Evaluate each expression when r 3 and s 3. 1 1 1 7. r 3 8. s 3 9. (rs) 2 10. r 2 r 2 1 27 27 81 1 11. s 3 s 2 1 12. r 2r 2r 4 1 13. s 3s 2r 3 14. r 3rs 3 3 3 9 Write each number in scientific notation. 15. 4700 4.7 103 16. 66,800 6.68 104 17. 1,410,000 1.41 106 18. 218,000 2.18 105 19. 0.0571 5.71 102 20. 0.00178 1.78 103 21. 0.00082 8.2 104 22. 0.971 9.71 101 23. 0.0000000505 5.05 108 Write each number in standard form. 24. 1.76 105 176,000 25. 2.6 104 26,000 26. 4.9 102 0.049 27. 5.04 106 0.00000504 Solve. Write your answer in scientific notation. 28. The distance from Earth to the Sun is about 93,000,000 mi. Write this distance in scientific notation. 9.3 107 mi 29. The speed of light is 3.00 1010 m/sec. How far does light travel in 1 h? Write the answer in scientific notation. 1.08 1014 m Chapter 2 Extra Practice 2–1 • Patterns and Iterations • pages 52–55 Determine the next three terms in each sequence. 1. 1, 5, 9, 13, ____, ____, ____ 17, 21, 25 2. 31, 26, 21, 16, ____, ____, ____ 11, 6, 1 3. 5, 3, 1, 1, ____, ____, ____ 3, 5, 7 4. 25, 18, 11, 4, ____, ____, ____ 3, 10, 17 1 1 1 1 5. 9, 3, 1, , ____, ____, ____ , , 3 9 27 81 1 1 2 4 8 16 32 6. , , , , ____, ____, ____ , , Extra Practice 10 5 5 5 5 5 5 7. 2, 8, 18, 32, ____, ____, ____ 50, 72, 98 8. 8, 6, 4, 2, ____, ____, ____ 0, 2, 4 9. 1.5, 3, 4.5, 6, ____, ____, ____ 7.5, 9, 10.5 10. 1, 2, 4, 7, ____, ____, ____ 11, 16, 22 Draw the iteration diagram for each sequence. Calculate the output for the first 7 iterations. 11. 128, 64, 32, 16, . . . 8, 4, 2 12. 10, 7, 4, 1, . . . 2, 5, 8 13. 1, 6, 36, 216, . . . 1,296; 7,776; 46,656 14. 12, 9.5, 7, 4.5, . . . 2, 0.5, 3 Extra Practice 665 Extra Practice 2–2 • The Coordinate Plane, Relations, and Functions • pages 56–59 Graph each point on a coordinate plane. 1Ð16. See additional answers. 1. A(4, 3) 2. B(3, 2) 3. C(5, 3) 4. D(4, 4) 5. E(0, 3) 6. F(2, 0) 7. G(5, 3) 8. H(3, 3) 9. J(5, 4) 10. K(4, 3) 11. L(3, 1) 12. M(2, 2) 13. N(1, 2) 14. P(5, 2) 15. Q(0, 4) 16. R(5, 0)

Given f(x) 3x 2, evaluate each of the following. 17. f(1)1 18. f(0) 2 19. f(1) 5 20. f(3) 11 21. f(2)4 22. f(2) 8 23. f(6) 20 24. f(6) 16

Write each relation as a set of ordered pairs. Give the domain and range. 25. 26. x 3 5 7 9 27. {(2, 4), y 2 4 6 8 (2, 4), (3, 9)}; Domain: {(3, 2), (5, 4), (7, 6), (9, 8)}; {2, 2, 3}; Domain: {3, 5, 7, 9}; Range: {4, 9} Range: {2, 4, 6, 8} 28. José charges $3 for the first hour of baby-sitting and then $5 per hour 27. {(2, 2), (0, 1), for each additional hour. The function that describes how he is paid is (2, 0), (4, 1)}; f(x) 3 5(x 1) where x is the number of hours he works. How Domain: {2, 0, 2, 4}; much does he earn if he works 7 h? $33 Range: { 1, 0, 1, 2}

Extra Practice 2–3 • Linear Functions • pages 62–65 Graph each function. 1Ð18. See additional answers. 1. y x 3 2. y x 3 3. y x 4. f(x) x 5 5. f(x) x 5 6. f(x) x 7. y 2x 2 8. f(x) 2x 2 9. f(x) 4 10. y 4 11. y 0 12. f(x) 3x 13. y x 5 14. y 3x 2 15. f(x) 2x 3 16. f(x) 4x 6 17. f(x) 3x 3 18. y x 1

Given f (x) 3x 4, find each value. 19. f(1) 7 20. f(1) 1 21. f(7) 25

Extra Practice 22. f(0) 4 23. f(6) 14 24. f(2) 2

Given g (x) 5x 3, find each value. 25. g(0) 3 26. g(1) 8 27. g(2) 13 28. g(3) 12 29. g(4) 17 30. g(2) 7 666 Extra Practice Extra Practice 2–4 • Solve One-Step Equations • pages 66–69 Solve each equation. 1. m 17 45 28 2. 9x 54 6 3. 17 d 5 22 4. 16 j 2 14 5. 24 c 9 33 6. 16n12 3 4 7. 8x 96 12 8. 0.8a 0.72 0.9 9. b 0.8 0.72 0.08 4 5 3 10. 36 c 81 11. x 10 16 12. 51 x 85 9 8 5 3 13. 13.24 x 4.2 17.44 14. 8.6 m 2.15 10.75 15. j 1 5 8 8 Translate each sentence into an equation. Use n to represent the unknown number. Then solve the equation for n. 16. When n is increased by 18, the result is 12. n 18 12; 30 17. When a number is decreased by 7, the result is 4. n 7 4; 3 n 18. The quotient of a number and 7 is 0.6. 0.6; 4.2 7 19. The product of 4 and a number is the same as the square of 6. 4n (6)2;9 20. The difference between a number and 13 is 14. n 13 14; 27 1 21. One fourth of 64 is the same as the product of 2 and some number. (64) 2n; 8 4 22. Liya decided to save $8 per week for the next 4 weeks so that her savings would total $100. Let n represent the amount she has before she begins saving. Write an equation that illustrates the situation. Then solve the equation. n 8(4) 100; n 68

Extra Practice 2–5 • Solve Multi-Step Equations • pages 72–75 Solve each equation and check the solution. 1. 6n 5 23 3 2. 4n 3 17 5 3. 55 8x 7 6 4. 36 5x 4 8 5. 3j 16 11 9 6. 2n 17 17 17 7. 2(3d 4) 10 3 8. 4(2x 1) 4 1 9. 3(2x 3) 9 3 10. 8x 7 2x 5 2 11. 3x 24 5x 24 6 12. 3c 5 7c 7 3 13. 3x 1 2x 1 0 14. 2k 3 3k 1 7k 1 1 15. 4a 7 2a 11 3 16. (16k 10) 11 2

2 Extra Practice 17. 4(1.5 x) 14 2 18. 4(3c 2) 38 6 2

Translate each sentence into an equation. Then solve. 19. Five more than 4 times a number is 33. Find the number. 4n 5 33; 7 20. Two less than 3 times a number is 13. Find the number. 3n 2 13; 5 21. When 20 is decreased by twice a number, the result is 8. Find the number. 20 2n 8; 6 22. Keisha bought 3 report binders that had the same price. The total cost came to $11.97, which included $0.57 sales tax. Write and solve an equation to find out how much each binder cost. 3b 0.57 11.97; $3.80 Extra Practice 667 Extra Practice 2–6 • Solving Linear Inequalities • pages 76–79 1Ð16. See additional Solve each inequality and graph the solution on a number line. answers. 1. 3a 2 10 a 4 2. 7n 2 19 n 3 1 1 3. n 7 6 n 2 4. c 8 10 c 6 2 3 5. 10 3r 7 r 1 6. 7 2a 5 a 6 7. 33 7n 2 n 5 8. 19 14 11c c 3 2 9. 2 18 5t t 4 10. x 8 10 x 3 3 11. 2(3w 4) 28 w 6 12. 3(4c 2) 18 c 2 13. 2a 5 8a 7 a 2 14. 2n 13 11n 14 n 3 2 4 15. 2 (9 6a) a 1 16. 12 (18 9c) c 1 3 9 Graph each inequality on the coordinate plane. 17Ð25. See additional answers. 17. y 2x 5 18. y 2x 3 19. y x 1 1 20. x y 5 21. x y 3 22. y x 1 2 1 23. 2x 4y 8 24. x 2y 10 25. 1 2x y 2 26. A pet store charges a minimum of $3 per hour to take care of a person’s pet. The inequality that describes how the store charges is y 3x where x is the number of hours and y is the amount of money charged. Graph the inequality. See additional answers.

Extra Practice 2–7 • Data and Measures of Central Tendency • pages 82–85 Thirty families were randomly sampled and surveyed as to the number of hours they watched television on a typical Friday. The results are listed below. 50312 01422 21046 11333 03521 02004 1. Construct a frequency table for these data. See additional answers. 2. Find the mean, median, and mode of the data. about 2.03, 2, 0 As part of her research for a term paper on home entertainment, Lydia surveyed video stores to find the cost of renting a movie for one day. The results are listed below. $2.50 $2.86 $1.99 $2.00 $3.10 $2.15 $1.55 $2.83 $3.49 $2.69 $1.85 $3.14 $2.62 $3.35 $3.32 Extra Practice $2.45 $2.12 $1.99 $2.05 $2.90 $2.49 $3.07 $1.68 $2.33 $3.00 $2.60 $2.00 $3.25 $2.25 $2.50 3. Construct a frequency table for these data. Group the data into intervals of $0.25. See additional answers. 4. Which interval contains the median of the data? $2.50Ð$2.74 668 Extra Practice Extra Practice 2–8 • Display Data • pages 86–89 The weights in pounds of the 30 students who tried out for the Snyder High School football team were as follows: 145 160 172 129 149 202 183 176 170 169 157 146 177 200 162 164 168 165 150 161 145 171 173 162 164 164 166 175 181 179 1. Construct a stem-and-leaf plot to display the data. See additional answers. 2. Identify any outliers, clusters, and gaps in the data. See additional answers. 3. Find the mode of the data. 164 4. Find the median of the data. 165.5 On a test that measures reasoning aptitude on a scale of 0 to 100, a class of 30 students received the following scores. 59 38 48 75 78 81 52 45 55 62 91 56 39 47 80 55 72 60 58 60 63 70 65 52 42 72 70 50 47 55 5. Construct a stem-and-leaf plot to display the data. See additional answers. 6. Identify any outliers, clusters,and gaps in the data. no outliers; cluster: 42-78; no gaps 7. Find the mode of the data. 55 8. Find the median of the data. 58.5 9. A newspaper took a random survey of its readers about DISTANCES TRAVELED the number of miles they travel to and from work each day. TO AND FROM WORK The data are recorded in this frequency table. Construct a Miles Frequency histogram of the data. See additional answers. 0 – 9 24 10 – 19 16 20 – 29 10 30 – 39 20 40 – 49 18 50 – 59 07 60 – 69 05 Chapter 3 Extra Practice 3–1 • Points, Lines, and Planes • pages 104–107 Use the figure at the right for Exercises 1–4. Which postulate justifies your answer? C 1. Name two points that determine line . points D and E; Postulate 1 D F 2. Name three points that determine plane . points D, E, and F; E Postulate 2 3. Name three lines that lie in plane . G DE, EF, DF; Postulate 3 Extra Practice 4. Name the intersection of planes and . DE or line l; Postulate 4 Use the number line at the right for Exercises 5–8. Find each length. 5. AD 5 6. EC 4 ABCDEF 7. FB 7 8. EF 2 –4 –2 0 2 4 9. In the figure below, RT 85. Find RS. 10. In the figure below, LN 79. Find ML. 35 43 R N M S L 4y + 12 4x – 13 T 5y – 5 3x

Extra Practice 669 Extra Practice 3–2 • Types of Angles • pages 108–111 Exercises 1–4 refer to the protractor at the right. 1. Name the straight angle. BAF 2. Name the three right angles. BAD, DAF, CAE 3. Name all the acute angles. 3. BAC 75¡, Give the measure of each. CAD 15¡, DAE 75¡, 4. Name all the obtuse angles.EAF 15¡ Give the measure of each. 4. BAE 165¡, CAF 105¡ 5. In the figure below, mQRS x° and 6. In the figure below, mMLO (4x 5)° mSRT 5x°. Find mSRT. 75¡ and mKLO (2x 11)°. Find mOLN. 39¡ R T N O

Q S KML

7. An angle measures 47°. What is the measure of its complement? 43¡

Extra Practice 3–3 • Segments and Angles • pages 114–117 Exercises 1–4 refer to the figure.

G H I J K L M N

–4–3 –2 –1 0 1 2 3 1. Name the midpoint of GK. I 2. Name the segment whose midpoint is point H. GI 3. Name all the segments whose midpoint is point J. IK, HL, GM 4. Assume that point O is the midpoint of GN. What is its coordinate? 0.5

In the figure below,JM and OL In the figure below,UV,WX, and YZ intersect at point K, and KN bisects intersect at point O, and OU bisects OKM. Find the measure of each angle. XOZ. Find the measure of each angle.

N (5x + 21)° O Y X O U J 68° M V (9x – 55)° K W Z L

5. OKM 136¡ 6. LKJ 136¡ 9. ZOW 116¡ 10. WOY 64¡

Extra Practice 7. MKL 44¡ 8. JKO 44¡ 11. XOU 32¡ 12. WOV 32¡

In the figure at the right, point F is the midpoint of EG. Find the length of each segment.

13. EF 14 14. EG 28 4a + 6 7a 5a 15. GH 10 16. EH 38 E F G H 670 Extra Practice Extra Practice 3–4 • Constructions and Lines • pages 118–121 In the figure at the right,AD HE and BF ⊥ GC. Find the measure of each angle. 1. AJB 47¡ 2. JKI 47¡ B C 3. CJD 43¡ A D 4. JIK 43¡ 43° J 5. GIK 137¡ IH K E 6. GJD 137¡ G 7. BKE 133¡ F 8. FKI 133¡

In the figure at the right,XU YV. Find the measure of each angle. 9. VYX 123¡ W 10. VYZ 57¡ U (8c – 13)° X 11. UXW 123¡ V (6c + 21)° 12. UXY 57¡ Y 13. Compare parallel and skew lines. Z Parallel lines are two coplanar lines that do not intersect. Skew lines are noncoplanar lines that do not intersect.

Extra Practice 3–5 • Inductive Reasoning • pages 124–127 Draw the next figure in each pattern. Then describe the twelfth figure in the pattern. 1. figure with 14 sides

2. square 12 dots by 12 dots

3. triangle with 12 rows and 144 small triangles Extra Practice

The figures below show one, two, three, and four segments drawn inside a triangle.

4. In each figure, the segments divide the interior of the triangle into regions. How many regions are formed in each of the figures shown? 2, 3, 4, and 5 5. Find the number of regions that would be formed when twelve segments are drawn through a triangle. 13 regions

Extra Practice 671 Extra Practice 3–6 • Conditional Statements • pages 128–131 Sketch a counterexample that shows why each conditional is false. 1Ð3. See additional answers. 1. If mXYZ mZYW 180°, then ZY ⊥ XW. 2. If point B is between points A and C, then B is the midpoint of AC. 3. If two lines are not parallel, then they intersect.

Write the converse of each statement. Then tell whether the given statement and its converse are true or false. 4. If the sum of the measures of two angles is 180°, then the angles are supplementary. true; If two angles are supplementary, then the sum of the measure is 180¡; true 5. If two lines are parallel, then they intersect. false; If two lines intersect, then they are parallel; false 6. If BC and BA are opposite rays, then B is the midpoint of AC. false; If B is the midpoint of AC, then BC and BA are opposite rays; true Write each definition as two conditionals and as a single biconditional. Conditionals: If two coplanar lines are parallel, then they do not intersect; if two coplanar lines 7. Parallel lines are coplanar lines that do not intersect. do not intersect, then they are parallel. Biconditional: Two coplanar lines are parallel if and only if they do not intersect. 8. Supplementary angles are two angles whose sum of their measures is 180°. Conditionals: If two angles are supplementary, then the sum of their measures is 180¡; if the sum of the measures of the two angles is 180¡, then they are supplementary. Biconditional: Two angles are supplementary if and only if the sum of their angles is 180¡.

Extra Practice 3–7 • Deductive Reasoning and Proof • pages 134–137

1. Given: m1 m4 1 and 2 are complementary. 1 2 3 4 3 and 4 are complementary. Prove: m2 m3 Statements Reasons 1. 1 and 2 are ___?__. complementary 1. given 3 and 4 are ___?__ . complementary 2. m1 m2 90° 2. definition of complementary angles m3 m4 ___?__ 90¡ 3. m1 m2 m3 m4 3. ___?__ substitution property 4. m1 m4 4. ___?__ given 5. m2 m3 5. ___?__ subtraction property of equality

T 2. Given: mTSW mTWS Prove: mTSR mTWX

RS W X

Extra Practice Statements TSW Reasons 1. TSR is supplementary to ___?__ . 1. ___?__ definition of supplementary angles TWX is supplementary to ___?__ . TWS 2. mTSW mTWS 2. ___?__ given mTWX If two angles have equal measure, then 3. m TSR ___?__ 3. ___?__ their supplements have equal measure. 672 Extra Practice Chapter 4 Extra Practice 4–1 • Triangles and Triangle Theorems • pages 150–153 Find the value of x in each figure. 1. 25 2. 30 3. 294. 125 130° 75° 87° x° x° x° 25° x° 75° 64° 30° x°

5. 120 6. x° 7. 77 8. x° 116° 135° 55° ° 40 58 ° 95 40 x° 37° x° 65° x°

9. In the figure below, 10. In the figure below, 11. In the figure below, ED ⊥ DF . AB JK. DE RT and Find mDFE. 55¡ Find mJCK. 97¡ mSDF mSFD. Find mSFE. 100¡

D E A CB D F n° (3c)° E (4c – 17)° 32° 80° JK R S F (5n – 50)° T G

Extra Practice 4–2 • Congruent Triangles • pages 154–157 1. Copy and complete this proof. A Given: AB CB; DBbisects ABC. D 1 Prove: ABD CBD 2 B C Statements Reasons 1. ___?__ AB CB; DB bisects ABC. 1. ___?__ given Extra Practice 2. m1 m2 or 1 2 2. ___?__ definition of angle bisector 3. ___?__ DB DB 3. ___?__ reflexive property 4. ABD CBD 4. ___?__ SAS postulate

Write a two-column proof. 2Ð3. See additional answers. T 2. Given: RS VT; R 3. Given: XVand WTintersect RV ST at point Y; XY VY; X Y Prove: RSV TVS V S Y is the midpoint of WT. V Prove: WXY TVY

T W Extra Practice 673 Extra Practice 4–3 • Congruent Triangles and Proofs • pages 160–163 Find the value of n in each figure. 1. 2. 3. 4. 36 n ft 4 ft 10 60 ° 8 m n 35° 35° 10 cm 8 m 6 in. 6 in. 4 60° n° 8 m 72° n cm

A D Copy and complete the proof. B 1 2 5. Given: Point B is the midpoint of AC and ED. C Prove: E D E Statements Reasons 1. ___?__ B is the midpoint of AC and ED. 1. ___?__ given 2. ___?__ AB BC ; EB BD 2. definition of midpoint 3. 1 and 2 are ___?__ vertical angles 3. ___?__ definition of vertical angles 4. ___?__ ___?__ 1, 2 4. ___?__ vertical angles theorem 5. ABE CBD 5. ___?__ SAS postulate 6. ___?__ E D 6. ___?__ CPCTC

Extra Practice 4–4 • Altitudes, Medians, and Perpendicular Bisectors • pages 164–167 Trace each triangle onto a sheet of paper. Sketch all the altitudes and all the medians. 1. B 2. E 3. H A

B D F G I C 2-3. See additional answers. A C

Exercises 4–9 refer to PQR with altitude QT. Tell whether each statement is true or false. 4. QT⊥ PR true Q 5. TQ PT false Extra Practice 6. PT TR false P R 7. mPTQ mRTQ true T 8. mQTP 90° true 9. P R false 674 Extra Practice Extra Practice 4–6 • Inequalities in Triangles • pages 172–175 Can the given measures be the lengths of the sides of a triangle? 1. 3 m, 6 m, 8 m yes 2. 9 ft, 7 ft, 2 ft no 3. 18 in., 13 in., 34 in. no 1 1 1 4. 15 cm, 15 cm, 15 cm yes 5. 2.4 yd, 6.7 yd, 3.9 yd no 6. 3 ft, 3 ft, 6 ft yes 2 4 2 7. 6 mm, 5 mm, 4 mm yes 8. 3 mi, 2 mi, 1 mi no 9. 2 yd, 5 ft, 72 in. yes

In each figure, give the ranges of possible values for x.

10. 11. 1 ft 12. 1 1 0 1 x 4 x m 5.4 m 2 2 x ft 1 yd x ft 8.2 m 1 2.8 x 13.6 10 ft 0 x 2 2 1! ft 13. In FGH, FG GHand HF FG. Which is the largest angle of the triangle? G 14. In ABC, BC 18, AB 16.5, and AC 14. List the angles of the triangle in order from largest to smallest. A, C, B 15. In PQR, mP 73°, mQ 57°, and mR 50°. List the sides of the triangle in order from longest to shortest. QR, PR, PQ

Extra Practice 4–7 • Polygon and Angles • pages 178–181 Find the unknown angle measure or measures in each figure. 105 87 1. n° 2. 114° 121° 113° 37° 108° n°

110° n°

3. 60 4. n° 131 146° 133°

122° ° Extra Practice 129° 108 n°

n°

4 5. Find the measure of each interior angle of a regular heptagon. 128 7 6. Find the measure of each interior angle of a regular decagon. 144 7. Find the sum of the measures of the interior angles of a regular polygon with 16 sides. 2,520 8. Find the sum of the measures of the interior angles of a regular polygon with 20 sides. 3,240 Extra Practice 675 Extra Practice 4–8 • Special Quadrilaterals: Parallelograms • pages 182–185 In Exercises 1–6, the figure is a parallelogram. Find the values of a, b, c, and d. 1. a cm 38, 26, 105, 75 2. 6, 55, 90, 35 3. a in. b° 6 in. 75° 26 cm

b ° ° b° a° ° cm d c 34 ° 35° c c° d° ° 6 in. d 38 cm 90, 34, 90, 56 3 1 4. AC 9 ft; AD 4 ft 5. VS 18 m; RS 14 m; 6. HG 5 yd; EG 8.6 yd; 4 2 RT 12 m FG 5.4 yd

A B R b mm S E F c mm b ft a in. d in. c in. c ft ft d a ft a mm d mm V b in. T DC 7 7 7 1 9, 14, 6, 9 4, 4, 4, 4 8 8 8 2 H G Tell whether each statement is true or false. 5.4, 5, 4.3, 4.3 7. A rhombus is a parallelogram. true 8. Every parallelogram is a quadrilateral. true 9. A square is a rectangle. true 10. Diagonals of a rectangle bisect each other. true 11. Diagonals of a square are perpendicular. true 12. Opposite sides of a square are parallel. true

Extra Practice 4–9 • Special Quadrilaterals: Trapezoids • pages 188–191 A trapezoid and its median are shown. Find the value of n.

1. 29 cm 33 2. 2.6 3. 152 mm 128 4. n ft 8 n cm 3.5 in. n mm 6! ft in. n 1.7 37 cm 104 mm 5 ft 2 5. n yd 12 6. 13 cm 23 7. 0.6 8. 3 ft n 3 n yd 1.5 ft 2* yd 3 yd 27 yd (n – 3) cm 2.4 ft 42 yd 27 cm

The given figure is a trapezoid. Find all the unknown angle measures.

9. AB 10. H 11. R S 104° 104° 52° 52° (3a + 20)°

Extra Practice I 71° 128° 109° (6a – 10)° (5a + 13)° 128° 76° 76° V T ° C D 71° 109 (5a – 14)° F

G

676 Extra Practice Chapter 5 Extra Practice 5–1 • Ratios and Units of Measure • pages 202–205 Complete. 1. 12 qt ___?__ c 48 2. 312 in. ___?__ yd ___?__ ft 8; 2 3. 3 gal ___?__ fl oz 384 4. 1.8 T ___?__ oz 57,600 5. 0.7 cm ___?__ m 0.007 6. 500 mg ___?__ g 0.5 7. 0.003 kg ___?__ g 3 8. 5.9 mL ___?__ L 0.0059 9. 3 gal ___?__ c 48 10. 6.4 L ___?__ mL 6,400 1 11. 31 ft ___?__ yd 10 12. 4.37 km ___?__ m 4,370 3 Name the best customary unit for expressing the measure of each. 13. weight of a computer lb 14. height of a seat in. 15. length of a room ft

Name the best metric unit for expressing the measure of each. 16. capacity of a cooler L 17. mass of a box of cereal g 18. length of a building m

Write each ratio in lowest terms. 1 19. 27 m:45 m 3:5 20. 60 g to 420 g 1 to 7 21. 30 min/6 h 12 Find each unit rate. 22. 220 mi in 4 h 55 mi/h 23. $16 for 320 prints $0.05/print 24. 15 L in 3 min 5 L/min 25. Which is the better buy, 6 grapefruit for $1.80, or 8 grapefruit for $2.56? 6 for $1.80 26. In 2 h 20 min Suzanne biked 14 mi. What was her biking rate? 6 mi/h

Extra Practice 5–2 • Perimeter, Circumference, and Area • pages 206–209 1. What is the perimeter of a regular hexagon with 6-cm sides? 36 cm 2. What is the circumference of a circle with a radius of 5.4 m? 33.912 m Extra Practice 3. Find the base of a triangle if area 42 cm2 and height 8 cm. 10.5 cm

Find the area of the shaded region of each figure. 4. 46 in.2 5. 50.24 cm2 6. 16.5 m2 3! in. 5 cm 5.5 m 8 in. 2.75 m 3 cm 4 m 4 m

7. If you triple the length of the radius of a circle, how does the area change? It is multiplied by 9. Extra Practice 677 Extra Practice 5–3 • Probability and Area • pages 212–215 A standard deck of playing cards has 52 cards. A card is drawn at random from a shuffled deck. Find each probability. 3 1. P(king) 1 2. P(black card) 1 3. P(red face card) 13 2 26

Find the probability that a point selected at random in each figure is in the shaded region. 3 4 5 4. 5. 9 ft 6. 15 in. 5 81 12 m 9

8 m 7 ft

12 in. 9 ft 6 m 9 m

6 in.

2 ft

1 3 1 7. 8. 9. or 4 4 32

8 cm 0.03125 6 cm 9 ft

3 cm 2 cm 3 ft 14 ft

10. Suppose Mrs. O’Malley left her purse within her 1500 ft2 apartment. What is the probability it is in the 15-ft by 12-ft kitchen? 3 25

Extra Practice 5–5 • Three-dimensional Figures and Loci • pages 220–223 Name the polyhedra shown below. Then state the number of faces, vertices, and edges each has. 1. 2. 3.

square pyramid; 5, 5, 8

hexagonal pyramid; 7, 7, 12 pentagonal prism; 7, 10, 15 Draw the figure. Check students’ drawings. Extra Practice 4. right rectangular prism 5. right cylinder 6. sphere 7. A figure has 5 triangular faces and 1 pentagonal face. What is the figure? pentagonal pyramid 678 Extra Practice Extra Practice 5–6 • Surface Area of Three-dimensional Figures • pages 224–227 Find the surface area of each figure. Assume that all pyramids are regular pyramids. Use 3.14 for . Round answer to the nearest whole number. 2 1. 2. 6 ft 126 ft 3. 4. 6 in. 4 cm 3 ft

8 m 8 in. 3.5 cm 9 ft 5 cm 103 cm2 40 ft 40 ft 804 m2 528 in.2 5. What is the surface area of a cone with a base that is 8 cm across and has a slant height of 5.6 cm? about 121 cm2

Extra Practice 5–7 • Volume of Three-dimensional Figures • pages 230–233 Find the volume to the nearest whole number. Use 3.14 for . 1. 2. 3. 4. 283 ft3 36 m2 24 in.

9.4 m

8.6 mm 12 ft 9 ft 13 mm 15 in. 15 in. 16 mm 3 ft 1789 mm3 1800 in.3 338 m3

5. How many cubic centimeters of water can a fish tank hold, if the tank is a rectangular prism 60 cm long, 40 cm wide, and 25 cm high? 60,000 cm3

Chapter 6 Extra Practice 6–1 • Slope of a Line and Slope-intercept Form • pages 244–247 Find the slope of the line containing the given points. 2 1 1. C(3, 1) and D(0, 1) 2. M(2, 4) and N(5, 6) m 3. S(5, 0) and T(4, 3) m 7 3 m 0 8 4. X(5, 3) and Z(5, 5) 4 5. J(6, 2) and K(0, 18) m 6. P(7, 3) and Q(2, 17) m 3 m 4 7. Q(4, 1) and R(5, 3)5 8. E(3, 2) and F(4, 2) 9. J(6, 4) and K(4, 4)

2 Extra Practice m m 4 m 0 9 Graph the line that passes through the given point P and has the given slope. 10Ð12. See additional answers. 1 3 3 10. P(1, 4), m 11. P(5, 2), m 12. P(2, 3), m 3 4 2 Find the slope of the line. 2 4 13. 4x 6y 12 m 14. 4x 5y 15 m 3 5 1 15. 8x y 2 m 8 16. x 2y 8 m 2 5 1 17. 5x 2y 7 m 18. 2x 20 6y m 2 3 1 19. Find the slope of a ramp that rises 8 ft for every 120 ft of horizontal run. m 15 Extra Practice 679 Find the slope and y-intercept for each line. 2 2 20. y x 5 m , b 5 21. y x 9 m 1, b 9 3 3 1 22. y 12x m 12, b 0 23. 2x 8y 16 m , b 2 4 5 1 1 24. 5x 7y 35 m , b 5 25. x 4y 24 m , b 6 7 2 8 Write an equation of the line with the given slope and y-intercept. 3 3 26. m 2, b 6 y 2x 6 27. m , b 0 y x 4 4 1 1 1 1 28. m 3, b 9 y 3x 9 29. m , b y x 8 2 8 2 5 5 30. m 0, b 7 y 7 31. m 1, b y x 9 9 Graph each equation. 32-34. See additional answers. 32. 3x 7y 21 33. 2x 8y 32 34. y 5x 4 35. Each week, the Weekly News prints 400 newspapers plus 20% of the total newspapers sold the previous week. The number of papers sold last week was 420. Write an equation to show how many newspapers will be printed this week. Solve. If 450 newspapers are sold this week, 1 how many will be printed next week? n 400 x, 484, 490 5

Extra Practice 6–2 • Parallel and Perpendicular Lines • pages 248–251 Find the slope of a line parallel to the given line and of a line perpendicular to the given line. 1 1. the line containing (2, 3) and (4, 9) m 3, m 3 10 3 2. the line containing (1, 7) and (2, 3) m , m 3 10 1 3. the line containing (0, 9) and (3, 6) m 5, m 5 4. the line containing (4, 3) and (0, 7) m 1, m 1 3 2 m , m 5. the line containing ( 3, 0) and ( 5, 3) 2 3 4 3 6. the line containing (4, 2) and (7, 6) m , m 3 4 Determine whether each pair of lines is parallel, perpendicular, or neither. 7. the line containing points C(2, 5) and D(5, 9) the line containing points E(2, 2) and F(6, 5) perpendicular 8. the line containing points M(4, 2) and N(3, 8) the line containing points O(6, 3) and P(1, 3) parallel 9. 7x y 4; 14x 2y 6 parallel 1 10. x 5y 20; 2x 10y 15 neither 2 11. x y 3; 3x 4y 9 neither perpendicular

Extra Practice 12. 4y x 14; 8x 2y 10 13. 4y 10 6x; 3x 2y 10 parallel 14. 6x 10y 20; 10x 6y 24 perpendicular 15. Plot and connect the points A(4, 5), B(4, 1), C(2, 3), and D(1, 8). Determine whether ABCD is a square. not a square

680 Extra Practice Extra Practice 6–3 • Write Equations for Lines • pages 254–257 Write an equation of the line with the given slope and y-intercept. 3 3 1. m 4, b 1 y 4x 1 2. m 2, b 7 y 2x 7 3. m , b 0 y x 4 4 1 1 1 1 2 4 2 4 4. m , b 5 y x 5 5. m 8, b y 8x 6. m , b y x 5 5 2 2 3 9 3 9 3 3 5 3 5 3 7. m , b 4 y x 4 8. m , b y x 9. m 5, b 0 y 5x 4 4 3 4 3 4 Write an equation of the line that has the given slope and passes through the given point. 10. m 3, A(3, 7) y 3x 16 11. m 1, B(5, 2) y x 3 2 2 1 1 12. m , C(3, 3) y x 5 13. m , D(4, 6) y x 4 3 3 2 2 14. m 5, E(8, 2) y 5x 42 15. m 6, F(3, 9) y 6x 27

Write an equation for the line whose graph is shown. 16. y 17. y 18. y 4 4 4 D 2 2 2 –4 –2 0 2 4 x –4 –2 0 2 4 x A –2 –4 –2 0 2 4 x –2 B –2 C E F –4 –4

1 y 3x 1 y x 3 y 2 2

Extra Practice 6–4 • Systems of Equations • pages 258–261

Determine the solution of each system of equations whose graph is shown. (1, 2) 1. y 2. y 3. y 4 4 4

2 2 2 (3, 2) (2, 3) x –4 –2 0 2 4 x –4 –2 0 2 4 x –4 –2 0 2 4 –2 –2 –2 Extra Practice

–4 –4 –4

Solve each system of equations by graphing. 4Ð9. See additional answers. 1 4. y 3x 1 (1, 2) 5. y 2x 2 (2, 4) 2 y x 3 y 3x 2 6. x y 3 (1, 2) 7. 2x y 3 (0, 3) 2x y 42x 2y 6 8. x y 3 (2, 1) 9. x 3y 6 (3, 1) 3x y 5 y 2x 5

Extra Practice 681 Extra Practice 6–5 • Solve Systems by Substitution • pages 264–267 Solve and check each system of equations by the substitution method. 1. x 2y 5 (3, 1) 2. 6x y 4 (0, 4) 3. 2x 3y 4 (1, 2) 4. x 3y 5 (2, 1) 4x 4y 8 x 4y 16 5x 2y 94x 8y 16 1 5. 3x 8y 18 6. 6x 3y 3 (3, 5) 7. y 3x 8 (4, 4) 8. x y 8 (8, 4) 1 x y 3 (6, 0) x 2y 13 x 3y 8 2 3x 6y 0 2 1 1 2 9. y 4x 2 10. y 3x 9 (3, 0) 11. 4x 3y 3 , 12. y 6x , 4 x y 3 x 8y 3 6y 3 10x 2 3 3x y 2 3 (1, 2) 13. The perimeter of a rectangle is 96 in. If the length is three times the width, find the dimensions of the rectangle. 12 in. by 36 in.

Extra Practice 6–6 • Solve Systems by Adding and Multiplying • pages 268–271 Solve each system of equations. Check the solutions. 1. x y 5 (2, 3) 2. 6x y 13 (1, 7) 3. x 5y 2 (3, 1) 4. 6x 3y 15 x y 14x y 3 y x 4 2x 4y 0 (2, 1) 1 1 5. 2x 3y 8 , 3 6. y 3x 14(4, 2) 7. y x 1 (8, 7) 8. x y 7 (9, 4) 2 3 y 6x 2x 3y 2 x y 15 x 2y 1 9. 3x 2y 5 10. 4y 3x 3 (3, 3) 11. 5y 10x 5 (1, 3)12. x 6y 16 (4, 2) 1 4y 8 4x x y 2 3x 2y 93y x 10 (1, 1) 3 13. Andrew has 25 coins with a total value of $3.05. The coins are all nickels and quarters. How many nickels and how many quarters does he have? 16 nickels, 9 quarters

Extra Practice 6–8 • Systems of Inequalities • pages 276–279 Determine whether the given ordered pair is a solution to the given system of inequalities. 1. (2, 1); 2x 5y 4 no 2. (3, 4); 3x 3y 2 yes 3. (1, 5); 4x y 5 yes x 8y 42x 6y 5 x 3y 0

Write a system of linear inequalities for the given graph. See additional answers. y y y 4. 4 5. 6. 4 4 2 2 2 x x –2 0 2 4 x –4 –2 0 2 4 –2 –4 –2 0 2 –2 –2 –4 –4 Extra Practice

Graph the solution set of the system of linear inequalities. 7Ð9. See additional answers. 7. x 2 8. y 2x 1 9. y 3x 5 2 y 3 y x 6 y x 1 3 682 Extra Practice Extra Practice 6–9 • Linear Programming • pages 282–285 Determine the maximum value of P 2x 3y for each feasible region.

y y 1. 412. 6 7 (1,4) 4 (5,2) 4 (1,3) (6,3) 2 (1,2) (10,1) 2 (0,1) 2246x 2246810x 2 2

Determine the minimum value of P 15x 12y for each feasible region.

y y 3. 81 4. (12,10) 126 (3,10) (8,10) (2,8) 8 8 (12,4) (16,5) 4 4 (8,5) (3,3) 481216 20x 481216 20x

5. A receptionist for a veterinarian schedules appointments. He allots 20 min for a routine office visit and 40 min for a surgery. The veterinarian cannot do more than 6 surgeries per day. The office has 7 h available for appointments. If x represents the number of office visits and y represents the number of surgeries, the income for a day is 55x 125y. What is the maximum income for one day? $1245

Chapter 7 Extra Practice 7–1 • Ratios and Proportions • pages 296–299 Is each pair of ratios equivalent? Write yes or no. 2.7 6 1.5 10 1. 4:8, 12:24 yes 2. 14:18, 9:7 no 3. , yes 4. , no 3.6 8 2.4 25 18 54 4 2 5. 10 to 7, 30 to 14 6. 12 to 8, 9 to 6 yes 7. , yes 8. , no no 10 30 5 10 Solve each proportion. 2 16 2 11 a 9 7.2 n 9. 72 10. 33 11. 80 12. 6 9 x 6 x 16 1.8 6 5

15 4.8 7 k 1 Extra Practice 13. 8.4:12 2.1:x 3 14. 6:1.9 n:7.6 24 15. 20 16. 10 y 6.4 8 12 2 Use a calculator to solve these proportions. 126 120 154 x x 429 137 118 17. 20 18. 66 19. 845 20. 411 21 x 231 99 325 165 x 354 21. A recipe for a sport drink calls for 3 parts cranberry juice to 8 parts lime juice. How much cranberry juice should be added to 20 pt of 1 lime juice? 7 pt 2 1 22. Cashew nuts cost $3 for 0.25 lb. How much will 1 lb cost? $18 2 23. Two college roommates share the cost of an apartment in a ratio of 5:6. The total monthly rent is $825. What is each person’s share? $375; $450

Extra Practice 683 Extra Practice 7–2 • Similar Polygons • pages 300–303 Determine if the polygons are similar. Write yes or no.

1. 105° 75° 2. 3. 14 yd 105° 75° 2 m 75° 2.5 m 75° 6 yd 4 m 4.5 m 3.75 ft 65° 2.5 ft no 7 yd 1.5 ft 2.25 ft 135°

yes 3 yd Find the value of x in each pair of similar figures. no

4. 5. x° 150° 6.

6 m x° 45° x m 155° 160° 8 m 2 m 30¡ 68° 1.5 m 112¡ 7. Draw any acute angle. Copy the angle using a straightedge and compass. Check students’ work. 8. A photograph that measures 5 in. by 8 in. is enlarged so that the 8 in. 1 side measures 10 in. How long is the 5-in. side in the enlargement? 6 in. 4

Extra Practice 7–3 • Scale Drawings • pages 306–309 Find the actual length of each of the following. 1 1. scale length is 5 cm 2. scale distance is 6.25 cm 3. scale length is 10 in. 1 2 scale is 2 cm:10 m 25 m scale is 2.5 cm:10 m 25 m scale is in.:1 ft 42 ft 4 Find the scale length for each of the following. 4. actual length is 15 ft 5. actual distance is 300 mi 6. actual distance is 1.5 mi 1 3 scale is in.:1 ft 3 in. scale is 2 cm:50 mi 12 cm scale is 1 in.:0.6 mi 2.5 in. 4 4 Find the actual distance using the map.

Hillsboro Sanford

Franklin

Springvale Lewiston

Scale: 6 mi

7. Franklin to Springvale 9 mi 8. Sanford to Lewiston 4 mi Extra Practice 9. Hillsboro to Franklin 12 mi 10. Hillsboro to Lewiston 10 mi 11. Springvale to Lewiston 12 mi 12. Sanford to Franklin 18 mi

684 Extra Practice Extra Practice 7–4 • Postulates for Similar Triangles • pages 310–313 Determine whether each pair of triangles is similar. If the triangles are similar, give a reason: write AA, SSS, or SAS.

1. yes; AA 2. 7 yes; SAS 3. 38° no 3 ° 40 6 3.5 42° 50°

4. yes; AA 5. no 6. yes; SSS ° ° 5 33 60 4 33° 50° 10 3 4 60° 6 M

P 7. The drawing at the right shows a smokestack and its shadow and a flagpole and its shadow. Explain why PQR MNO. See additional answers.

RQO N

Extra Practice 7–5 • Triangles and Proportional Segments • pages 316–319 T 1. Copy and complete this proof. Q Given: PQR STV; PV VR;SW WV Prove: QV PR TW SV P VRSW V Statements Reasons 1. PQR STV; PV VR; SW WV 1. ___?__ given 2. V is the midpoint of PR. 2. ___?__ definition of midpoint W is the midpoint of SV. 3. QVis a median of PQR. 3. ___?__ definition of median TWis a median of STV. Lengths of medians of triangles are QV PR 4. 4. ___?__ in the same proportion as the lengths TW SV of the corresponding sides. Extra Practice Find x in each pair of similar triangles to the nearest tenth. 2. 46.7 3. 3 2 4.3 4. 8.5 12 3 x 2 x x 8.5 35 40 17 30

5. These cross sections of tents are similar triangles. If the support pole of the smaller tent is 4 ft, how tall is the support pole for the larger tent? 4.8 ft 10 ft 12 ft Extra Practice 685 Extra Practice 7–6 • Parallel Lines and Proportional Segments • pages 320–323 In each figure, AB CD. Find the value of x to the nearest tenth. M 2.3 R 1. 2. B 3 D 7.3 3. 6.7 2 8 3 4 AB A B x J x 4 10 5 x C D C 7 D A C

4. C 2.4 5. R 10 S 14.5 6. 7 E 5.5 3 C A 6 7 A B A x 10.5 6 10 x 8 CD19 x B DF E D B 8

Spruce Street 7. This map shows a vacant plot of land that is to be developed by creating four new N equally-spaced north-south streets between Elm and Birch Streets. Copy the map and Elm Street construct the points where the new streets Birch Street

would intersect Spruce Street. S See additional answers.

Chapter 8 Extra Practice 8–1 • Translations and Reflections • pages 338–341 On a coordinate plane, graph ABC with vertices A(3, 2), B(2, 7), and C(9, 5). Then graph its image under each transformation from the original position. 1–8. See additional answers for graphs. 1. 6 units up (ABC) 2. reflected across the y-axis (ABC) 3. Compare the slopes of all the sides of ABC in both positions above. 2 2 2 1 1 1 AB 5, AB 5, AB 5, BC , BC , BC , AC , AC , AC 7 7 7 2 2 2 On a coordinate plane, graph figure WXYZ with vertices W(3, 9), X(1, 7), Y(1, 2), and Z(5, 4). Then graph its image under each transformation from the original position. 4–5. See additional answers. 4. 7 units right 5. reflected across the x-axis 1 1 1 , , 6. Compare the slopes of WX, W X , and W X . 2 2 2

Extra Practice 7. On a coordinate plane, graph RST with vertices R( 4, 0), S(1, 4), and T(6, 6). Graph its image under a reflection across the line with equation y x. 8. On a coordinate plane, graph figure MNOP with vertices M(2, 1), N(4, 3), O(9, 1), and P(7, 2). Graph its image under a reflection across the line with equation y x. 686 Extra Practice Extra Practice 8–2 • Rotations in the Coordinate Plane • pages 342–345 For each figure, draw the image after the given rotation about the origin. Then calculate the slope of each side before and after the rotation. See additional answers. 1. Use the rule (x, y) 2. Use the rule (y, x) for a 3. Use the rule (y, x) for for a 180° clockwise 90° counterclockwise a 90° clockwise rotation. rotation. rotation. y y y L Y 6 6 4 4 4 2 X K 2 2 –8 –6 –4 –2 0 2 4 x Z M –2 –6 –4 –2 0 2 4 6 x –6 –4 –2 0 2 4 6 x D A –2 –2 –4 –4 –4 –6 –6 –6 –8 C B

4. Triangle XYZ is rotated twice about the origin, as shown in the table below. Compare the slopes to determine how much of a rotation was completed each time. Each rotation is at most one full turn. first, 90¡; second, 180¡ from original Original Position After Rotation 1 After Rotation 2 side slope side slope side slope YZ –2 Y′Z′ ! Y″Z″ –2 XY * X′Y′ –3 X″Y″ * XZ 5 X′Z′ – 8 X″Z″ 5

Extra Practice 8–3 • Dilations in the Coordinate Plane • pages 348–351 Copy each graph on graph paper. Then draw each dilation image. See additional answers. 1. Center of dilation: origin 2. Center of dilation: point A 3. Center of dilation: Scale factor: 2 Scale factor: 3 origin Scale factor: 1 2 y y y x 6 0 2 4 6 8 x –6 –4 –2 0 2 4 –2 4 –2 –4 2 –4 –6 A –6 0 2 4 6 x –8 –8 Extra Practice

The following sets of points are the vertices of figures and their dilation images. For each two sets of points, give the scale factor. 1 scale factor 4. A(2, 0), B(6, 0), C(4, 4) 5. R(2, 1), S(2, 7), T(10, 1) 2 A(4, 0), B(12, 0), C(8, 8) scale factor 2 R(2, 1), S(2, 3), T(6, 1) 6. J(8, 3), K(5, 3), 7. D(2, 4), E(8, 4), F(8, 7), G(2, 7) L(5, 7), M(8, 7) D(6, 6), E(8, 6), F(8, 7), G(6, 7) 1 J(8, 3), K(1, 3), scale factor L(1, 15), M(8, 15) scale factor 3 3 Extra Practice 687 Extra Practice 8–4 • Multiple Transformations • pages 352–355 For each exercise, draw the result of the first transformation as a 1Ð3. See additional dashed figure and the result of the second transformation in red. answers. 1. a reflection over 2. a clockwise rotation of 90° 3. a counterclockwise the x-axis followed by about the origin, followed rotation of 180˚ about a translation 6 units by a reflection over the origin, followed by to the left. the y-axis. a dilation with center y y at the origin and a 6 4 scale factor of 2. y 4 2 –6 –4 –2 0 x 2 –2 0 2 4 x –4 0 2 4 6 x –6

Determine the transformations necessary to create figure 2 from figure 1. There may be more than one possible answer. 4Ð6. See additional answers. 4. y 5. y 6. y 6 6 6 ➀ 4 4 ➁ 4 ➀ 2 2 2 ➁ –6 –4 –2 0 2 4 6 x –6 –4 –2 0 2 4 6 x –6 –4 –2 0 2 4 6 x –2 –2 –2 –4 –4 –4 ➀ ➁ –6 –6 –6

Extra Practice 8–5 • Addition and multiplication with Matrices • pages 358–361 Find the dimensions of each matrix. 3 6 1 2 3 6 1. 2 242. 9 1 3. 4 8 3 2 4 5 5 9 5 Use the following matrices in Exercises 4–12. 2 0 6 9 11 5 J 1 5 K 4 3 L 7 0 4 6 0 8 2 1 Find each of the following. 4Ð13. See additional answers. 4. K L 5. J K 6. J L 1 1 7. 3L 8. J 9. K

Extra Practice 2 3 1 10. 2J K 11. L (3J) 12. K L 2 13. Tyler Junior High School ordered school pennants. The seventh grade ordered 28 black, 24 white, and 16 green. The eighth grade ordered 30 black, 20 white, and 15 green. The ninth grade ordered 14 black, 25 white, and 27 green. Write two different 3 3 matrices to show this information. 688 Extra Practice Extra Practice 8–6 • More Operations and Matrices • pages 362–365 Refer to the matrices below. Find the dimensions of each product, if possible. Do not multiply. If not possible to multiply, write NP. 4 8 4 5 3 3 9 A 6 1 B [5 1 3] C D 0 5 8 9 6 5 7

1. AB NP 2. AC 3 3 3. AD 3 2 4. BC NP 5. CD NP 6. DC 2 317. BA 2 8. CA 2 2

Find each product. If not possible, write NP. 1 3 2 6 5 1 9. 4 [5 13] 12 10. [4 1 0] 0 3 [8 27] 20 4 2 10 2 6 7 1 3 6 0 3 2 11. [20] 12. [8 1] [26 17] 2 4 0 2 1 4 0 1 3 5 0 2 5 3 2 5 13. 2 5 2 2 1 14. NP 1 0 3 4 3 0 1 1 3 0 3 12 23 4 21 5 5

Extra Practice 8–7 • Transformations and Matrices • pages 368–371 Represent each geometric figure with a matrix. See additional answers. y y y 1. 6 2. 6 3. K 6 A 4 4 D E 4 L

2 2 J 2 C –6 –4 –2 0 2 4 6 x –4 –2 0 2 4 6 x –6 –4 –2 0 2 4 6 x –2 –2 –2 M B –4 –4 –4 G F N –6 –6 –6

2 5 7 See additional Find the reflection images of the triangle represented by . answers.

4 1 5 Extra Practice 4. over the y-axis 5. over the x-axis 6. over the line y x

2 4 7 8 Find the reflection images of the quadrilateral represented by . See additional answers. 5 2 5 9 7. over the line y x 8. over the x-axis 9. over the y-axis

Interpret each equation as indicating: The reflection image of point ___?__ over ___?__ is the point ___?__ . 1 0 3 3 0 1 1 4 ( 1, 4), 10. 11. 0 1 5 5 ( 3, 5), y-axis, (3, 5) 1 0 4 1 y x, (4, 1) Extra Practice 689 Chapter 9 Extra Practice 9–1 • Review Percents and Probability • pages 384–387

A spinner with 8 equal sectors labeled Outcome A B C D E F G H A through H is spun 100 times with the Frequency 8 14 12 17 9 15 14 11 following results.

What is the experimental probability of spinning each of the following results? 9 3 1. B 7 2. E 3. H 11 4. C 50 100 100 25 17 5. a letter that comes before D 6. a letter that comes after D 49 50 100 List all the elements of the sample space for each of the following experiments. 7. You toss a penny and a dime. (H, T), (H, H), (T, H), (T, T) A B 2 4 8. You spin each of these spinners once. See additional answers. Find the probability of each of the following. 1 D C 8 6 52 9. Drawing a ten of hearts from a standard deck of cards. 10. Rolling a die and getting a prime number. 1 2

Extra Practice 9–3 • Compound Events • pages 392–395 Two dice are rolled. 1. Find the probability that the sum of the numbers rolled is either 4 or 5. 7 36 2. Find the probability that the sum of the numbers rolled is even and less than 7. 1 4 7 7 3. Find P(not a prime). 12 4. Find P(a sum of 8 or not prime). 12 Ashante’s Little League coach chooses the line-up by placing the 9 names into a hat and then pulling them out one by one. Find each probability. 2 5 5. batting first or third 9 6. not batting in an even-numbered 9 position 7 7. batting last or in the first two thirds of the batting order 9 1 8. batting second or in the first third of the order 3 You spin this spinner. Find each probability. 5 8 1 9. spinning 4 or an odd number 2 8 7

5

3

10. spinning a prime or an odd number 6

8 4 7 5 11. spinning a prime or an even number 8 3 Extra Practice 12. spinning a prime or a number greater than 4 4

690 Extra Practice Extra Practice 9–4 • Independent and Dependent Events • pages 396–399 A bag contains marbles, all the same size. There are 5 red, 4 blue, 2 yellow, and 1 green. Marbles are drawn at random from the bag, one at a time, and then replaced. Find each probability. 51 5 1. P(red, then blue) 36 2. P(blue, then yellow) 18 3. P(green, then red) 144 4. P(blue, then not blue) 2 5. P(not green, then yellow) 11 6. P(green, then not red) 7 9 72 144 A box contains tennis balls. There are 4 white, 3 yellow, 1 green, and 2 pink. One ball at a time is taken at random from the box and not replaced. Find each probability. 4 1 4 15 7. P(green, then yellow) 30 8. P(white, then pink) 45 9. P(white, then not white) 1 1 16 10. P(yellow, then green) 11. P(green, then not white) 12. P(white, then not green) 30 18 45 A neon sign reading HOTEL CHELSEA has two of its letters go out. 5 13. What is the probability that both letters are vowels? 33 14. What is the probability that the first letter is an E and the second is also an E? 1 22 5 15. What is the probability that the first is L and the second is not L? 33 16. You are given tickets to two concerts at a theater with 3000 seats. What is the probability that you will sit in the orchestra section for the first concert, and then in the second balcony for the second concert, if the orchestra has 1800 seats and the second balcony has 600 seats? 3 25

Extra Practice 9–5 • Permutations and Combinations • pages 402–405 For each situation, tell whether order does or does not matter. 1. You are recording the numbers and letters in an e-mail address. does matter 2. You are at a video store and selecting 3 movies to rent for the weekend. does not matter 3. You are selecting candidates for president, vice president, and secretary. does matter 4. You are selecting a 5-member committee from students in the class. does not matter

5. There are 5 different library books you would like to borrow, but the Extra Practice library allows you to borrow only 3 books at a time. How many ways can you select 3 of the books? 10 6. How many different ways can you arrange six videos in a row on a shelf? 720 7. A restaurant menu states that when you buy a dinner special you can select 3 side orders from 12 that are listed. How many ways can you do this? 220 8. Nine teams take part in an intramural volleyball tournament. How many different arrangements of first-, second-, and third-place winners are possible? 504

Extra Practice 691 Extra Practice 9–6 • Scatter Plots and Box-and-Whisker Plots • pages 406–409 This table shows the average scores of students who participated in an annual math contest. Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 Average Score 8.2 7.5 7.9 8.7 5.6 6.2 7.8 6.4 7.0 7.2

1. Make a scatter plot of the data. Check students’ drawings. 2. What is the range of average scores? 3.1 3. Does your scatter plot show a positive correlation, a negative correlation, or no correlation? no correlation

These box-and-whisker plots show the weights of the members of three high school football teams. Football Player Weights

Tigers

Rams

Lions

100 110 120 130 140 150 160 170 180 190 200 220210

4. Which team has the highest median weight? Rams 5. What is the lower quartile of the Tigers’ weights? 145 6. What is the upper quartile of the Lions’ weights? 180 7. What is the median weight of the Tigers? 155 8. Which team had the least range of weights? the greatest? Lions; Rams 9. Which team had weights most closely clustered about its median? Lions Extra Practice 9–7 • Standard Deviation • pages 412–415 Compute the variance and standard deviation for each set of data. 8, 8 1. 3, 6, 9, 12, 15 18, 18 2. 5, 5, 5, 5, 5 0, 0 3. 0.5, 2.5, 4.5, 6.5, 8.5 4. 1, 3, 5, 7, 9 8, 8 5. 4, 7, 10, 13, 16 18, 18 6. 4, 8, 12, 16, 20 32, 32 7. 2.3, 4.3, 6.3, 8.3, 10.3 8, 8 8. 1.6, 5.6, 9.6, 13.6, 17.6 9. 7.6, 3.4, 6, 8.3, 5.7 32, 32 2.9, 2.9 Find the variance and standard deviation for each set of data. 10. The top five scores in an Olympics gymnastics trial were: 9.1, 8.5, 7.9, 8.2, and 8.5. 0.1584, 0.1584 11. The prices of lunches in five country high schools are: $3.00, $3.50, $2.75, $3.25, and $3.75. 0.125, 0.125 12. Ping took two tests. On the first test, his score was 78, while the mean score was 72 and the standard deviation was 3. On the second test, his score was 70, while the mean score was 68 and the standard deviation was 0.5. On which test did Ping score Extra Practice better, relative to the scores of his classmates? the second 13. Alicia took two tests. On Test A, her score was 82, while the mean score was 90 and the standard deviation was 10. On Test B, her score was 76, while the mean score was 82 and the standard deviation was 4. On which test did Alicia score better, relative to the scores of her classmates? Test B

692 Extra Practice Chapter 10 Extra Practice 10–1 • Irrational Numbers • pages 426–429 Find the value to the nearest hundredth. 1. 13 3.61 2. 30 5.48 3. 62 7.87 4. 150 12.25 5. 189 13.75 6. 270 16.43 7. 666 25.81 8. 106 10.30

Write each in simplest radical form. 9. 45 35 10. 32 42 11. 147 73 12. 52 213 13. 28 27 14. 162 92 15. 125 55 16. 360 610 17. (35)(210) 302 18. (43)(26) 242 19. (25)2 20 20. (23)(47) 821 5 57 64 21. (22)(58) 40 22. 23. 42 7 7 2 45 43 22 26 3 24. 9 5 25. 56 5 26. 58 5

35 3 43 6 5 27. 28. 29. 30 415 4 28 2 6 6 30. If the area of a square is 236 ft2, find the length of each side to the nearest tenth of a foot. 15.4 ft

Extra Practice 10–2 • The Pythagorean Theorem • pages 430–433 Use the Pythagorean Theorem to find the unknown length. Round your answers to the nearest tenth.

1. 3 in. 2. 9.9 cm 3. 4. 15 yd 7.5 yd 5 in. 20 cm 4 in. 7 cm 10 cm 13 yd 7 cm 22.4 cm

5. 18 ft 6. 7. 8. 3 ft 12 cm 35 in. 21 in. 8 m 17.7 ft 28 cm 25.3 cm 28 in. 12 m 14.4 m Determine if each figure is a right triangle. Write yes or no. Extra Practice

9. 10. 11. 13 yd 12. 25 ft 17 m 30 in. 15 ft 8 m 5 yd 18 in. 12 yd 22 ft 15 m 28 in. no yes yes no

Solve. Round your answers to the nearest tenth. 13. Find the length of a diagonal of a rectangle with a length of 24 ft and a width of 8 ft. 25.3 ft 14. Find the width of a rectangle with a length of 9 m and a diagonal length of 11 m. 6.3 m Extra Practice 693 Extra Practice 10–3 • Special Right Triangles • pages 436–439 Find the unknown side measures. First find each in simplest radical form and then find each to the nearest tenth. 1–8. See additional answers. 1. 2. 3. 4. 60° 12 m 4 in.

30 cm

4 in. 60° 5 yd

5. 6. 7. 60° 8. 3 cm ° 60 9 yd 24 in. 14 m

9 yd

9. The diagonal of a square measures 6 cm. Find the length of a side of the square to the nearest tenth. 4.2 cm 10. The side of a square measures 10 in. Find the length of the diagonal of the square to the nearest tenth. 14.1 in.

Extra Practice 10–4 • Circles, Angles, and Arcs • pages 440–443 Find x. 1. 2. 3. 70° x° x° x° 190° O O

88° 70 44 170

4. 40° 5. 100° 6. 85°

x°

110°

x° 20° 115° 35 30° 40 x° 80

7. 8. 38° 9. 160° x° 30° Extra Practice ° x° 70 30°

130 ° x 84° 65 61

694 Extra Practice 10. An inscribed angle intercepts an arc of 130°. What is the measure of the inscribed angle? 65¡ 11. An inscribed angle measures 48°. What is the measure of the arc it intercepts? 96¡ 12. An inscribed angle ABC, measures 74°. What is the measure of the major arc ABC? 212¡ 13. An inscribed angle JKL, measures 50°. What is the measure of the central angle that contains the points J and L? 100¡

Extra Practice 10–6 • Circles and Segments • pages 448–451 Find x. 1. 2. 3. 23 4. 9 x 6 8 9 x 3 x x

4 9 15 10 16 12.5 5. In circle O, two chords, ABand CDintersect at point K. AK 12 cm, KB 10 cm, and KD 8 cm. Find the measure of CK. 15 cm 6. In circle O, radius OMis perpendicular to chord JKat point L. Find the measure of JKif JL 18 cm. 36 cm

Extra Practice 10–7 • Constructions with Circles • pages 454–457 1. Construct a regular hexagon. 1Ð6. Check students’ constructions. 2. Construct a square. 3. Copy this equilateral triangle. 4. Copy this square. Inscribe the Inscribe the triangle in a circle. square in a circle. Extra Practice

5. Copy this regular pentagon. 6. Copy this regular hexagon. Inscribe the pentagon in a circle. Circumscribe the hexagon around a circle.

Extra Practice 695 Chapter 11 Extra Practice 11–1 • Add and Subtract Polynomials • pages 468–471 Simplify. 1. (3a 7) (4a 5) 7a 12 2. (6n p) (n 7p) 7n 8p 3. (4x 2 3x) (x 2 x) 3x 2 4x 4. (3n 2 4n) (3n 2 4n) 8n 5. (3j 4k 2) (2j 2k 5) 5j 2k 3 6. (4x 2 12x 9) (x 2 2x 1) 5x 2 10x 10 7. (7a 5) (2a 3) 5a 2 8. (8x y) (5x y) 3x 2y 9. (3x 2 4y) (x 2 y) 4x 2 3y 10. (a 2 5a 6) (a 2 a 12) 2a 2 6a 18 11. (ab b a) (ab b a) 0 12. (4d 2 2de e 2) (3d 2 de 3e 2) d 2 de 4e 2 2 2 2 2 2 2 2 2 13. (m 16n 3n ) (9n 2 3m n ) 2 14. (a 12b b ) (4a 8b 4b ) 4m 25n 2n 5a 2 20b 5b 2 15. (5c 2 8cd d 2) (c 2 2c) 16. (7p 2 5q 2) (p 2 6pq q 2) 2 2 4c 8cd 2c d 6p 2 6pq 6q 2 17. Last week, Marisol worked 10 h at her part-time job, where she earns x dollars per hour, and 35 h at her full-time job, where she earns y dollars per hour. This week, she worked 15 h at her part-time job and 35 h at her full-time job. What were her earnings during the two weeks, expressed in terms of x and y? 25x 70y

Extra Practice 11–2 • Multiply by a Monomial • pages 472–475 Simplify. 1. (3x)(4y) 12xy 2. (5a)(4) 20a 3. (a 2)(2ab 3) 2a 3b 3 4. (m)(3mn) 3m 2n 5. (c)(6cd) 6c 2d 6. (2p 2)(3p 2q) 6p4q 7. (7x 2y)(8xy2) 56x 3y 3 8. (4c 2)2 16c4 9. 2x(7x 2 6y) 14x 3 12xy 10. 8n(2n 2 5p) 16n3 40np 11. 2a 2[(a 2 a)] 2a 4 2a 3 12. 3k 2[(3k 2 k)] 9k 4 3k 3 13. 7cd(2c 2 3d 2) 14c3d 21cd 3 14. 8c 2d(c 3d c 2d) 8c5d 2 8c4d 2 15. 3a 2b(5a 3c 3ab 4) 15a 5bc 9a 3b 5 16. 9x 2yz(x 2y y 3z) 9x 4y 2z 9x 2y 4z 2 17. 3jkl(j 2k 2l jkl 3) 3j 3k 3l 2 3j 2k 2l 4 18. 9abc 3(a 2bc 3 ab 4c) 9a 3b 2c 6 9a 2b 5c 4 19. 15xyz(xyz x 2y 3z 2) 20. 3d(d 3 2d 2 d) 3d 4 6d 3 3d 2 15x 2y 2z 2 15x 3y 4z 3 21. 4c(c 2 5c 6) 4c 3 20c 2 24c 22. rs(5r 2 3rs 4) 5r 3s 3r 2s 2 4rs 23. xy(3a 2 2b c) 3a 2xy 2bxy cxy 24. rs 2(4r 2 rs 3s 2) 4r 3s 2 r 2s 3 3rs 4 4 3 3 2 2 2 3 5 2 4 5 5 3 6 6 2 9 5 Extra Practice 25. 2xy z (x yz x y z xy z ) 2x y z 2x y z 2x y z

26. In 2001, a supermarket employed x clerks, each of whom earned y dollars per week. The weekly pay rate increased by d dollars each year. In 2004, the number of clerks quadrupled. What was the total paid each week to the staff of clerks in 2001? What was it in 2004? xy, 4xy 12xd

696 Extra Practice Extra Practice 11–3 • Divide and Find Factors • pages 478–481 Find the factors for the following. 1. 4x 6y 2(2x 3y) 2. 8a 2 12b 2 4(2a 2 3b 2) 3. 24n 2 6 6(4n 2 1) 4. 7xy 21x 7x(y 3) 5. jk jkl jk(1 l) 6. 7pq 21q 7q(p 3r) 7. 7ab 4bc b(7a 4c) 8. 9d 2e 5e 2 e(9d 2 5e) 9. 13x 2y 15yz 2 y(13x 2 15z 2) 10. v 2w vw vw(v 1) 11. 3a 5 3a 5 3a 2b 2 3a 2(2a 3 b 2) 12. 4y 4y 6 4y(1 y 5) Find the GCF and its paired factor for the following. 13. 48a 56b 8(6a 7b) 14. 39x 13x 2 13x(3 x) 15. 18c 2 27cd 2 9c(2c 3d 2) 16. 28xy2 42yz 2 14y(2xy 3z 2) 17. 30m 4n 3 60m 3n 4 30m 3n 3(m 2n) 18. 60x 3 45x 2 15x 2(4x 3) 19. 6a 3b 12a 2b 2 6a 2b(a 2b) 20. 8x 4b 3 12x 3b 2 4x 3b 2(2xb 3) 21. r 2s 2 r 2s rs 2 rs(rs r s) 22. xa 3b 3 ya 2b 2 2ab ab(xa 2b 2 yab 2) 23. 16d 5 40d 4e 2 56d 2e 4 24. 63x 3y 56w 3z 28r 3t 7(9x 3y 8w 3z 4r 3t) 8d 2(2d 3 5d 2e 2 7e 4) 25. A carpenter has two planks of wood, one 8 in. long and the other 40 in. long. She wants to use all the wood in the two planks to cut a set of small pieces, each the same size and as long as possible. How long will each cut piece be, and how many can she cut? 8 in., 6 pieces

Extra Practice 11–4 • Multiply Two Binomials • pages 482–485 Simplify. 1. (3a 4b)(5c 2) 15ac 6a 20bc 8b 2. (6x 5y)(z 3) 6xz 18x 5yz 15y 3. (2r 7s)(r 2t) 2r 2 4rt 7rs 14s 4. (6a 7p)(2a 3q) 12a 2 18aq 14ap 21pq 5. (m 4n)(3p 4n) 6. (2x 5y)(2z w) 4xz 2xw 10yz 5yw 3mp 4mn 12np 16n 2 7. (8r 3s)(5r 2t) 40r 2 16rt 15rs 6s 8. (8m n)(2p n) 16mp 8mn 2np n 2 9. (4x 3y)(x 5y) 4x 2 23xy 15y 2 10. (6 5n)(3 2n) 18 27n 10n 2 11. (5x 3)(x 3) 5x 2 18x 9 12. (x 7y)(3x y) 3x 2 22xy 7y 2 2 2 2 13. (c 7d)(5c 2d) 5c 37cd 14d 14. (7x 1)(6x 7) 42x 43x 7 Extra Practice 15. (6x y)(5x 3y) 30x 2 13xy 3y 2 16. (m 4)(3m 5) 3m 2 7m 20 17. (a 3b)(a 3b) a 2 6ab 9b 2 18. (c 9)(c 9) c 2 18c 81 19. (4x 5y)(4x 5y) 16x 2 40xy 25y 2 20. (7c e)(7c e) 49c 2 14ce e 2 21. (d 4)(d 4) d 2 16 22. (5a 2)(5a 2) 25a 2 4 23. (y 1)(y 1) y 2 1 24. (g 6)(g 6) g 2 36 25. (4m 1)(4m 1) 16m 2 1 26. (7x 2y)(7x 2y) 49x 2 4y 2

27. The dimensions of a rectangle are (3x 2) ft and (x 5) ft. Write an expression for the area of the rectangle. (3x 2 17x 10) ft2

Extra Practice 697 Extra Practice 11–5 • Find Binomial Factors in a Polynomial • pages 488–491 Find factors for the following. 1. 6wy 9wz 4xy 6xz(3w 2x)(2y 3z)2. 10ac 2bc 15ad 3bd (5a b)(2c 3d) 3. rt rv 3st 3sv (r 3s)(t v) 4. x2 7x 6xy 42y (x 6y)(x 7) 5. 8n 2 2np 4nq pq (4n p)(2n q) 6. 3y 2 xy 12yz 4xz (x 3y)(y 4z) 7. n 2 4n 2mn 8m (2m n)(n 4) 8. 6k 2 8k 3km 4m (3k 4)(2k m) 9. 12a 2c 8a 2d 2 3bc 2bd 2 10. 2r 3 4r 2t 5rt 10t 2 (2r 2 5t)(r 2t) (4a 2 b)(3c 2d2) 11. 24w 2y 16w 2z 2 9xy 6xz 2 12. 8xz 12x 6yz 9y (4x 3y)(2z 3) (8w 2 3x)(3y 2z 2) 2 2 2 13. 4a b a c 28b 7c (a 2 7)(4b c) 14. 4a 24ab 5a 30b (4a 5)(a 6b) 15. 2ac 2ad 3bc 3bd (2a 3b)(c d) 16. 3ac 2 15bc 2 4ab 20b 2 (a 5b)(4b 3c 2) 17. 6ac 9ad 6ae 2bc 3 2be (3a b)(2c 3d 2e) 18. 16eg 12eh 8e 2 4fh 2ef (4e f)(4g 3h 2e) 19. A rectangle has an area that can be expressed as 6a 2 2ab 3ac bc. If the width can be expressed as 3a b, find an expression for the length. 2a c 20. The area of a rectangle can be expressed as 3s 2 2rs 6st 4rt. Find expressions that might represent the dimensions of the rectangle. 2r 3s, s 2t

Extra Practice 11–6 • Special Factoring Patterns • pages 492–495 Find binomial factors of the following, if possible. (Four do not have such factors.) 1. y 2 2y 1 (y 1)2 2. x 2 18x 81 (x 9)2 3. x 2 22x 121 (x 11)2 4. a 2 14a 49 (a 7)2 5. n 2 12n 36 (n 6)2 6. y 2 7y 49 none 7. d 2 64 (d 8)(d 8) 8. r 2 1 (r 1)(r 1) 9. 4n 2 9 (2n 3)(2n 3) 10. 9j 2 6j 1 (3j 1)2 11. 25d 2 20d 4 (5d 2)2 12. 16 24c 9c 2 (4 3c)2 13. 4c 2 28cd 49d 2 (2c 7d)2 14. 81r 2 s 2 (9r s)(9r s) 15. 25p 2 144q 2 (5p 12q)(5p 12q) 16. 121k 2 66kl 9l 2 (11k 3l)2 17. 64a 2 25b 2 none 18. 64x 2 80xy 25y 2 (8x 5y)2 19. 25c 2 64d 2 (5c 8d)(5c 8d) 20. 4x 2 20xy 25y 2 (2x 5y)2 21. 81s 2 50t 2 none 22. 49p 2 140pq 100q 2 (7p 10q)2 23. 9x 2 36x 64 none 24. 64c 2 16c 1 (8c 1)2

Find a monomial factor and two binomial factors for each of the following. 2 2 2 3 2 2 Extra Practice 25. 12x 27 26. 36x 24x 4 4(3x 1) 27. x 6x 9x x(x 3) 3(2x 3)(2x 3) 28. The expression for the area of a certain square is 14x 49 x 2. Find an expression for the length of a side of the square. x 7

698 Extra Practice Extra Practice 11–7 • Factor Trinomials • pages 498–501 Identify binomial second-term factors for the following. 1. x 2 6x 8 4, 2 2. m 2 11m 24 8, 3 3. x 2 x 30 5, 6 4. y 2 11y 30 6, 5 5. d 2 6d 27 9, 3 6. p 2 15p 44 11, 4 7. a 2 17ab 72b 2 9b, 8b 8. x 2 17xy 42y 2 14y, 3y 9. r 2 15rt 54t 2 9t, 6t 10. j 2 3jk 54k 2 9k, 6k 11. t 2 tr 30r 2 6r, 5r 12. l 2 19ln 18n 2 18n, ln

Identify binomial second-term signs for the following. 13. x 2 x 20 , 14. t 2 14t 33 , 15. a 2 a 56 , 16. c 2 24c 23 , 17. a 2 2ab 15b 2 , 18. j 2 3jk 10k 2 , Factor the following trinomials. 19Ð27. See additional answers. 19. z 2 37z 36 20. r 2 15r 36 21. x 2 9x 36 22. v 2 16vw 36w 2 23. f 2 13f 36 24. l 2 20lm 36m 2 25. g 2 5g 36 26. j 2 9jk 36k 2 27. h 2 5h 36

28. A rectangular trench x feet deep is being dug for the foundation of a wall. The area of the bottom of the trench is (x 2 22x 48) ft2. Compare the depth of the trench to its width. Then compare the depth of the trench to its length. 2 ft narrower than depth, 24 ft longer than depth

Extra Practice 11–9 • More on Factoring Trinomials • pages 506–509 Find FOIL coefficients for the following trinomials. 1. 6x 2 19x 10 6, 15, 4, 10 2. 8m 2 30m 27 8, 36, 6, 27 3. 6c 2 11c 3 6, 2, 9, 3 4. 21a 2 13a 2 21, 7, 6, 2 5. 10x 2 23x 12 10, 15, 8, 12 6. 18n 2 9n 2 18, 12, 3, 2

Find binomial factors for the following trinomials. 7Ð18. See additional answers. Extra Practice 7. 25x 2 25x 4 8. 6x 2 5x 4 9. 14n 2 5n 24 10. 81y 2 24y 20 11. 15a 2 38ab 24b 2 12. 36t 2 19t 6 13. 10x 2 23x 14 14. 16x 2 41x 25 15. 8a 2 14ab 3b 2 16. 56r 2 6rs 2s 2 17. 2m 2 9m 81 18. 9k 2 27k 8

19. A rectangle has an area of 12a 2 a 1. Find expressions that might be the length and width of the rectangle. 3a 1, 4a 1 Extra Practice 699 Chapter 12 Extra Practice 12–1 • Graph Parabolas • pages 520–523 Check students’ graphs. Graph each function for the domain of real numbers. For each graph, Vertices and opening of give the coordinates of the vertex. the graphs are given. 1. y x 2 (0, 0) upward 2. y 3x 2 1 (0, 1) upward 3. y 2x 2 3 (0, 3) downward 4. y x 2 4 (0, 4) upward 5. y x 2 3 (0, 3) downward 6. y 2x 2 1 (0, 1) upward 7. y 4x 2 1 (0, 1) upward 8. y 3x 2 1(0, 1) downward 9. y x 2 2 (0, 2) downward Determine whether the graph of each equation below opens upward or downward. 10. y 3x 2 8 downward 11. y x 2 4 downward 12. y 4x 2 5 upward 13. y x 2 9 downward 14. y 2x 2 5 upward 15. y 9x 2 9 downward 16. y 6x 2 2 upward 17. y 3x 2 9 upward 18. y 5x 2 9 downward 19. y 5x 2 2 downward 20. y x 2 16 upward 21. y 5x 2 1 upward

22. Given the equations (a) y 2x 2 3 and (b) y 2x 2 3, explain the differences and similarities in the two graphs.Possible answer. They both have the y-axis as the line of symmetry; the vertex of (a) is (0, 3), the vertex of (b) is (0, 3).

Extra Practice 12–2 • The General Quadratic Function • pages 524–527 Estimate the coordinates of the vertex for each parabola by graphing the equation on a graphing calculator. Then use x b to find the 2a coordinates. 1. y x 2 4x 9 (2, 5) 2. y 2x 2 8x 8 (2, 0) 3. y 2x 2 12x 13 (3, 5) 2 2 2 4. y 5 2x (0, 5) 5. y x 2x 3 ( 1, 2) 6. 3x 4 x y 3 3 , 1 1 1 7. y x 2 2x 3 (1, 4) 8. y x 2 0, 9. y x 2 4x 5 2 4 4 4 (2, 9) Find the vertex. Then graph each equation. Check students’ graphs. 10. y 2x 2 12x 18(3, 0)11. y 2 x 2 4x (2, 6) 12. y 3x 2 1 6x (1, 4) 5 1 13. y x 2 6x 4 (3, 5) 14. y 7 x 2 5x , 13 15. y x 2 8x 22 (4, 6) 2 4 16. y x 2 6x 9 (3, 0) 17. y x 2 6x 7 (3, 2) 18. y x 2 4x 1 (2, 5)

19. Find a quadratic equation in the form y ax 2 bx c in which c 1 and the vertex is (2, 5). y x 2 4x 1 Extra Practice

700 Extra Practice Extra Practice 12–3 • Factor and Graph • pages 530–533 Use a graphing calculator to determine the number of solutions for each equation. For equations with one or two solutions, find the exact solutions by factoring. 1. 0 x 2 36 x 6, x 6 2. 0 x 2 x 2 x 2, x 1 3. 0 x 2 x 12 x 3, x 4 1 1 1 4. 0 2x 2 x 1 no solution 5. x 2 x , x 6. 0 x 2 6x 9 x 3 4 2 2 7. 10 x 2 3x x 5, x 2 8. x 2 18 3x x 3, x 6 9. 0 x 2 11x 30 x 5, x 6 10. x 2 6x 9 0 x 3 11. 0 x 2 0.5x 3 12. 0 x 2 36 no solution x 1.5, x 2 13. 0 x 2 6x 16 14. 0 x 2 x 1 no solution 15. 0 x 2 4x 5 no solution x 8, x 2 Write an equation for each problem. Then factor to solve. 16. The square of a number is 6 more than the number. y x 2 x 6; 2 or 3 17. The square of a number is 4 more than 3 times the number. y x 2 3x 4; 1 or 4 18. The square of a number is 24 more than 2 times the number. y x 2 2x 24; 6 or 4 19. The square of a number is 27 more than 6 times the number. y x 2 6x 27; 9, 3

Extra Practice 12–4 • Complete the Square • pages 534–537 Complete the square. 1. x 2 12x x 2 12x 36 2. x 2 16x x 2 16x 64 3. x 2 4.2x x 2 4.2x 4.41 2 2 1 49 4. x 2 x x 2 x 5. x 2 7x x 2 7x 6. x 2 8x x 2 8x 16 3 3 9 4 1 25 7. x 2 6x x 2 6x 9 8. x 2 x x 2 x 9. 2x 2 5x 2x 2 5x 4 4 Solve by completing the square. Check your solutions. 10. x 2 12x 11 0 11. x 2 2x 3 0 12. x 2 8x 9 0 x 11, x 1 x 3, x 1 x 1, x 9 2 2 2 13. 2x 2x 12 0 14. 3x 11x 4 0 1 15. 5x 5 x 1, x 1 x 3, x 2 x 4, x 16. x 2 24x 119 0 17. x 2 22x 112 0 3 18. x 2 4x 117 0 x 17, x 7 x 8, x 14 x 9, x 13 19. The width of a rectangular pool is 5 m less than the length. The area is 24 m2. Find the length and width. 8 m, 3 m

20. The hypotenuse of a right triangle is 25 m. One leg is 17 m shorter Extra Practice than the other. Find the lengths of the legs. 24 m, 7 m 21. The area of Harry’s room is 132 ft2. The length is 1 ft more than the width. Find the length and width. 12 ft, 11 ft

Extra Practice 701 Extra Practice 12–5 • The Quadratic Formula • pages 540–543 Use the quadratic formula to solve each equation. 1. x 2 5x 0 0, 5 2. x 2 7x 6 0 6, 1 3 3. x 2 6x 0 0, 6 4. 2x 2 13x 15 0 , 5 2 5 5. x 2 6x 4 0 3 5 6. 3x 2 8x 5 0 1, 3 7. x 2 2x 15 0 5, 3 8. x 2 7x 30 0 10, 3 2 9. 5x 2 3x 2 0 , 1 10. x 2 x 0 0, 1 5 11. 4x 2 20 5 12. 3 5x 2 8x 4 31 5 Choose factoring or the quadratic formula to solve each equation. 1 13. 0 x 2 2x 3 14. 3x 2 8x 3 x 3, x 15. x 2 2x 24 x 6, x 4 x 3, x 1 3 2 2 7 13 2 16. 0 3x 2x 4 17. x 9 7x x 18. x 2x 15 x 5, x 3 1 13 2 x 2 3 2 2 3 13 19. x 6x 16 0 20. 0 2x 7x 4 1 21. 0 x 3x 1 x x 2, x 8 x , x 4 2 2 Write and solve an equation for each problem. 22. Five times an integer is 4 more than the integer squared. y x 2 5x 4; 4, 1 23. The square of an integer minus three times the integer equals 2. y x 2 3x 2; 1, 2

Extra Practice 12–6 • The Distance Formula • pages 544–547 Calculate the distance between each pair of points. Round to the nearest tenth. 1. A(9, 5), B(6, 1) 5 units 2. X(0, 7), Y(3, 4) 4.2 units 3. M(5, 6), N(5, 2) 8 units 4. G(0, 3), H(0, 6) 9 units 5. X(0, 0), Y(3, 4) 5 units 6. A(1, 2), B(4, 7) 5.83 units 7. K(2, 2), L(2, 2) 5.7 units 8. X(2, 6), Y(4, 6) 6 units 9. M(2, 2), N(3, 5) 7.1 units 10. X(4, 3), Y(6, 7) 4.5 units 11. M(9, 2), N(5, 7) 6.4 units 12. A(9, 3), B(4, 1) 5.4 units

Calculate the midpoint between each pair of points. 13. A(4, 7), B(2, 3) (1, 5) 14. M(2, 5), N(8, 9) 15. X(2, 2), Y(6, 6) (4, 4) ( 3, 7) 3 16. D(4, 5), E(4, 5) (4, 0) 17. A(3, 7), B(3, 11) (3, 9) 18. K(2, 2), L(2, 5) 0, 2 5 5 9 19. X(4, 5), Y(6, 7) (5, 1) 20. X(8, 4), Y(3, 9) , 21. A(3, 8), B(6, 14) , 11 2 2 2 22. The vertices of a triangle are A(1, 3), B(8, 4), and C(5, 0). What are the lengths of the sides to the nearest tenth? side AB, 7.1 units; side AC, 5 units; side BC, 5 units 23. A triangle ABC has vertex A at (3, 1) and vertex B at (1, 4). The length of side BCis 6 units, and the length of side ACis 5 units. Find the Extra Practice coordinates of vertex C. (7, 4) 24. Find the point on the x-axis that is the same distance from (1, 3) as from (8, 4). (5, 0) 25. Find the point on the y-axis that is the same distance from (2, 2) as from (2, 6). (0, 4) 702 Extra Practice Chapter 13 Extra Practice 13–1 • The Standard Equation of a Circle • pages 562–565 Write an equation for each circle. 1Ð6. See additional answers. 1. radius 5, center (0, 0) 2. radius 3, center (4, 2) 3. radius 10, center (5, 1)

4. y 5. y 6. y 4 12 –16 –12 –8 –4 0 x 2 8 –4

4 –8 –4 –2 0 2 4 x –2 –12 –12 –8 –4 0 4 x –4 –4 –16

Find the radius and center of each circle. 7. x 2 y 2 64 8, (0, 0) 8. x 2 y 2 21 21, (0, 0) 9. (x 3)2 (y 5)2 49 7, (3, 5) 10. (x 4)2 (y 2)2 26 26, (4, 2) 11. (x 5)2 (y 4)2 41 41, (5, 4) 12. (x 4)2 y2 70 70, (4, 0) 13. x 2 (y 1)2 6 6, (0, 1) 14. (x 5)2 (y 5)2 100 10, (5, 5)

15. The graph of x 2 y 2 25 is translated 4 units to the right and 3 units up. Write the equation of the circle in the new position. (x 4)2 (y 3)2 25 16. The graph of x 2 y 2 25 is translated 6 units to the left and 5 units up. Write the equation of the circle in the new position. (x 6)2 (y 5)2 25

Extra Practice 13–2 • More on Parabolas • pages 566–569 Find the focus and directrix of each parabola. 1. x 2 8y (0, 2), y 2 2. x 2 24y (0, 6), y 6 3. x 2 8y (0, 2), y 2 15 2 9 9 2 0, , 2 4. x 18y 0, , y 5. x 15y 0 4 15 6. x 28y 0 (0, 7), y 7 2 2 y 2 2 2 11 11 7. 2x 32y 8. 4x 20y 5 4 9. 8x 44y 0, , y (0, 4), y 4 0, , 8 8 2 3 2 4 5 2 3 3 10. 54y 18x 0 0, , 11. 56y 14x 0 y 12. 7x 42y 0, , y 4 4 2 2 3 (0, 1), y 1 Extra Practice 2 y 2 2 13. 8x 64y 4 14. 6x 48y 0 15. 9x 90y 0 5 5 (0, 2), y 2 (0, 2), y 2 0, , y 2 2 Find the standard equation for each parabola with vertex located at the origin. 9 15 16. Focus 0, x 2 9y 17. Focus 0, x 2 15y 4 4 2 8 18. Focus 0, x 2 y 19. Focus (0, 12.5) x 2 50y 5 5 20. Focus (0, 1.5) x 2 6y 21. Focus (0, 7.5) x 2 30y

22. An elevated highway is supported by a parabolic arch that can be described by the equation x 2 40y. Find the value of a. Find the value of x when y 10. 10, 20 Extra Practice 703 Extra Practice 13–4 • Ellipses and Hyperbolas • pages 574–577 Graph each equation. 1Ð18. See additional answers. 1. x 2 4y 2 4 2. 4x 2 y 2 4 3. 9x 2 4y 2 36 4. 16x 2 9y 2 144 5. 25x 2 4y 2 100 6. 9x 2 y 2 9 7. 4x 2 9y 2 36 8. 9x 2 y 2 9 9. x 2 4y 2 16 10. 25x 2 4y 2 100 11. x 2 4y 2 4 12. 9x 2 16y 2 144 13. 25x 2 y 2 25 14. 25x 2 9y 2 225 15. x 2 9y 2 9 16. x 2 25y 2 25 17. 9x 2 16y 2 144 18. 25x 2 9y 2 225

19. Find the equation of the ellipse with foci (2, 0) and (2, 0) and x-intercepts (4, 0) and (4, 0). 3x 2 4y 2 48 20. Find the equation of the ellipse with foci (6, 0) and (6, 0) and x-intercepts (10, 0) and (10, 0). 16x 2 25y 2 1600 21. Find the equation of the ellipse with foci (3, 0) and (3, 0) and x-intercepts (5, 0) and (5, 0). 16x 2 25y 2 400 22. Find the equation of the hyperbola with center (0, 0) and foci on the x-axis if a 6 and b 8. 16x 2 9y 2 576 23. Find the equation of the hyperbola with center (0, 0) and foci on the x-axis if a 1 and b 4. 16x 2 y 2 16 24. Find the equation of the hyperbola with center (0, 0) and foci on the x-axis if a 4 and b 5. 25x 2 16y 2 400

Extra Practice 13–5 • Direct Variation • pages 580–583 Find the equation of direct variation for each pair of values. 1 y x 1. x 54 and y 18 3 2. x 4 and y 12 y 3x 3. x 7 and y 42 y 6x 2 4. x 15 and y 10 y x 5. x 3 and y 12 y 4x 6. x 1.5 and y 10.5 3 y 7x In each of the following, y varies directly as x. 7. If y 7 when x 3, 8. If y 30 when x 40, find y when x 15. 35 find y when x 32. 24 9. If y 76 when x 4, 10. If y 2.4 when x 8, find y when x 5. 95 find y when x 0.3. 0.09

In each of the following, y varies directly as x 2. 11. If y 176 when x 4, 12. If y 468 when x 3, find y when x 5. 275 find y when x 12. 7488 13. If y 180 when x 6, 14. If y 112 when x 0.4, find y when x 4. 80 find y when x 3. 6300 Extra Practice The distance (d) a vehicle travels at a given speed is directly proportional to the time (t) it travels. 15. If a vehicle travels 24 mi in 40 min, how far can it travel in 2 h? 72 mi 16. If a vehicle travels 40 mi in 50 min, how far can it travel in 20 min? 16 mi

704 Extra Practice 17. In an electric circuit, the voltage varies directly as the current. If the voltage (v) is 90 volts when the current (c) is 15 amps, find the voltage when the current is 20 amps. 120 volts 18. The distance (d) an object falls is directly proportional to the square of the time (t) it falls. If an object falls 400 ft in 5 sec, how far will it fall in 10 sec? 1600 ft

Extra Practice 13–6 • Inverse Variation • pages 584–587 For each pair of values, write an equation in which y varies inversely as x. 64 360 y y 1. x 4 and y 16 x 2. x 6 and y 60 x 630 19.2 y y 3. x 3.5 and y 180 x 4. x 0.6 and y 32 x 8.64 5.4 5. x 2.4 and y 3.6 y 6. x 3 and y 1.8 y x x In each of the following, y varies inversely as x. 7. If y 13 when x 2, find y when x 13. 2 8. If y 32 when x 3, find y when x 16. 6 4 9. If y 4 when x 2, find y when x 6. 3 10. If y 1.4 when x 5, find y when x 3.5. 2

In each of the following, y varies inversely as the square of x. 11. If y 9 when x 2, find y when x 6. 1 12. If y 2 when x 10, find y when x 5. 8 13. If y 128 when x 1, find y when x 4. 8 14. If y 800 when x 20, find y when x 25. 512

In each of the following, travel time varies inversely as travel speed. 15. If it takes 40 min to travel a certain distance as at a speed of 25 mi/h, how long will it take to travel that distance at 40 mi/h? 25 min 16. If it takes 20 min for an airplane to travel a certain distance at a speed of 120 mi/h, how long will it take the plane to travel that distance at Extra Practice 100 mi/h? 24 min

The brightness of a light bulb varies inversely as the square of the distance from the source. 17. If a light bulb has a brightness of 600 lumens at 2 ft, what will be its brightness at 8 ft? 37.5 lumens 18. If a light bulb has a brightness of 1000 lumens at 3 ft, what will be its brightness at 15 ft? 40 lumens

Extra Practice 705 Extra Practice 13–7 • Quadratic Inequalities • pages 590–593 Graph each inequality. 1Ð6. See additional answers. 1. y 0.5x 2 x 1 2. y x 2 x 3 3. (x 3)2 (y 2)2 9 4. 9x 2 4y 2 36 5. x 2 4y 2 4 6. 25x 2 9y 2 225 Graph each system of inequalities. 7Ð15. See additional answers. 7. x 2 y 2 16 8. x 2 y 2 4 9. y 0.5x 2 2 x 2 y 2 25 x 2 y 2 25 y x 3 10. y x 2 x 1 11. x 2 (y 2)2 16 12. 9x 2 16y 2 144 y 0.5x 2 3 y x 2 2x 1 x 2 9y 2 9 13. 25x 2 4y 2 100 14. y x 2 5 15. (x 1)2 (y 1)2 16 y x 2 3 x 2 4y 2 416x 2 9y 2 144 Describe the part of the coordinate plane that is shaded. 2 2 2 2 2 x y 2 16. x y r 17. 2 2 1 18. ax bx c y (a 0) the region outside the circle a b an ellipse and region inside region inside the parabola

Extra Practice 13–8 • Exponential Functions • pages 594–597 Graph each function. State the y-intercept. 1Ð6. See additional answers. 1. y 6x 1 2. y 8x 1 1 x 1 x 3. y 1 4. y 2 2 8 3 5. y 34x 336. y 25x 1

7. INVESTMENTS Determine the amount of an investment if $10,000 is invested at an interest rate of 4% each year for 6 yr. about $12,653.19

8. REAL ESTATE The Connor family bought a house for $185,000. Assuming that the value of the house will appreciate 4.5% each year, how much will the house be worth in 5 yr? about $230,543.66

9. VEHICLE OWNERSHIP A pickup truck sells for $27,000. If the annual rate of depreciation is 12%, what is the value of the truck in 6 yr? about $12,538.91

10. BUSINESS Mr. Rogers purchased a combine for $175,000 for his farm. It is expected to depreciate at a rate of 18% per year. Find the value of the combine in 3 yr. about $96,489.40

11. BIOLOGY In a certain state, the population of black bears has been decreasing at the rate of 0.75% per year. In the year 2000, there were 400 black bears in the state. If the population continues to decline at the same rate, what will the population be in 2020? about 344 bears

Extra Practice 12. ENERGY The Environmental Protection Agency (EPA) has called for businesses to find cleaner sources of energy. Coal is not considered to be a clean source of energy. In 1950, the use of coal by residential and commercial users was 114.6 million tons. Since then, the use of coal has decreased by 6.6% per year. Estimate the amount of coal that will be used in 2020. about 962,645 tons 706 Extra Practice Extra Practice 13–9 • Logarithmic Functions • pages 600–603 Write each equation in logarithmic form. 4 4 2 16 16 3 1 1 1. 9 6561 log9 6561 4 2. log2 4 3. 7 log7 3 3 81 3 81 343 343 Write each equation in exponential form. 1 1 5 1 1 5 4. log1 5 5. log4 5 6. log6 7776 5 6 7776 5 3125 1 5 3125 1024 4 5 1024 Evaluate each expression.

7. log5 1 0 8. log9 81 2 9. log1 125 3 5 1 10. log18 18 1 11. log1 5 12. log10 0.01 2 2 32 Solve each equation. 16 1 13. log8 a 3 512 14. log 3 m 2 15. log4 y 3 4 9 64 16. log5 (2x 1) log5 (3x) 17. log9 (d 5) log9 (3d) 18. log1 (t 10) log1 (3t 4) 1 2.5 2 2 7

Chapter 14 Extra Practice 14–1 • Basic Trigonometric Ratios • pages 614–617 B

Use the figures at the right to find each ratio. √2 1 1 2 1 2 1. sin A 2. cos A 3. tan A 1 2 2 2 2 A 1 C 1 2 4. sin B 5. cos B 1 2 6. tan B 1 D 2 2 2 2 17 8 8 15 8 7. sin E 17 8. tan E 15 9. cos E 17 E 15 F 15 8 15 10. sin D 17 11. cos D 17 12. tan D 8 H 3 313 2 √13 13. sin G 2 21314. cos G 15. tan G 2 13 13 3 13 13 3 G I 3 313 2 2 13 3 16. sin H 17. cos H 18. tan H 2 13 13 13 13 19. A tree is 75 ft tall. You 20. Suppose you stand 21. A ladder is leaning stand x ft away from 30 ft away from a against a building. the tree, and the building and measure The foot of the ladder Extra Practice tangent of the angle the angle to the top to is 20 ft away from the to the top is about be 52°. Find the height building, and the top is 1.5. How far of the building to the 15 ft from the ground. are you from nearest tenth. 38.4 ft How long is the ladder? the tree? 25 ft about 50 ft 75 x 15

52° x 30 20

Extra Practice 707 Extra Practice 14–2 • Solve Right Triangles • pages 618–621 Find lengths to the nearest tenth and angle measures to the nearest degree. Find the following in LMN. Find the following in ABC. L B 1. LM 9.0 3. mB 42¡ 15 53° 13.4 2. mN 37¡ 4. AC 9.0 9.9 N 12 M 5. m A 48¡ A C

Find the following in XYZ. Find the following in JKL. K 6. XY 9.4 X 9. KL 5.3 7. m X 58¡ 5 10. JK 11.3 28° J 8. mY 32¡ Y 11. mK 62¡ 10 L Z 8 12. Find the angle of elevation to the top of the 1046-ft John Hancock Building in Chicago from a point 700 ft from the base. about 56¡

Extra Practice 14–3 • Graph the Sine Function • pages 624–627 Find each ratio by drawing a reference angle. 3 1 1. sin 300° 2 2. sin 210° 2 2 3. sin 135° 4. sin 450° 1 2 3 2 5. sin 585° 6. sin 660 2 2 2 7. sin 360° 0 8. sin 495° 2 1 3 9. sin 420° 2 10. sin 690° 2 1 2 11. sin 330° 2 12. sin 855° 2

Extra Practice 14–4 • Experiment with the Sine Function • pages 628–631 See additional answers for graphs. 1. Graph y sin 6x. State the period. The period is 60¡. 2. Graph y 3 sin x. State the amplitude. The amplitude is 3. 3. Graph y sin x 2. Describe the position of the graph. the graph of sin x 2 units up 4. Graph y sin x 2. Describe the position of the graph. the graph of sin x 2 units down

State the period and amplitude of the graph of each equation and describe the position of the graph. 5Ð10. See additional answers. Extra Practice 5. y 3 sin x 4 6. y 1.5 sin 2x 7. y 8 sin 2x 3 8. y 4.5 sin 2x 2.5 9. y 1.5 sin x 2.5 10. y 9 sin 2x

708 Extra Practice Preparing for Standardized Tests 709 Test-Taking Tip Test-Taking If you are allowed to make use a calculator, sure you are familiar with how it works so waste that you won’t time trying to figure out the calculator when taking the test. 716Ð719 See Pages Preparing for Standardized Tests In the following pages, you will see examples of four will see you pages, the following In On some tests, you are permitted to use a calculator. You permitted use a calculator. to are you On some tests, you choose the best answer. you special grid in the corresponding circles. and color reasoning. your explaining reasoning. your explaining In addition to the Test-Taking Tips like the one shown at the right, like the one shown Tips Test-Taking to the addition In After being introduced to each type of question, you can practice that type of that can practice question, you to each type of After being introduced

Get a good night’s rest before the test. Cramming the night before does the night before the test. Cramming before rest Get a good night’s results. your not improve that you on problems dwell time when taking a test. Don’t your Budget answer your to leave that question blank on make sure Just cannot solve. sheet. like words Also look for order and EXCEPT. like NOT for key words Watch and LAST. FIRST, GREATEST, LEAST, Number and Operations Number Algebra Geometry Measurement Analysis and Probability Data

• • • • • • • • gridded responseshort response the problem. solve in a enter the answer You you Then responseextended 712Ð715 work and/or your showing the problem, solve You work and/or your a multi-part showing solve problem, You 720Ð724 Type of QuestionType choicemultiple Description from which choices are given answer possible or five Four 710Ð711 here are some additional thoughts that might help you. some additional thoughts that might are here question. Each set of practice questions is divided into five sections that represent the that represent questions is divided into five sections question. Each set of practice tests. categories most commonly assessed on standardized should check with your teacher to determineshould check with your if calculator use is permitted on the test you can be used. what type of calculator will be taking, and, if so, types of questions commonly seen on standardized tests. A description of of each type tests. commonly seen on standardized types of questions in the table below. question is shown TEST-TAKING TIPS TEST-TAKING USING A CALCULATOR PRACTICE TYPES OF TEST QUESTIONS At some time in your life, you will have to take a standardized test. Sometimes this test may test. Sometimes standardized will have to take a you life, some time in your At high from will graduate even if you or or course, determine go on to the next grade if you test-taker. a better is dedicated to making you textbook This section of your school. Becoming a Better Test-Taker Becoming Preparing for Standardized Tests Standardized for Preparing Preparing for Standardized Tests 710 of mathematics. Anotheranswer choicemightbethatthecorrect answer isnotgiven. diagram, you maybeabletoeliminatesomeofthepossibilitiesby usingyour knowledge problem. Drawing adiagram mayhelpyou tosolvetheproblem. Onceyou draw the Sometimes aquestiondoesnotprovide you withafigure thatrepresents the your shading isdark enoughandcompletelycovers thebubble. a circle oranoval theletterofyour choice. orjusttowrite Alwaysmakesure that To record amultiple-choiceanswer, you maybeaskedtoshadeinabubblethatis asked tochoosethebestanswer from fourorfivepossibleanswers. tests. These questionsare sometimescalledselected-response questions.Youare Multiple-choice questionsare themostcommontypeofquestiononstandardized Multiple-Choice Questions Example 1 Preparing forStandardized Tests 36 6 a Pythagorean Theorem. distance between theslideandclimbingpole. Let’s usethe Use theDistance Formula orthePythagorean Theorem tofindthe these values. So we caneliminateChoicesB andC. distance between thetwopointsmustbegreater thaneitherof Since thetwopointsare triangle, ofaright the twovertices in they-coordinates is9m. that thedifference inthex-coordinates is6mandthedifference Draw adiagram oftheplayground onacoordinate plane. Notice isthedistancebetween theslideandpole? What 2). pole islocatedat(–1, andtheclimbing –7), Theslideislocatedat(5, of asquare represents 1m. Eachside A coordinate onamapofplayground. planeissuperimposed to try first. to try answer. Sometimes you canmakeaneducated guessaboutwhichanswer choice If you are ontime, short you cantesteachanswer choicetofindthecorrect choice A,B, C,orD, theanswer isChoiceE. So, thedistance between theslideandpoleis313 D C 2 B A 2 E 313 117 9 b none ofthese 913 9 m 6 m 15 m 81 2 2 c c c c c 2 2 2 2 m Take thesquarerootofeachsideandsimplify. Substitution Theorem Pythagorean m. Since thisisnotlistedas ( pole Climbing 1, 2 ) O Correct shading Too lightshading Incomplete Shading y A A A B B B C C C ( Slide 5, 7 D D D x ) Preparing for Standardized Tests 711 C C . 2 2 C $6827 $5841 $5778 $8622 $8098 $6563 50 yd 300 yd 2 to 1 7 to 10 B B D D Spending per Person D 14 in.28 in. 21 in. A Preparing for Standardized Tests E B 2 2 Country 7 in. 24 in. The median is less than the mean. The mean is less than the median. is 2844. The range true. A and C are true. B and C are 25 yd 225 yd 3 to 1 7 to 5 Japan United States Switzerland Norway Germany Denmark E A B A A A C C C Data Analysis and Probability Measurement Measurement D D Refer to the table. Which statement is trueWhich statement to the table. Refer about this set of data? The circumference of a circle is equal to the is equal of a circle The circumference sides that hexagon with perimeter a regular of of radius the length of the What is 22 in. measure 3.14 for inch? Use nearest to the the circle a is planning to install carpeting in Eduardo 12 ft 6 in. by that measures room rectangular of carpet does he yards many square 18 ft. How need for the project? is a One Marva is comparing two containers. 30 cm. cylinder with diameter 14 cm and height 15 cm and The other is a cone with radius of the volume What is the ratio height 14 cm. cone? of the cylinder to the volume of the Test-Taking Tip Test-Taking Questions 2, 5, and 7 The units of measure given in the question may not be the same as those given in the answer choices. Check that your solution is in the proper unit. 9. 6. 7. 8. x 32 ) 0.08 4, 3 Library ( is the total 0.08x 32x . What is the . 2 C House y ) y y 20% 400% 100 ft 388 ft O is the number of 1, 5 B B B D D D School ( C E D 54 in. C E B 32 0.08 y? B and mi mi mi 32x 0.08x x

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A A A B A A C C C C Geometry Algebra Number and Operations Number and D D Eric plotted his house, school, and the library Eric plotted his house, Each side of a square plane. on a coordinate 1 mi. represents What is the distance his house to from the library? The grounds outside of the Custer County outside of the Custer The grounds shaped like a right contain a garden Museum 8 ft, One leg of the triangle measures triangle. is 18 ft of the garden and the area cost of renting the car and x the car cost of renting which equation describes the relation miles, between At Speedy Car Rental, it costs $32 per day to Rental, Car Speedy At y per mi. If a car and then $0.08 rent Carmen designed a rectangular banner that designed a rectangular Carmen The owner a local business. 8 ft for was 5 ft by her to make a larger of the business asked What was the 20 ft. banner measuring 10 ft by the first banner from in size increase percent to the second banner? A roller coaster casts a shadow 57 yd long. 57 yd coaster casts a shadow A roller with a coaster is a 35-ft tree to the roller Next that is 20 ft long at the same time of shadow coaster to What is the height of the roller day. whole foot? the nearest length of the other leg? 4. 5. 3.

1. Multiple-Choice Practice Multiple-Choice the best answer. Choose 2. Preparing for Standardized Tests 712 never negative. from ananswer Anexampleofagrid sheetisshown attheright. ovals, numbered 0–9.Since there answers are isnonegativesymbolonthegrid, of ovals orcircles withdecimalandfraction symbols, andfourorfivecolumnsof sheet. containsarowThe grid offourorfiveboxes atthetop, tworows For response, gridded you mustmark onananswer your printed answer onagrid possible answers. because you mustcreate theanswer yourself, notjustchoosefrom fourorfive These questionsare sometimescalled Gridded-response questionsare anothertypeofquestiononstandardized tests. Gridded-Response Questions Example 1 These values canalso befilledinonthegrid. Many gridded-response questionsresult inananswer thatisafraction oradecimal. Preparing forStandardized Tests PR Now find In thediagram, • • • • • How do youfillinthegridforanswer? are similar, tosolvefor aproportion write it intotheexpression 3x You needtofindthe value ofx What doyouneedtofind? blank answer box. in.Be surehave written nottofillinabubbleunder a answer boxFill in onlyonebubbleforevery thatyou ortheleftsideofyour answer.the right box. You mayleaveblankanyboxes you donotneedon left answer box, answer orwiththelastdigitinright You your answer maywrite withthefirstdigit inthe answer boxes. anydigitsorsymbolsoutsidethe Do notwrite Write onlyonedigitorsymbolineachanswer box. Write your answer intheanswer boxes. 4(3x 12x 3(4) 3x PR. M RN 12 2x 1 3 3) 4 T 0 x 3 or15 3 P 4 10x 10(x 8 MPT P x x M R 2 3 20 2) Find RPN. 3 tofindPR. student-produced response Divide eachsideby2. Subtract 12 and10x Distributive Property Cross products Substitution Definition ofsimilarpolygons so thatyou cansubstitute PR. Since thetriangles x. from eachside. or grid-in, M 4 15 9 8 7 6 5 4 3 2 1 . T x 2 9 0 8 7 6 5 4 3 2 1 . / P 9 8 7 6 5 4 3 2 1 0 . / 9 8 7 6 5 4 3 2 1 0 . 9 8 7 6 5 4 3 2 1 . 9 0 3 8 7 6 5 4 3 2 1 . / x 3 9 8 7 6 5 4 3 2 1 . 9 8 7 6 5 4 3 2 1 0 . / N 9 0 8 7 6 5 4 3 2 1 . / 9 8 7 6 5 4 3 2 1 0 . 15 9 8 7 6 5 4 3 2 1 0 . / 10 9 8 7 6 5 4 3 2 1 0 . R Preparing for Standardized Tests 713 20 ft 25 ft 15 ft 10 ft Do not leave a blank answer box in the middle of an answer. . 0 1 2 3 4 5 6 7 8 9 Preparing for Standardized Tests / . 0 1 2 3 4 5 6 7 8 9 . 1 2 3 4 5 6 7 8 9 0 / . 1 2 3 4 5 6 7 8 0 9 / . 1 2 3 4 5 6 7 8 9 0 .5 . 1 2 3 4 5 6 7 8 9 10/3 / . 1 2 3 4 5 6 7 8 9 0 . 1 2 3 4 5 6 7 8 9 . 1 2 3 4 5 6 7 8 9 0 , / . 0 1 2 3 4 5 6 7 8 9 0 3 1 / . 1 2 3 4 5 6 7 8 9 0 . . 1 2 3 4 5 6 7 8 9 .5 1 3 0 3 1 . 0 1 2 3 4 5 6 7 8 9 or / . 0 1 2 3 4 5 6 7 8 9 0 0 0 5 to find the area of the triangle. to find the area 5 1 / . 1 2 3 4 5 6 7 8 0 9 bh 1 2 . 1 2 3 4 5 6 7 8 9 2/4 Area of a triangle Substitution Simplify. . 0 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 or 0.5 / . 1 2 3 4 5 6 7 8 9 0 bh (1)(1) 1 2 1 2 1 2 w 25(20) or 500 w 15(10) or 150 area of garden area . 1 2 3 4 5 6 7 8 9 1/2 area of shaded region area as there is no way to correctly grid 3 is no way to correctly as there Leave the answer as the improper fraction fraction as the improper Leave the answer The shaded region of the rectangular garden will contain garden of the rectangular The shaded region roses. to the area What of the garden the ratio of the area is of the shaded region? of the garden. find the area First, A of the shaded region. Then find the area A as a fraction. of the areas the ratio Write How do you grid the answer? How to write the decimal point sure decimal. Be or the can either grid the fraction You responses. acceptable answer are following The box. bar in the answer or fraction A triangle 1 in. a base of length has of 1 in. and a height of the What is the area inches? triangle square in the formula A Use A Example 3 Sometimes an answer is an improper fraction. Never change the improper fraction to a fraction change the improper Never fraction. is an improper an answer Sometimes decimal. or the equivalent grid fraction either the improper Instead, mixed number. Example 2 Example 6. The diagram shows a triangle graphed on a Gridded-Response Practice coordinate plane. If AB is extended, what is the value of the y-intercept? 13 Solve each problem and complete the grid. y Number and Operations A (2, 3)

1. A large rectangular meeting room is being planned for a community center. Before O x building the center, the planning board decides to increase the area of the original room by B (3, 2) 40%. When the room is finally built, budget C (1, 3) cuts force the second plan to be reduced in area by 25%. What is the ratio of the area of the room that is built to the area of the original 7. Tyree networks computers in homes and room? 1.05 offices. In many cases, he needs to connect each computer to every other computer with 2. Greenville has a spherical tank for the city’s a wire. The table shows the number of wires water supply. Due to increasing population, they he needs to connect various numbers of plan to build another spherical water tank with computers. Use the table to determine Preparing for Standardized Tests a radius twice that of the current tank. How how many wires are needed to connect many times as great will the volume of the new 20 computers. 190 tank be as the volume of the current tank? 8 Computers Wires Computers Wires 3. In Earth’s history, the Precambrian period was about 4600 million years ago. If this number of 10 510 years is written in scientific notation, what is 21 615 the exponent for the power of 10? 9 33 721 4. A virus is a type of microorganism so small it 46 828 must be viewed with an electron microscope. The largest shape of virus has a length of about 8. A line perpendicular to 9x 10y 10 passes 0.0003 mm. To the nearest whole number, how many viruses would fit end to end on the head through ( 1, 4). Find the x-intercept of the of a pin measuring 1 mm? 3333 line. 13/5 or 2.6

Algebra 9. Find the positive solution of 6x2 7x 5. 5/3

5. Kaia has a painting that measures 10 in. by 14 in. She wants to make her own frame that Geometry has an equal width on all sides. She wants the total area of the painting and 10. The diagram shows RST on the coordinate frame to be 285 in.2. What 10 in. plane. The triangle is first rotated 90˚ will be the width of the 14 in. counterclockwise about the origin and frame in inches? 5/2 or 2.5 then reflected in the y-axis. What is the x-coordinate of the image of T after the two transformations? 4

y Test-Taking Tip

Question 1 T (2, 4) Remember that you have to grid the decimal point or R (5, 3) fraction bar in your answer. If your answer does not fit on the grid, convert to a fraction or decimal. If your answer still cannot be gridded, then check your S (3, 1) computations. O x

714 Preparing for Standardized Tests Preparing for Standardized Tests 715 135 130 147 193 154 180 Height (m) x 5 3 in. 1601 46 24 in. 6.25 32 Preparing for Standardized Tests Length of Call (min) 157 y Name 0

50 40 30 90 80 70 60

6.0 Charge (cents) Charge Power and Light Building and Power City Hall 1201 Walnut One Kansas City Place Pavilion Town Regency Hyatt Data Analysis and Probability Data Analysis The table shows the heights of the tallest the heights of The table shows the To Missouri. City, buildings in Kansas tenth, what is the positive difference nearest and the mean of the the median between data? A long-distance telephone service charges a If 40 cents per call and 5 cents per minute. what function model is written for the graph, is the slope of the function? In a dart game, the dart must land within the a dart game, In to win a on the dartboard innermost circle what is the a dart If hits the board, prize. that it will hit the as a percent, probability, innermost circle? On average, a B-777 aircraft uses 5335 gal of uses a B-777 aircraft On average, much how this rate, 2.5-h flight. At fuel on a flight? Round needed for a 45-min fuel will be gallon. to the nearest 17. 18. 19. 16. A 47.7 14 in. to the nearest tenth to the nearest . to the nearest Round 3 ft 75 cm 12 4.5 cm . Round to the nearest π. Round 1119 176 21.8 B C 30 cm Measurement square foot. square The Pep Club plans to decorate some large Club plans to decorate The Pep They will cover Week. for Spirit garbage barrels with decorated only the sides of the barrels feet of paper will many square How paper. one in the like the 8 barrels they need to cover 3.14 for Use diagram? An octahedron is a solid with An octahedron all that are eight faces How triangles. equilateral does the many edges have? octahedron Kara makes decorative paperweights. One of paperweights. makes decorative Kara with a diameter her favorites is a hemisphere of the What is the surface area of 4.5 cm. including the bottom on which it hemisphere 3.14 for Use rests? tenth of a square centimeter. tenth of a square The record for the fastest land speed of a The record for one mile is approximately car traveling two jet by The car was powered 763 mi/h. was the speed of the car in What engines. to the nearest feet per second? Round whole number. of a degree. Find the measure of A the measure Find 13. 11. 14. 15. 12. Preparing for Standardized Tests 716 the problemis clearly stated. The solutionof rubric, or scoring guide, orscoring short-response forscoring rubric, questions. free-response, ended, solution. These are sometimescalled well at the asany method,explanation,and/orjustificationyou usedtoarrive Short-response questionsrequire you toprovide asolutiontotheproblem, as Short-Response Questions Example Preparing forStandardized Tests rdtSoeCriteria Full Score Credit Partial None FULL CREDITSOLUTION one thatcovers 5000ft Two sizes are offertilizer available— rectangle 75ftby measuring 54ft. His backyard isa His front yard isarectangle 55ftby measuring 32ft. hewillneedforthisseason. Solbergwantstobuyallthelawnfertilizer Mr. he buytohave theleast amountofwaste? How manybagsofeachsize should theseason. fourtimesduring the fertilizer Mr. Solberg needs 15,000 tobuy 1bagthatcovers ft buy 2 of the bags that cover 5000buy 2ofthebagsthatcover ft Since hecannotbuyafraction ofabag,hewill need to 23,240 1 large bag, hewill stillneed tocover he will have toomuchfertilizer. Ifhebuys If Mr. Solberg 15,000 buys2bagsthatcover ft isarectangle,of thelawn so A since thefertilizer istobe applied 4times. Each portion Find thearea andmultiplyby4 ofeach partofthelawn Find how many small bags it takes to cover 8240 manysmall bagsittakesFind tocover how ft 2 bags that cover 50002 bagsthat cover ft ulcei:Theanswer iscorrectandafullexplanation is Fullcredit: 2 ata rdt Therearetwo different ways credit. toreceive partial Partialcredit: 1 ocei:Eitherananswer isnotprovided ortheanswer does Nocredit: 0 8240 4[(55 provided thatshowsatthefinalanswer. eachstepinarriving Theanswer isincorrect,but theexplanation andmethodof ¥ Theanswer iscorrect,but theexplanation provided is ¥ not make sense. or solving theproblem iscorrect. incomplete orincorrect. 15,000 8240 ft or student-produced questions. 5000 32) 2 and anothercovering 15,000ft (75 osrce-epne pnrsos,open- open-response, constructed-response, 1.648 2 2 each. . 54)] lw. 23,240 ft The following isasample 2 each. 2 2 , 2 He needstoapply . 2 . 2 and stated. are clearly and reasoning calculations The steps, not shown. if yourworkis correct answer fora is given tests, nocredit standardized On some Preparing for Standardized Tests 717 The wrong operations wrong The The first step of The There is not an There are used, so the answer is incorrect. Also, there are no units of measure given with any of the calculations. multiplying the area by 4 was left out. explanation of how was obtained. 23,240 Preparing for Standardized Tests , which is 2 2 2.98 44,720 5810 ft 5810 4 86 130 would result in too much result would 15,000 8240 2 54) 86 1.648 1.162 54 75 (75 44,720 130 55 32 15,000 5000 5000 32) (55 23,240 5810 8240 Mr. Solberg will need 3 bags of fertilizer. need will Solberg Mr. The area of the lawn is greater than 5000 ft 5000 than of the lawn area is greater The First find the total number of square feet of lawn. feet of square number the total find First part of the yard. of each the area Find 23,240 Mr. Solberg needs to buy 1 large bag and 2 small bags. bag to buy 1 large needs Solberg Mr. waste. the amount covered by the smaller bag, but buying the covered bag, but by the smaller the amount ft bag that covers 15,000 Therefore, Mr. Solberg will need to buy 2 of the smaller need will Solberg Mr. Therefore, bags of fertilizer. NO CREDIT SOLUTION and incomplete. is incorrect In this sample solution, the response PARTIAL CREDIT SOLUTION PARTIAL after the first However, is incorrect. this sample solution, the answer In correct. are reasoning statement all of the calculations and PARTIAL CREDIT SOLUTION PARTIAL justification is no there However, correct. is the answer this sample solution, In the calculations. for any of 7. Hector is working on the design for the Short-Response Practice container shown below that consists of a cylinder with a hemisphere on top. He has Solve each problem. Show all your work. written the expression πr2 2πrh 2πr2 to represent the surface area of any size Number and Operations container of this shape. Explain the meaning of each term of the expression. See additional answers. 1. In 2000, approximately $191 billion in merchandise was sold by a popular retail chain store in the United States. The population at r that time was 281,421,906. Estimate the average h amount of merchandise bought from this store r by each person in the U.S. about $680

2. At a theme park, three educational movies run 8. Find all solutions of the equation continuously all day long. At 9 A.M., the three 5 1 2 , shows begin. One runs for 15 min, the second 6x 13x 5. 2 3 for 18 min, and the third for 25 mi. At what time will the movies all begin at the same time 9. In 1999, there were 2,192,070 farms in the U.S., again? 4:30 P.M.

Preparing for Standardized Tests while in 2001, there were 2,157,780 farms. Let x represent years since 1999 and y represent 3. Ming found a sweater on sale for 20% off the the total number of farms in the U.S. Suppose original price. However, the store was offering the number of farms continues to decrease at a special promotion, where all sale items were the same rate as from 1999 to 2001. Write an discounted an additional 60%. What was the equation that models the number of farms for total percent discount for the sweater? 68% any year after 1999. y 2,192,070 17,145x

4. The serial number of a DVD player consists of Geometry three letters of the alphabet followed by five digits. The first two letters can be any letter, but 10. Refer to the diagram. What is the measure the third letter cannot be O. The first digit of 1? 65 cannot be zero. How many serial numbers are possible with this system? 1,521,000,000

Algebra 115˚

5. Solve and graph 2x 9 5x 4. 13 x 3 ; See additional answers for graph. 6. Vance rents rafts for trips on the Jefferson River. 1 You have to reserve the raft and provide a $15 deposit in advance. Then the charge is $7.50 per hour. Write an equation that can be used to find the charge for any amount of time, where y is the total charge in dollars and x is 11. Quadrilateral JKLM is to be reflected in the the amount of time in hours. y 15 7.50x line y x. What are the coordinates of the vertices of the image? J '(2, 2), K '(0, 4), L'(3, 1), y M '(1, 2)

J (2, 2) Test-Taking Tip M (2, 1) K (4, 0) Question 4 O x Be sure to completely and carefully read the problem before beginning any calculations. If you read too quickly, you may miss a key piece of information. L (1, 3)

718 Preparing for Standardized Tests Preparing for Standardized Tests 719 76 75 71 67 79 75 73 72 x 7 14 18 21 10 4 See additional answers. 32 Country Time(s) See additional answers. 20% or 0.2 Time (min) Preparing for Standardized Tests 15 Favorite Spectator Sport Favorite y Basketball Football Soccer Golf Other Men’s 1000-m Speed Skating Event 1000-m Men’s Year 197619801984 U.S. 1988 U.S. 1992 Canada 1994 U.S.S.R. 1998 Germany 2002 U.S. Netherlands Netherlands 0

9000 8000 7000 6000 5000 4000 3000 10000 (ft) Altitude Data Analysis and Probability and Data Analysis The table shows the winning times for the the winning shows The table event. speed skating 1000-m men’s Olympic data and describe a scatter plot of the Make to rounded are Times the pattern in the data. second. the nearest Bradley surveyed people about their favorite Bradley spectator sport. a person is chosen at If the people surveyed, from what is the random favorite spectator that the person’s probability sport is basketball? The graph shows the altitude of a small shows The graph to model the graph. a function Write airplane. what the model means in termsExplain of the altitude of the airplane. 18. 19. 20. 3 5 159 ft 4x h 1 in. to 2 r 45 ft 3 Front view ft , 0 5 4 about 274,798 AU 60 ft 603 49 ft 3 in. ˚ 60 r 150 Top view Measurement between 31 and 32 shirtsbetween Find the ratio of the volume of the cylinder to the ratio Find the volume of the pyramid. The Astronomical Unit (AU) is the distance (AU) Unit The Astronomical is usually rounded It Earthfrom to the Sun. is The star Alpha Centauri to 93,000,000 mi. What is Earth.25,556,250 million miles from this distance in AU? on shirtsLinesse handpaints unique designs takes her about 4.5 h to and sells them. It many shirts how this rate, a design. At create month 22 days per can she design if she works of 6.5 h per day? for an average pancake was made in largest The world’s foot, cubic the nearest To England in 1994. what was the volume of the pancake? At what point does the graph of y does the graph what point At intersect the x-axis? intersect Village an subdivision, the Columbia In will be below, shaped lot, shown unusually the exact perimeter Find used for a small park. of the lot. 17. 14. 15. 16. 12. 13. Preparing for Standardized Tests 720 behind your computations. solution includingfigures, sketchesofgraphing calculatorscreens, orthereasoning Make sure thatwhentheproblem saystoShow yourwork, response questions. you receive or nocredit. full,partial, The following extended- forscoring isasamplerubric show whether allofyour isalsousedtodetermine work insolvingtheproblem. Arubric Extended-response questionsare similartoshort-response questionsinthatyou must toreceiveparts fullcredit. questions. Extended-response questionsare oftencalledopen-ended Extended-Response Questions Example Preparing forStandardized Tests rdtSoeCriteria Full Score Credit None Partial Part a Part FULL CREDITSOLUTION b. a. Various onthepolygontouseforgame. willbeperformed transformations represented onacoordinate planetobeusedinthegraphicsforavideogame. Polygon c. Most extended-response questionshavemultipleparts. You mustanswer all ,2 ata rdt Agenerally correctsolutionisgiven thatmay contain Partialcredit: 3, 2,1 Describe howDescribe thecoordinates of ofthevertices Be sure tolabelallofthevertices. Graph image onWXYZ Another transformation isperformed coordinates of ofthevertices W'X'Y'Z'? and itsimageunderthistransformation. What transformation produced 4 Full credit: A correct solution is given that is supported by Acorrectsolutionisgiven well- thatissupported Fullcredit: 4 ocei:Anincorrectsolutionisgiven indicatingnomathematical Nocredit: 0 • • the vertices, includingletternamesandcoordinates. A completegraph andlabelsfor includeslabels fortheaxesandorigin • WXYZ W'X'Y'Z' WXYZ The vertices ofthepolygonshould becorrectlyThe vertices graphed andlabeled. contrasting colors. Optionally, thepolygon anditsimagecould begraphedintwo The verticesofthepolygons shouldbeconnectedcorrectly. transformation showsareflection inthe The verticesoftheimage shouldbelocatedsuchthatthe understanding oftheconcept,ornosolutionisgiven. The morecorrectthesolution,greater thescore. developed, accurate explanations. minor flaws inreasoningorcomputationanincompletesolution. ,2), with vertices W(3, and itsimageW'X'Y'Z' are W'(2, 3), W'X'Y'Z'. X'(4, 4),Y'(1,3),andZ'3, 4 4), X(4, under areflection inthey-axis. Y(3, or you show ofyour part every . This time, ofthe thevertices WXYZ constructed-response ) and 1), y-axis. relate tothe Z(2, 2). Graph 3) isafigure WXYZ not shown. if yourworkis correct answer fora is given tests, nocredit standardized On some Preparing for Standardized Tests 721 are not correct. Y and The first step doubling The More credit would have For full credit, the graphFor the square footage for the square of paint was two coats left out. been given if all of the points were reflected images for The correctly. X in Partbe c must also accurate, which is true for this graph. ' Preparing for Standardized Tests x. x are the same point, ' W'(3, 2) X(4, 4) Y (3, Ð1) The coordinates of Z and Z coordinates The X Since switched. been have and X the polygon has been in the line y reflected Z'(2, Ð3) y are (3, 2) and (3, 2). The ' 0 x W(Ð3, 2) X(4, 4) X'(4, 4) W'(3, 2) Z(Ð2, Ð3) Y(3, Ð1) y = x X'(Ð4, 4) W'(2, Ð3) Y'(Ð3, Ð1) y 0 Z(Ð2, Ð3) Y'(Ð1, 3) This sample graph includes no labels for the axes and for the vertices of the This sample graph graphed. of the image points have been incorrectly Two polygon and its image. W(Ð3, 2) Z'(Ð3, Ð2) The coordinates of W and W coordinates The x-coordinates are the opposite of each other and the of each are the opposite x-coordinates are the same. y-coordinates PARTIAL CREDIT SOLUTION PARTIAL Part a Part c Part b Part b Partial credit is given because the reasoning is correct, but the reasoning was based on the incorrect graph in Part a.

For two of the points, W and Z, the y-coordinates are the same and the x-coordinates are opposites. But, for points X and Y, there is no clear relationship.

Part c Full credit is given for Part c. The graph supplied by the student was identical to the graph shown for the full credit solution for Part c. The explanation below is correct, but slightly different from the previous answer for Part c.

I noticed that point X and point X' were the same. I also guessed that this was a reflection, but not in either axis. I played around with my ruler until I found a line that was the line of reflection. The transformation from WXYZ to W'X'Y'Z' was a reflection in the line y x. Preparing for Standardized Tests

This sample answer might have received a score of 2 or 1, depending on the judgment of the scorer. Had the student graphed all points correctly and gotten Part b correct, the score would probably have been a 3.

NO CREDIT SOLUTION Part a The sample answer below includes no labels on the axes or the coordinates of the vertices of the polygon. The polygon WXYZ has three vertices graphed incorrectly. The polygon that was graphed is not reflected correctly either.

Part b I don’t see any way that the coordinates relate.

Part c It is a reduction because it gets smaller.

In this sample answer, the student does not understand how to graph points on a coordinate plane and also does not understand the reflection of figures in an axis or other line.

722 Preparing for Standardized Tests Preparing for Standardized Tests 723 to B 2, to x E 1, Feb. 16 ft . He then wants . He 10 12 F F D and D. 811 to F Month to Preparing for Standardized Tests E A ˚ 46 9 to A, B, C, D, E, 4a–c. See additional answers. 60 32 D to Depth of the Reservoir Depth of A 157 B C y to 5a–d. See additional answers. Find the missing side measures of EDF. the missing side measures Find Explain. of ABC. the missing side measures Find Explain. the total distance of the path: A Find What is the slope of the line joining the What is the slope What 6 and 7? points with x-coordinates does the slope represent? an equation for the segment of the Write is the slope of the What 5 to 6. from graph in terms line and what does this represent of the reservoir? depth of the reservoir? What was the lowest and When was this depth first measured recorded? C The director wants to place one person at The director each point to place other band members approximately one foot apart segments of the on all many people should he formation. How place on each segment of the formation? many total people will he need? How 0

360 350 340 330 320 Geometry and so on.) (ft) Depth a. b. c. The Silver City Marching Band is planning to Band City Marching The Silver this formation with the members. create The depth of a reservoir was measured on the on was measured of a reservoir The depth of each month. (Jan. first day a. b. c. d. 4. 5. in.? 1 4 answers. cm. A 3a–c. See additional 8 . 2 ). Express each value ). Express ˚ 1990 2000 288,091 396,375 Population approximately equal to approximately City

1a–c. See additional answers. 2a–c. See additional answers.

Draw and label a diagram. Draw an equation that can be used to find Write the width of the deck. the width of the deck. Find centimeter is measure What is the approximate 0.3937 in. in inches? of an angstrom in 1 in.? are many angstroms How molecule has a diameter of 2 angstroms, a If molecules placed side by many of these how measuring side would fit on an eraser For which city was the increase in population which city was the increase For What was the increase? the greatest? of increase which city was the percent For What was the in population the greatest? increase? percent of a that the population increase Suppose was the population in 2000 city was 30%. If 346,668, find the population in 1990. is exactly 10 An angstrom Phoenix, AZ TXAustin, Charlotte, NC 983,403Mesa, AZ NVLas Vegas, 465,622 1,321,045 395,934 258,295 656,562 540,828 478,434 Algebra Number and Operations Number and a. b. c. The Marshalls are building a rectangular in- building a rectangular are The Marshalls The pool will be pool in their backyard. ground They want to build a deck of equal 29 ft. 24 ft by of the The final area the pool. width all around pool and deck will be 1800 ft b. c. a. b. c. a particular the smallest units of are Molecules propertiessubstance that still have the same as is The diameter of a molecule that substance. (A in angstroms measured in scientific notation. a. Refer to the table. Refer 3. 2.

1. Extended-Response Practice Extended-Response work. Show all your problem. Solve each Measurement Data Analysis and Probability

6. Rodrigo stands 50 yd away from the base of a 8. The table shows the average monthly building. From his eye level of 5 ft, Rodrigo sees temperatures in Barrow, Alaska. The months the top of the building at an angle of elevation are given numerical values from 1–12. of 25˚. (Jan. 1, Feb. 2, and so on.)

Average Monthly Temperature Month ûF Month ûF 25˚ 1 –14 7 40 5 ft 50 yards 2 –16 8 39 3 –14 9 31 a. What is the height of the building? Round 4–11015 to the nearest tenth of a foot. 74.9 ft 52011–1 b. If Rodrigo moved back 15 more yards, how 6 35 12 –11 would the angle of elevation to the top of the building change? smaller

Preparing for Standardized Tests c. If the building were taller, would the angle a. Make a scatter plot of the data. Let x be the of elevation be greater than or less than 25˚? numerical value assigned to the month and greater y be the temperature. 7. Kabrena is working on a project about the solar b. Describe any trends shown in the graph. system. The table shows the maximum c. Find the mean of the temperature data. distances from Earth to the other planets in millions of miles. d. Describe any relationship between the mean of the data and the scatter plot. 8a–d. See additional answers. Distance from Earth to Other Planets Planet Distance Planet Distance 9. A dart game is played using the board shown. The inner circle is pink, the next ring is blue, Mercury 138 Saturn 1031 the next red, and the largest ring is green. A Venus 162 Uranus 1962 dart must land on the board during each round Mars 249 Neptune 2913 of play. 9a–c. See additional answers. Jupiter 602 Pluto 4681

a. The maximum speed of the Apollo moon 3 in. missions spacecraft was about 25,000 mi/h. Make a table showing the time it would 3 in. 3 in. 3 in. take a spacecraft traveling at this speed to reach each of the four closest planets. b. Describe how to use scientific notation to calculate the time it takes to reach any planet. 21 in. c. Which planet would it take approximately 13.3 yr to reach? Explain. 7a–c. See additional answers. a. What is the probability that a dart landing on the board hits the pink circle? b. What is the probability that the first dart Test-Taking Tip thrown lands in the blue ring and the second dart lands in the green ring? Question 6 While preparing to take a standardized test, familiarize c. Suppose players throw a dart twice. For yourself with the formulas for surface area and volume which outcome of two darts would you of common three-dimensional figures. award the most expensive prize? Explain your reasoning.

724 Preparing for Standardized Tests Technology Reference Guide

Graphing Calculator Overview

This section summarizes some of the graphing calculator skills you might use in your mathematics classes using the TI-83 Plus or TI-84 Plus. General Information

• Any yellow commands written above the calculator keys are accessed with the 2nd key, which is also yellow. Similarly, any green characters or commands above the keys are accessed with the ALPHA key, which is also green. In this text, commands that are accessed by the 2nd and ALPHA keys are shown in brackets. For example, 2nd [QUIT] means to press the 2nd key followed by the key below the yellow [QUIT] command. • 2nd [ENTRY] copies the previous calculation so it can be edited or reused. • 2nd [ANS] copies the previous answer so it can be used in another calculation. • 2nd [QUIT] will return you to the home (or text) screen. Technology Reference Guide • 2nd [A-LOCK] allows you to use the green characters above the keys without pressing ALPHA before typing each letter. • Negative numbers are entered using the ( ) key, not the minus sign, . • The variable x can be entered using the X,T,,n key, rather than using ALPHA [X]. • 2nd [OFF] turns the calculator off.

Key Skills THE STANDARD VIEWING WINDOW A good window to start with to graph an Use this section as a reference for further equation is the standard viewing window. It instruction. For additional features, consult the appears in the WINDOW screen as follows. TI-83 Plus or TI-84 Plus user’s manual.

ENTERING AND GRAPHING EQUATIONS Press . Use theX,T,,n key to enter any variable for your equation. To see a graph of the equation, pressGRAPH .

SETTING YOUR VIEWING WINDOW Press WINDOW . Use the arrow or ENTER keys to To easily set the values for the standard viewing move the cursor and edit the window settings. window, press ZOOM 6. Xmin and Xmax represent the minimum and maximum values along the x-axis. Similarly, ZOOM FEATURES Ymin and Ymax represent the minimum and To easily access a viewing window that shows maximum values along the y-axis. Xscl and Yscl only integer coordinates, press ZOOM 8 ENTER . refer to the spacing between tick marks placed on the x- and y-axes. Suppose Xscl 1. Then To easily access a viewing window for statistical the numbers along the x-axis progress by 1 unit. graphs of data you have entered, press ZOOM 9. Set Xres to 1.

Technology Reference Guide 725 USING THE TRACE FEATURE ENTERING INEQUALITIES To trace a graph, press TRACE . A flashing Press 2nd [TEST]. From this menu, you can cursor appears on a point of your graph. At the enter the , , , , , and symbols. bottom of the screen, x- and y-coordinates for the point are shown. At the top left of the ENTERING AND DELETING LISTS screen, the equation of the graph is shown. Use Press STAT ENTER . Under L1, enter your list the left and right arrow keys to move the cursor of numerical data. To delete the data in the list, along the graph. Notice how the coordinates use your arrow keys to highlight L1. Press change as the cursor moves from one point to CLEAR ENTER . Remember to clear all lists the next. If more than one equation is graphed, before entering a new set of data. use the up and down arrow keys to move from one graph to another.

PLOTTING STATISTICAL DATA IN LISTS Press . If appropriate, clear equations. Use SETTING OR MAKING A TABLE the arrow keys until Plot1 is highlighted. Plot1 Press 2nd [TBLSET]. Use the arrow or ENTER represents a Stat Plot, which enables you to keys to move the cursor and edit the table graph the numerical data in the lists. Press settings. Indpnt represents the x-variable in ENTER to turn the Stat Plot on and off. You may your equation. Set Indpnt to Ask so that you need to display different types of statistical may enter any value for x into your table. graphs. To see the details of a Stat Plot, press Depend represents the y-variable in your 2nd [STAT PLOT] ENTER . A screen like the one equation. Set Depend to Auto so that the below appears. calculator will find y for any value of x.

USING THE TABLE

Technology Reference Guide Technology Before using the table, you must enter at least one equation in the screen. Then press 2nd [TABLE]. Enter any value for x as shown at the bottom of the screen. The function entered as Y1 will be evaluated at this value for x. In the two columns labeled X and Y1, you will see the At the top of the screen, you can choose from values for x that you entered and the resulting one of three plots to store settings. The second y-values. line allows you to turn a Stat Plot on and off. Then you may select the type of plot: scatter PROGRAMMING ON THE TI–83 PLUS plot, line plot, histogram, two types of box- PRGM When you press , you see three and-whisker plots, or a normal probability plot. menus: EXEC, EDIT, and NEW. EXEC allows Next, choose which lists of data you would like you to execute a stored program by selecting to display along the x- and y-axes. Finally, the name of the program from the menu. EDIT choose the symbol that will represent each allows you to edit or change an existing program. data point. NEW allows you to create a new program. For additional programming features, consult the TI–83 Plus or TI–84 Plus user’s manual.

726 Technology Reference Guide Cabri Jr. Overview

Cabri Junior for the TI-83 Plus and TI-84 Plus is a geometry application that is designed to reproduce the look and feel of a computer on a handheld device. General Information

Starting Cabri Jr. To start Cabri Jr., press APPS and choose Cabri Jr. Press any key to continue. If you have not run the program on your calculator before, the F1 menu will be displayed. To leave the menu and obtain a blank screen, press CLEAR . If you have run the program before, the last screen that was in the program before it was turned off will appear. See Quitting Cabri Jr. for instructions on clearing this screen to obtain a blank screen.

In Cabri Jr., the four arrow keys ( , , , ), along with ENTER , operate as a mouse would on a computer. The arrows simulate moving a mouse, and ENTER simulates a left click on a mouse. For example, when you are to select an item, use Technology Reference Guide the arrow keys to point to the selected item and then press ENTER . You will know you are accurately pointing to the selected item when the item, such as a point or line, is blinking.

Quitting Cabri Jr. To quit Cabri Jr., press 2nd [QUIT], or [OFF] to completely shut off the calculator. Leaving the calculator unattended for approximately 4 minutes will trigger the automatic power down. After the calculator has been turned off, pressing ON will result in the calculator turning on, but not Cabri Jr. You will need to press APPS and choose Cabri Jr. Cabri Jr. will then restart with the most current figure in its most recent state.

As Cabri Jr. resembles a computer, it also has dropdown menus that simulate the menus in many computer programs. There are five menus, F1 through F5.

Navigating Menus To navigate each menu, press the appropriate key for F1 through F5. The arrow keys will then allow you to navigate within each menu. The and keys allow you to move within the menu items. The and keys allow you to access a submenu of an item. If an item has an arrow to the right, this indicates there is a submenu. Although not displayed, the menu items are numbered. You can also select a menu item by pressing the number that corresponds to each item. For example, to select the fourth menu item in the list, press [4]. If you press a number greater than the number of items in the list, the last item will be selected. If you press [0], you will leave the menu without selecting an item. This is the same as pressing CLEAR .

Technology Reference Guide 727 Key Skills [F4] TRANSFORMING OBJECTS This menu provides the tools to transform Use this section as a reference for further geometric figures. Using figures that are already instruction. For additional features, consult created, you can access this menu to create the TI-84 Plus user’s manual. figures that are symmetrical to other figures, reflect figures over a line of reflection, translate [F1] MANAGING FIGURES figures using a line segment or two points that The menu below provides the basic operations define the translation, rotate figures by defining when working in Cabri Jr. These are commands the center of rotation and angle of rotation, and normally found in menus within computer dilate figures using the center of the dilation applications. and a scale factor.

[F2] CREATING OBJECTS [F5] COMPUTING OBJECTS This menu provides the basic tools for creating This menu provides the tools for displaying, geometric figures. You can create points in labeling, measuring, and computing. You can three different ways, a line and line segment make an object visible or invisible, label points by selecting two points, a circle by defining on figures, alter the way objects are displayed, the center and radius, a triangle by finding measure length, area, and angle measures, three vertices, and a quadrilateral by finding display coordinates of points and equations of four vertices. lines, make calculations, and delete objects from the screen. Technology Reference Guide Technology

[F3] CONSTRUCTING OBJECTS This menu provides the tools to construct new While a graphing calculator cannot do objects from existing objects. You can construct everything, it can make some tasks easier. To perpendicular and parallel lines, a perpendicular prepare for whatever lies ahead, you should try bisector of a segment, an angle bisector, a to learn as much as you can about the midpoint of a line segment, a circle using the technology. The future will definitely involve center and a point on the circle, and a locus. technology and the people who are comfortable with it will be successful. Using a graphing calculator is a good start toward becoming familiar with technology.

728 Technology Reference Guide Glossary/Glosario

A mathematics multilingual glossary is available at www.math.glencoe.com/multilingual_glossary. The glossary includes the following languages. Arabic English Korean Tagalog Bengali Haitian Creole Russian Urdu Cantonese Hmong Spanish Vietnamese

English Español ■ A ■ absolute value (p. 12) The distance of any number, x, valor absoluto (p. 12) La distancia a la que se from zero on the number line. Absolute value is encuentra un número, x, del cero en la recta numérica. represented by x. Se representa: x. acute triangle (p. 150) A triangle with triángulo acutángulo (p. 150) Un three acute angles that measure less than 90°. triángulo con tres ángulos que miden A menos de 90°. 0° mA 90° addition property of equality (p. 66) For all real propiedad aditiva de la igualdad (p. 66) Para todos los numbers a, b, and c, if a b, then a c b c and números reales a, b, y c, si a b, entonces a c b c y c a c b. c a c b. addition property of inequality (p. 76) For all real propiedad aditiva de la desigualdad (p. 76) Para todos numbers a, b, and c, if a b, then a c b c and los números reales a, b, y c, si a b entonces a c b c a c b. If a b, then a c b c. c y c a c b. Si a b, entonces a c b c. addition property of opposites (p. 21) The sum of a propiedad aditiva de los opuestos (p. 21) La suma de number and its opposite equals 0. a (a) 0. un número y su opuesto es igual a 0. a (a) 0 additive inverse (p. 21) The opposite of a number. The aditivo inverso (p. 21) El opuesto de un número. El additive inverse of a is a, and the additive inverse of aditivo inverso de a es a y el aditivo inverso de a es a. a is a. adjacent angles (p. 109) Two angles in the same plane ángulos adyacentes (p. 109) Dos ángulos en el mismo that have a common vertex and a common side but no plano que tienen un vértice común y un lado común pero common interior points. ningún punto interno común. alternate exterior angles (p. 120) Two nonadjacent ángulos alternos externos (p. 120) Dos ángulos exterior angles on opposite sides of the transversal. exteriores no adyacentes en lados opuestos a la transversal. Glossary/Glosario alternate interior angles (p. 120) Two nonadjacent ángulos alternos internos (p. 120) Dos ángulos interior angles on opposite sides of the transversal. internos no adyacentes en lados opuestos a la transversal. altitude of a triangle (p. 164) A perpendicular segment altura de un triángulo (p. 164) Un segmento from a triangle’s vertex to the line containing the opposite perpendicular desde el vértice de un triángulo al lado side. opuesto. amplitude (p. 629) In a periodic function, half the amplitud (p. 629) En una función periódica, la mitad de difference between its maximum and minimum y-values. la diferencia entre los valores máximo y mínimo de y.

angle (p. 108) The figure formed by two rays ángulo (p. 108) La figura formada por dos that have a common endpoint. rayos que tienen un punto extremo en común.

Glossary/Glosario 729 English Español

angle of depression (p. 619) The acute angle formed by ángulo de depresión (p. 619) El ángulo agudo formado a horizontal line and a line slanting downward. por una línea horizontal y una línea que se inclina hacia abajo. angle of elevation (p. 619) The acute angle formed by a ángulo de elevación (p. 619) El ángulo agudo formado horizontal line and a line slanting upward. por una línea horizontal y una línea que se inclina hacia arriba. angle of rotation (p. 342) In a rotation, the amount of ángulo de rotación (p. 342) En una rotación, la turn expressed as a fractional part of a whole turn or as cantidad de una vuelta expresada como una parte the angle of rotation in degrees. fraccional de una vuelta completa. associative property of addition (p. 21) For all real propiedad asociativa de la adición (p. 21) Para todos numbers a, b, and c, a (b c) (a b) c. los números reales a, b, y c, (a b) c a (b c). associative property of multiplication (p. 27) For all propiedad asociativa de la multiplicación (p. 27) Para real numbers a, b, and c, a(bc) (ab)c. todos los números reales a, b, y c, a(bc) (ab)c. asymptotes (p. 576) The values that hyperbolic asíntotas (p. 576) Los valores a que las funciones functions approach but never reach. hiperbólicas se acercan pero nunca alcanzan. axis of a cylinder (p. 220) The segment joining the eje de simetría de un cilindro (p. 220) El segmento que centers of the two bases. une los centros de las bases.

■ B ■

bell curve (p. 415) A frequency distribution that curva de campana (p. 415) Una distribución de consists of a smooth curved line connecting the frecuencia que consiste de una línea curva lisa que midpoints of a histogram. In a normal distribution of conecta los puntos medios de un histograma. En una data, the curve is shaped like a bell. distribución normal de datos, la curva tiene la forma de una campana. biconditional statement (p. 129) A statement in the if- proposición bicondicional (p. 129) Una proposición en and-only-if form. In the biconditional “P if and only if Q,” la forma de si y solamente si. En la bicondicional “P si y P is both a necessary condition and a sufficient condition solamente si Q”, P es ambos una condición necesaria y for Q. suficiente para Q. binomial (p. 468) A polynomial with two terms. binomio (p. 468) Un polinomio con dos términos. Q W bisector of an angle (p. 115) A ray that P bisectriz de un ángulo (p. 115) Un rayo divides an angle into two congruent que divide un ángulo en dos ángulos R adjacent angles. adyacentes congruentes. PW is the bisector of P. PW es la bisectriz del P.

bisector of a segment (p. 114) Any line, segment, ray, bisectriz de un segmento (p. 114) Cualquier línea, or plane that intersects the segment at its midpoint. segmento, rayo o plano que interseca el segmento en su punto medio. boundary (p. 77) The line separating two half-planes in frontera (p. 77) La línea que separa dos semiplanos en

Glossary/Glosario the coordinate plane. el plano coordenado. box-and-whisker plot (p. 407) A means of visually diagrama de bloque (p. 407) Un medio visual de displaying data that shows the median of a set of data, the representar datos que muestra la mediana de un median of each half of data, and the least and greatest conjunto de datos, la mediana de cada mitad de datos y el value of the data. valor menor y mayor de los datos.

730 Glossary/Glosario English Español ■ C ■ cells (p. 30) Areas that are formed by the vertical celdas (p. 30) Áreas que las forman las columnas columns and horizontal rows on a spreadsheet. verticales y las filas horizontales en una hoja de cálculos. center of rotation (p. 342) The point about which a centro de rotación (p. 342) El punto alrededor del cual figure is rotated in a rotation. se gira una figura. chord (p. 441) A segment with both endpoints on cuerda (p. 441) Un segmento con ambos puntos the circle. extremos en el mismo círculo. circle (p. 562) In a plane, the set of all círculo (p. 562) En un plano, el P points that are a given distance for a fixed conjunto de todos los puntos a una point. That fixed point is the center of the distancia dada de un punto fijo. El punto P is the center of the circle. circle. P es el centro del círculo. fijo es el centro del círculo. circle graph (p. 446) A means of displaying data that diagrama de círculo (p. 446) Un medio de mostrar represents items as parts of a whole circle; these parts are datos que representan artículos como partes de un called sectors. círculo entero; estas partes se llaman sectores. circumference (p. 206) The distance around a circle. circunferencia (p. 206) La distancia alrededor un círculo. circumscribed polygon (p. 455) A polygon polígono circunscrito (p. 455) Un polígono with all sides tangent to the same circle. con todos los lados tangente al mismo círculo. closed half-plane (p. 77) The graph of either half-plane semiplano cerrado (p. 77) La gráfica de uno de los dos and the line that separates them. semiplanos y la línea que los separa. clusters (p. 87) Isolated groups of values on a stem-and- conglomerados (p. 87) Grupos aislados de valores en leaf plot. un diagrama de tallo y hoja. cluster sampling (p. 82) Statistical sampling in which muestra por conglomerado (p. 82) Una muestra de the members of the population are randomly selected estadística en que los miembros de la población se from particular parts of the population and then surveyed seleccionan al azar desde sectores particulares de la in groups, not individually. población y se inspeccionan en grupos, no individualmente. coefficient (p. 468) The numerical, nonvariable portion coeficiente (p. 468) La porción numérica, no variable of a monomial. de un monomio. Glossary/Glosario collinear points (p. 104) Points that R puntos colineales (p. 104) Puntos P Q lie on the same line. que están en la misma línea. P, Q, and R are collinear. P, Q, y R son colineales. combination (p. 404) A set of items chosen from a combinación (p. 404) Un conjunto de artículos larger set without regard to order. seleccionados de un conjunto más grande sin considerar el orden. combined variation (p. 587) A variation in which a variación combinada (p. 587) Una variación en que una quantity varies directly as one quantity and inversely as cantidad varía directamente como una cantidad e another. inversamente como otra. commutative property of addition (p. 21) For all real propiedad conmutativa de la adición (p. 21) Para numbers a, b, and c, a b b a. todos los números reales a, b, y c, a b b a.

Glossary/Glosario 731 English Español

commutative property of multiplication (p. 27) For all propiedad conmutativa de la multiplicación (p. 27) real numbers a, b, and c, ab ba. Para todos los números reales a, b, y c, ab ba. complementary angles (p. 109) Two angles whose ángulos complementarios (p. 109) Dos ángulos cuyas measures have a sum of 90°. medidas tienen una suma de 90°. complement of an event (p. 393) The set of all complemento de un evento (p. 393) El conjunto de todos outcomes in the sample space, not in A, when A is a los resultados en un espacio muestral, no en A, cuando A es subset of U. This is symbolized as A. un subconjunto de U. Esto se representa como A. completing the square (p. 534) Making a perfect completar el cuadrado (p. 534) Hacer un cuadrado square for an expression in the form ax 2 bx. perfecto para una expresión en la forma de ax 2 bx. compound event (p. 392) An event consisting of two or suceso compuesto (p. 392) Un suceso que consiste de more simple events. dos o más sucesos simples. concave polygon (p. 178) A polygon with at least one polígono cóncavo (p. 178) Un polígono con por lo diagonal that contains points in the exterior of the menos una diagonal que contiene puntos en el exterior polygon. del polígono. conditional statement (p. 128) An if-then statement proposición condicional (p. 128) Una proposición si - having two parts—a hypothesis and a conclusion. entonces con dos partes, una hipótesis y una conclusión. vertex vértice cone (p. 221) A three-dimensional figure cono (p. 221) Una figura tridimensional base with a curved surface and one circular base. base con una superficie curva y una base circular.

congruent (p. 154) Term used to describe figures with congruente (p. 154) El término usado para describir the same size and shape. figuras con el mismo tamaño y forma. B congruent triangles (p. 154) triángulos congruentes (p. 154) Triangles whose vertices can be D Triángulos con ángulos paired in such a way that all angles E correspondientes congruentes y and sides of one triangle are C lados correspondientes congruentes. congruent to corresponding angles A F

and corresponding sides of the other. ABC EDF conic section (p. 572) The section formed by a plane sección cónica (p. 572) La sección formada por un intersecting two circular cones whose vertices are at the plano que interseca dos conos circulares cuyos vértices origin. están en el origen. conjecture (p. 124) A conclusion reached through conjetura (p. 124) Una conclusión que se deriva inductive reasoning. mediante el razonamiento inductivo. consecutive sides (p. 178) Two sides of a polygon that lados consecutivos (p. 178) Dos lados de un polígono have a common vertex. que tienen un vértice común. consecutive vertices (p. 178) The endpoints of any side vértices consecutivos (p. 178) Los puntos extremos de of a polygon. cualquier lado de un polígono. constant (p. 468) A monomial that contains no variables. constante (p. 468) Un monomio que no tiene variables. construction (p. 118) A precise drawing of a geometric construcción (p. 118) Un dibujo de una figura figure made with the aid of only two tools: a compass and geométrica hecha con la ayuda de solamente dos

Glossary/Glosario an unmarked straightedge. herramientas: un compás y una regla sin marcas. convenience sampling (p. 82) Statistical sampling in muestra de conveniencia (p. 82) Una muestra de which members of a population are selected because they estadística en que los miembros de una población se are readily available, and all are surveyed. seleccionan porque están fácilmente disponibles y todos son entrevistados.

732 Glossary/Glosario English Español converse (p. 129) A statement formed by interchanging converso (p. 129) Una declaración formada al the hypothesis and conclusion of a conditional statement. intercambiar la hipótesis y la conclusión de una proposición condicional. converse of the Pythagorean Theorem (p. 431) If the converso del teorema pitagórico (p. 431) Si la suma de sum of the squares of the measures of two sides of a los cuadrados de dos lados de un triángulo es igual al triangle is equal to the square of the measure of the third cuadrado del tercer lado, entonces el triángulo es un side, then the triangle is a right triangle. triángulo rectángulo. convex polygon (p. 178) A polygon with no diagonals polígono convexo (p. 178) Un polígono sin diagonales that contain points in the exterior of the polygon. que contienen puntos en el exterior del polígono. coordinate of a point (p. 105) The real number that coordenada del punto (p. 105) El número real asociado corresponds to a point. An ordered pair of numbers con un punto en la recta numérica. Un par ordenado de associated with a point on a grid are the coordinates of números asociado con un punto en el plano. the point. y 4 coordinate plane (p. 56) A two- 3 plano coordenado (p. 56) Un sistema dimensional mathematical grid system 2 bidimensional que consiste de dos 1 consisting of two perpendicular number rectas numéricas perpendiculares, lines, called the x-axis and the y-axis. 4321O 1 2 3 4 x llamadas eje de x y eje de y. The point where the axes intersect is 2 the origin. 3 4 coplanar points (p. 104) Points that lie on the same puntos coplanares (p. 104) Puntos que están en el plane. mismo plano. corollary (p. 161) A statement that follows directly from corolario (p. 161) Una declaración que sigue a theorem. directamente a un teorema. corresponding angles (pp. 120, 154) Two angles in ángulos correspondientes (pp. 120, 154) Dos ángulos corresponding positions relative to two lines cut by a en posiciones correspondientes relativos a dos líneas transversal. Also, angles in the same position in intersecadas por una transversal. También, ángulos en la congruent or similar polygons. misma posición en polígonos congruentes o similares. corresponding sides (p. 154) Sides in the same position lados correspondientes (p. 154) Lados en la misma in congruent or similar polygons. posición en polígonos congruentes o similares. cosine (p. 614) In a right triangle, the cosine of acute A coseno (p. 614) En un triángulo rectángulo, el coseno del length of side adjacent to A la longitud de lado adyacente a A is equal to: . ángulo agudo A es igual a: . length of hypotenuse la longitud de la hipotenusa counterexample contraejemplo

(p. 128) An instance that satisfies the (p. 128) Un ejemplo que satisface la Glossary/Glosario hypothesis but not the conclusion of the conditional hipótesis pero no la conclusión de una proposición statement. condicional. cross section (p. 223) The two-dimensional figure sección transversal (p. 223) La figura bidimensional formed when a three-dimensional shape is cut with a formada cuando una figura tridimensional es cortada por plane. un plano. customary units (p. 202) Units of measurement unidades inglesas (p. 202) Las unidades de medida commonly used in the United States. usualmente usadas en los Estados Unidos. cylinder (p. 220) A three-dimensional shape base cilindro (p. 220) Una figura tridimensional made up of a curved region and two congruent base que consiste de una región curva y dos bases circular bases that lie in parallel planes. base circulares congruentes que están en planos base paralelos.

Glossary/Glosario 733 English Español ■ D ■

data (p. 82) Factual information used as a basis for datos (p. 82) Información objetiva usada como base reasoning, discussion, or calculation. para razonar, discusión o calcular. deductive reasoning (p. 134) A process of reasoning in razonamiento deductivo (p. 134) Un proceso de which the truth of the conclusion necessarily follows from razonar en donde la verdad de la conclusión the truth of the premises. necesariamente sigue la verdad de las premisas. dependent events (p. 397) Events whose outcomes sucesos dependientes (p. 397) Sucesos cuyos affect one another. resultados se afectan uno a otro. dependent system (p. 259) Two lines whose graphs sistema dependiente (p. 259) Dos líneas cuyas coincide and thus have an infinite set of solutions. gráficas coinciden y tienen un conjunto infinito de soluciones. dependent variables (p. 57) The elements of the range; variables dependientes (p. 57) Los elementos del also called the output values of a function. alcance; también llamados los valores de salida de una función. determinant (p. 274) The difference of the products of determinante (p. 274) La diferencia entre los productos the diagonal entries of a 2 x 2 square matrix. de los datos diagonales de una matriz 2 x 2.

Q diagonal (p. 178) A segment that joins P two nonconsecutive vertices of a polygon. diagonal (p. 178) Un segmento que une SR dos vértices no consecutivos de un SQ is a diagonal. polígono. SQ es una diagonal.

dilation (p. 348) A transformation that produces an dilatación (p. 348) Una transformación que produce image that is the same shape as the original figure but a una imagen que tiene la misma forma que la figura different size. original pero un tamaño diferente. directrix (p. 566) A line whose distance from a point on directriz (p. 566) Una línea cuya distancia desde un a parabola is equal to the distance from the same punto en una parábola es igual a la distancia desde el parabolic point to the focus. mismo punto parabólico al foco. direct square variation (p. 581) A function written in variación cuadrada directa (p. 581) Una función escrita the form y kx 2 where k is a nonzero constant. en la forma y kx 2, donde k es una constante no igual a cero. direct variation (p. 580) A function that can be written variación directa (p. 580) Una función que puede in the form y kx, where k is a nonzero constant. In a escribirse en la forma y kx, donde k es una constante direct variation, the value of one variable increases as the no igual a cero. other variable increases. distance (p. 105) The absolute value of the difference distancia (p. 105) El valor absoluto de la diferencia between the coordinates of any two points. entre las coordenadas de dos puntos.

distance formula (p. 544) For any points P1(x1, y1) and fórmula de distancia (p. 544) Para los puntos P1(x1, y1)

P2(x2, y2), the distance between P1 and P2 is given by: y P2(x2, y2), la distancia entre P1 y P2 se da por: 2 2 2 2 P1P2 (x2 x1) ( y2 y1) . P1P2 (x2 x1) (y 2 y 1) . distributive property (p. 34) Each factor outside propiedad distributiva (p. 34) Cada factor fuera del Glossary/Glosario parentheses can be used to multiply each term within paréntesis puede usarse para multiplicar cada término the parentheses. a(b c) ab ac dentro del paréntesis. Por ejemplo, a(b c) ab ac. domain of a relation (p. 56) The set of all possible dominio de una relación (p. 56) El conjunto de todos values of the x-coordinates for a relation. los valores posibles de las coordenadas de x para una relación.

734 Glossary/Glosario English Español ■ E ■ edge (p. 220) The set of linear points at which two faces arista (p. 220) El conjunto de puntos lineales en donde of a polyhedron intersect. dos caras de un poliedro se cruzan. ellipse (p. 574) In a plane, the figure created by a point elipse (p. 574) En un plano, la figura creada por un moving about two fixed points, called foci. The sum of the punto que se mueve alrededor de dos puntos fijos, distance from the foci to any point on the ellipse is a llamado los focos. La suma de la distancia desde los focos constant, F1P F2P 2A. a cualquier punto sobre la elipse es una constante, F1P F2P 2A. empty set (p. 6) A set containing no elements. The conjunto vacío (p. 6) Conjunto que carece de elementos. symbol for the empty set is . This is also called the El símbolo para el conjunto vacío es . También se llama null set. conjunto nulo. equation (p. 7) A mathematical statement that two ecuación (p. 7) Una declaración matemática en que dos numbers or expressions are equal. números o expresiones son iguales.

A equiangular triangle (p. 150) A triangle triángulo equiangular (p. 150) Un with three congruent angles. triángulo con tres ángulos congruentes. equilateral triangle (p. 150) A triangle with B C triángulo equilátero (p. 150) Un triángulo three congruent sides. AB BC AC con tres lados congruentes. AB C equivalent ratios (p. 296) Two ratios that can both be razones equivalentes (p. 296) Dos razones que pueden named by the same fraction. ambas ser nombradas por la misma fracción. expanding binomials (p. 482) The multiplication and expansión del binomio (p. 482) La multiplicación y subsequent simplification of two binomials. simplificación subsiguiente de dos binomios. experiment (p. 384) An activity that is used to produce experimento (p. 384) Una actividad que se usa para data that can be observed and recorded. producir datos que se pueden observar y registrar. experimental probability (p. 384) The probability of an probabilidad experimental (p. 384) La probabilidad de event determined by observation or measurement. un suceso determinado por una observación o medida. exponent (p. 34) A superscripted number showing how exponente (p. 34) Un número superescrito que many times the base is used as a factor. For example, in muestra cuántas veces la base se usa como un factor. Por 24, 4 is the exponent. ejemplo, en 24, 4 es el exponente. exponential form (p. 34) A number written with a base forma exponencial (p. 34) Un número escrito con una and an exponent. For example, the exponential form of base y un exponente. Por ejemplo, la forma exponencial (2)(2)(2)(2) is 24. de (2)(2)(2)(2) es 24. exponential function (p. 594) A function that can be función exponencial (p. 594) Función que puede described by an equation of the form y ax, where a 0 describirse mediante una ecuación de la forma y ax, Glossary/Glosario and a 1. donde a 0y a 1. exterior angle of a polygon (p. 179) An ángulo exterior de un polígono (p. 179) angle both adjacent to and supplementary Un ángulo adyacente y suplementario al 1 to an interior angle of a polygon. ángulo interno de un polígono. 1 is an exterior angle. 1 es un ángulo externo. exterior angles (p. 120) The angles formed by a ángulos exteriores (p. 120) Los ángulos formados por transversal that are not between two coplanar lines. una transversal que no están entre dos líneas coplanares. extremes (p. 296) The first and last terms of a extremos (p. 296) Los primeros y últimos términos de proportion. (p. 407) In statistics, the data gathered that una proporción. (p. 407) En estadísticas, los datos varies most from the median. reunidos que más varian de la mediana.

Glossary/Glosario 735 English Español ■ F ■

face (p. 220) The surface of a polyhedron. cara (p. 220) La superficie de un poliedro. factorial (p. 403) The product of all whole numbers factorial (p. 403) El producto de todos los números from n to 1. Written as n!. enteros desde n a 1. Escrito como n!. factors (p. 473) Elements whose product is a given factores (p. 473) Elementos cuyo producto es una quantity. cantidad determinada. finite set (p. 6) A set whose elements can be counted conjunto finito (p. 6) Un conjunto cuyos elementos or listed. pueden contarse o enumerarse. foci (p. 574) In an ellipse, the two fixed points whose focos (p. 574) En una elipse, los dos puntos fijos cuyas combined distances to any point on the ellipse is distancias combinadas a cualquier punto sobre la elipse constant. es constante. focus (p. 566) The fixed point whose distance from a foco (p. 566) Los puntos fijos cuya distancia desde un point on a parabola is equal to the distance from the punto en una parábola es igual a la distancia desde el same parabolic point to the directrix. mismo punto parabólico a la directriz. frequency distribution (p. 414) A visual display that distribución de frecuencia (p. 414) Una muestra visual shows the relative frequency of data. que demuestra la frecuencia relativa de datos. frequency table (p. 82) A method of recording data that tabla de frecuencia (p. 82) Un método de registrar shows how often an item appears in a set of data. datos que muestra la frecuencia con que un artículo aparece en un conjunto de datos. function (p. 56) A set of ordered pairs in which each función (p. 56) Un conjunto de pares ordenados en element of the domain is paired with exactly one element donde cada elemento del dominio se aparea con in the range. exactamente un elemento del alcance. function notation (p. 57) The notation that represents notación de función (p. 57) La notación que representa the rule associating the input value (independent la regla que asocia el valor de entrada (variable variable) with the output value (dependent variable). The independiente) con el valor de salida (variable most commonly used function notation is the “f of x” dependiente). La notación más comúnmente usada es la notation, written f (x). notación “f de x”, escrita f (x). fundamental counting principle (p. 402) The principle principio fundamental de conteo (p. 402) El principio that states: If there are two or more stages of an activity, que afirma: Si hay dos o más etapas de una actividad, el the total number of possible outcomes is the product of número total de resultados posibles es el producto del the number of possible outcomes for each stage of the número de resultados posibles para cada etapa de la activity. actividad. ■ G ■

gaps (p. 87) Large spaces between values on a stem- separacione (p. 87) Espacios grandes entre los valores and-leaf plot. en un diagrama de tallo y hoja. general quadratic function (p. 524) A quadratic función cuadrática general (p. 524) Una función function written in the form f (x) ax 2 bx c, where a, cuadrática escrita en la forma f (x) ax 2 bx c, donde b, and c are real numbers, and a 0. a, b, y c son números reales, y a 0. greatest common factor (GCF) (p. 479) The greatest máximo factor común (MFC) (p. 479) El entero más integer that is a factor of two or more integers. The GCF grande que es un factor de dos o más enteros. El MFC de

Glossary/Glosario of two or more monomials is the greatest common dos o más monomios es el factor numérico común más numerical factor and the least power of the common grande y la potencia menor de los factores variables variable factors. comunes. greatest possible error (GPE) (p. 202) Half of the máximo error posible (p. 202) La mitad de la unidad smallest unit used to make a measurement. más pequeña usada para hacer una medida.

736 Glossary/Glosario English Español ■ H ■ half-plane (p. 77) The graphed region showing all semiplano (p. 77) La región que muestra todas las solutions to a linear inequality. soluciones de una desigualdad lineal. histogram (p. 87) A type of bar graph used to visually histograma (p. 87) Un tipo del diagrama de barra usado display frequencies. para visualmente mostrar las frecuencias. hyperbola (p. 572) A curve formed by the intersection hipérbola (p. 572) Una curva formada por la of a double-right circular cone with a plane that cuts both intersección de un cono recto doble con un plano que halves of the cone. corta ambas mitades del cono. C hypotenuse hypotenuse leg hipotenusa (p. 175) The side opposite hipotenusa (p. 175) El lado opuesto al the right angle in a right triangle. cateto ángulo recto en un triángulo rectángulo. B A leg cateto

■ I ■ identity property of addition (p. 21) The sum of any propiedad aditiva de la identidad (p. 21) La suma de number and zero is that number. For example, cualquier número y cero es ese número. Por ejemplo, a 0 0 a a. a 0 0 a a. identity property of multiplication (p. 27) The product propiedad multiplicativa de identidad (p. 27) El of any number and 1 is that number. For example, producto de un número y 1 es ese número. Por ejemplo, a 1 1 a a. a 1 1 a a. image (p. 338) The new figure resulting from a imagen (p. 338) La nueva imagen que resulta de una translation. traslación. included angle (p. 155) In a triangle, the term used to ángulo incluido (p. 155) En un triángulo, el término describe an angle’s relative position to the two sides that usado para describir la posición relativa de un ángulo a form it. los dos lados que lo forman. included side (p. 155) In a triangle, the term used to lado incluido (p. 155) En un triángulo, el término usado describe a side’s relative position to the two angles para describir la posición relativa de un lado a los dos common to it. ángulos comunes a él. inconsistent system (p. 258) Two lines that are parallel sistema inconsistente (p. 258) Dos líneas que son and thus have no solutions. paralelas y no tienen soluciones. independent events (p. 396) Events whose outcomes sucesos independientes (p. 396) Sucesos cuyos are not affected by one another. resultados no se afectan el uno al otro. Glossary/Glosario independent system (p. 258) Two linear equations that sistemas independientes (p. 258) Dos ecuaciones intersect at only one point. lineales que se intersecan en un solo punto. independent variables (p. 57) The elements of the variables independientes (p. 57) Los elementos del domain; also called the input values of a function. dominio; también se llaman los valores de entrada de la función. indirect measurement (p. 326) The calculation of such medida indirecta (p. 326) El cálculo de una medida que a measurement that is difficult to measure directly. Using es difícil de medir directamente. El usar triángulos similar triangles is one method of indirect measurement. similares es un método de medida indirecta. indirect proof (p. 170) A proof in which one begins with prueba indirecta (p. 170) Una demostración en que se the desired conclusion and assumes that it is not true. comienza con la conclusión deseada y se presume que no One then reasons logically until reaching a contradiction es cierta. Entonces se razona lógicamente hasta alcanzar of the hypothesis or of a known fact. una contradicción de la hipótesis.

Glossary/Glosario 737 English Español

inductive reasoning (p. 124) Logical reasoning where razonamiento inductivo (p. 124) Razonamiento lógico the premises of an argument provide some, but not donde las premisas de un argumento proveen algunos absolute, support for the conclusion. apoyos para la conclusión. inequality (p. 11) A mathematical sentence that desigualdad (p. 11) Una frase matemática que contiene contains one of the symbols , , , or . uno de los símbolos , , , o . infinite set (p. 6) A set whose elements cannot be conjunto infinito (p. 6) Un conjunto cuyos elementos counted or listed. no pueden contarse o enumerarse. initial side (p. 624) In the x and y coordinate plane, the lado inicial (p. 624) En el plano coordenado de x e y, side of an angle from which degree measurement begins. el lado de un ángulo desde donde comienza la medida en grados.

inscribed polygon (p. 455) A polygon with all polígonos inscritos (p. 455) Polígonos cuyos vertices lying on the same circle. vértices están en un mismo círculo.

integers (p. 10) The set of whole numbers and their enteros (p. 10) El conjunto de números enteros y sus opposites. opuestos. interior angles (p. 120) The angles between coplanar ángulos interiores (p. 120) Los ángulos entre líneas lines that have been intersected by a transversal. coplanares que han sido intersecadas por una transversal. interior angles of a polygon (p. 178) The angles ángulos interiores de un polígono (p. 178) Los ángulos determined by the sides of a polygon. determinados por los lados de un polígono. interquartile range (p. 408) The difference between the amplitud intercuartílica (p. 408) La diferencia entre los values of the lower and upper quartiles. valores de los cuartiles superior e inferior. intersection of geometric figures (p. 104) The set of intersección de figuras geométricas (p. 104) El points common to two or more figures. conjunto de puntos comunes a dos o más figuras. inverse operation (p. 66) An operation that undoes operación inversa (p. 66) Operación que anula lo que what the previous operation did; used when simplifying ha hecho una operación anterior; se usa para reducir y/o and/or solving a math sentence. For example, addition resolver enunciados matemáticos. Por ejemplo, la adición and subtraction are inverse operations. y la sustracción son operaciones inversas. inverse square variation (p. 585) A function that can be variación cuadrada inversa (p. 585) Una función que written in the form y k or x 2y k, where k is a puede escribirse en la forma y k ó x 2y k, donde k es x 2 x 2 nonzero constant and x 0. una constante no igual a cero y x 0. inverse variation (p. 584) A function that can be variación inversa (p. 584) Una función que puede written in the form y k, where k is a nonzero constant escribirse en la forma y k, donde k es una constante no x x and x 0. igual a cero y x 0. irrational numbers (p. 10) A number that cannot be números irracionales (p. 10) Número que no puede written as a fraction, a terminating decimal, or a escribirse como una fracción, un decimal terminal o un repeating decimal. Examples are and 2. decimal periódico. Por ejemplo, y 2. isosceles triangle (p. 150) A triangle with at least two triángulo isósceles (p. 150) Un triángulo con por lo congruent sides. menos dos lados congruentes. iteration (p. 53) A process that is continually repeated. iteración (p. 53) Proceso que se repite continuamente. For example, the iterative process of multiplying by 2 is Por ejemplo, el proceso iterativo de multiplicar por 2 se

Glossary/Glosario used to create the numerical sequence 1, 2, 4, 8, . . .. usa para crear la sucesión numérica 1, 2, 4, 8, . . ..

738 Glossary/Glosario English Español ■ J ■ joint variation (p. 587) A variation in which a quantity variación conjunta (p. 587) Una variación en donde varies directly as the product of two or more other una cantidad varía directamente como el producto de dos quantities. o más otras cantidades.

■ L ■ lateral edges (p. 220) The set of linear points at which aristas laterales (p. 220) El conjunto de puntos lineales lateral faces meet. See prism. en donde se encuentran las aristas laterales. Ver prisma. lateral faces (p. 220) The faces of prisms and pyramids caras laterales (p. 220) Las caras de los prismas y las that are not bases. See prism and pyramid. pirámides que no son las bases. Ver prisma y pirámide. line (p. 104) A set of points that extends infinitely in línea (p. 104) Un conjunto de puntos que se extiende opposite directions. infinitamente en direcciones opuestas.

y linear function (p. 62) A function that funciones lineales (p. 62) Una función can be represented by a linear equation. que puede ser representada por una When graphed, a linear function yields a y 2x 1 ecuación lineal. Su gráfica es un línea straight line. O x recta.

linear programming (p. 282) A method used to solve programación lineal (p. 282) Un método que se usa business-related problems involving linear inequalities. para resolver problemas relacionados con los negocios Also used to find the maximum or minimum of an que contienen desigualdades lineales. También se usa expression involving a solution to the system of para encontrar el máximo o el mínimo de una expresión inequalities. que contiene una solución al sistema de desigualdades. line of best fit (p. 406) The line that can be drawn recta de óptimo ajuste (p. 406) La recta que se puede near most of the points on a scatter plot that shows a trazar cerca de la mayoría de los puntos en un diagrama de relationship between two sets of data. This is also called dispersión y que muestra una relación entre dos conjuntos a trend line. de datos. También se conoce como la recta de tendencia. line of reflection (p. 338) The line over which a figure is línea de reflejo (p. 338) La línea sobre la cual una reflected or flipped. figura se refleja.

B line of symmetry (p. 338) A line on A A línea de simetría (p. 338) Una línea Glossary/Glosario which a figure can be folded, so that sobre la cual una figura puede doblarse, when one part is reflected over that line it C C de tal manera que al reflejar una parte D B matches the other part exactly. sobre esta línea coincide exactamente AC is a line of symmetry. AC es un línea de simetría. con la otra parte. line segment (p. 105) A part of a line containing two segmento de línea (p. 105) Parte de una línea que endpoints and all points in between. contiene dos puntos extremos y todos los puntos entre ellos. lower quartile (p. 407) In statistics, the median of the cuartil inferior (p. 407) En estadísticas, la mediana de la lower half of the data gathered. mitad inferior de los datos reunidos. logarithm (p. 600) In the function x b y,yis called the logaritmo (p. 600) En la función x b y,yes el logarithm, base b, of x. logaritmo en base b, de x.

Glossary/Glosario 739 English Español

logarithmic equation (p. 601) An equation that ecuación logarítmica (p. 601) Ecuación que contiene contains one or more logarithms. uno más logaritmos.

■ M ■

R P

major arc (p. 440) An arc that is larger than A arco mayor (p. 440) Un arco que es más a semicircle. grande que un semicírculo. G

mPRG 180° matrix (p. 275) (plural: matrices) A rectangular array of matriz (p. 275) Arreglo rectangular de números numbers arranged into rows and columns. Usually, acomodados en hileras y columnas. Los números en una square brackets enclose the numbers in a matrix. matriz por lo general se encierran en corchetes. mean (p. 83) The sum of the data divided by the media (p. 83) La suma de los datos dividido entre el number of data. Also known as the arithmetic average. número de datos. También se conoce como el promedio aritmético. measures of central tendency (p. 83) Statistics or medidas de tendencia central (p. 83) Medidas usadas measurements used to describe a set of data. Examples of para describir un conjunto de datos. Ejemplos son la these are the mean, the median, and the mode. media, la mediana y el modo. median (p. 83) The middle value of the data when the mediana (p. 83) El valor medio de los datos cuando los data are arranged in numerical order. datos se arreglan en orden numérico. median of a trapezoid (p. 188) The segment that joins mediana de un trapezoide (p. 188) El segmento que the midpoints of a trapezoid’s legs. une los puntos medios de los lados del trapezoide. median of a triangle (p. 164) A segment with mediana de un triángulo (p. 164) Un segmento cuyos endpoints that are a vertex of a triangle and the midpoint puntos extremos son un vértice del triángulo y el punto of the opposite side. medio del lado opuesto. metric units (p. 202) Units of measurement that are unidades métricas (p. 202) Unidades de medidas que based on multiples of 10. In the metric system, three basic se basan en los múltiplos de 10. Existen tres unidades units of measurement exist; the meter (to measure básicas: el metro (mide longitud), el gramo (mide masa) y length), the gram (to measure mass), and the liter (to el litro (mide volumen). measure volume). midpoint (p. 114) The point that punto medio (p. 114) El punto que divides a segment into two congruent S M T divide un segmento en dos segments. SM MT segmentos congruentes.

R P minor arc (p. 440) An arc that is smaller arco menor (p. 440) Arco que es más than a semicircle. The degree measure of a A pequeño que un semicírculo. La medida minor arc is the same as the number of angular de un arco menor es igual al degrees in the corresponding central angle. G número de grados en el ángulo central correspondiente. mPG 180°

Glossary/Glosario mode (p. 83) The number that occurs most often in a moda (p. 83) El número que ocurre más set of data. frecuentemente en un conjunto de datos. monomial (p. 468) An expression that is either a single monomio (p. 468) Una expresión que es o un entero, number, a variable, or the product of a number and one una variable, o el producto de un número y una o más or more variables with whole-number exponents. variables con exponentes enteros.

740 Glossary/Glosario English Español multiplication property of equality (p. 67) For all real propiedad multiplicativa de la igualdad (p. 67) Para numbers a, b, and c, if a b, then ac bc. todos los números reales a, b, y c, si a b, entonces ac bc. multiplication property of zero (p. 27) The product of propiedad multiplicativa de cero (p. 27) El producto de any term and 0 is 0. For example, a 0 0 a 0. cualquier término y 0 es 0: a 0 0 a 0. multiplicative inverses (p. 27) Two numbers whose inversos multiplicativos (p. 27) Dos números cuyo product is one; also called a reciprocal. producto es uno; también llamado recíproco. multiplicative property of inequality (p. 76) For all real propiedad multiplicativa de la desigualdad (p. 76) Para numbers a, b, and c, if a b and c 0, then ac bc; if todos los números reales a, b, y c, si a b y c 0, entonces a b and c 0, then ac bc; if a b and c 0, then ac bc; si a b y c 0, entonces ac bc; si a b y c 0, ac bc; if a b and c 0, then ac bc. entonces ac bc; si a b y c 0, entonces ac bc. mutually exclusive (p. 392) Term used to describe mutuamente exclusivo (p. 392) Término usado para events that cannot occur at the same time. describir sucesos que no pueden ocurrir a la misma vez. ■ N ■ n factorial (p. 403) The number of permutations of n n factorial (p. 403) El número de permutaciones de n different items; n factorial is written n!. artículos diferentes; n factorial se escribe n!. negative correlation (p. 406) The inverse relationship correlación negativa (p. 406) La relación inversa entre between two sets of data. On a scatter plot, a negative dos conjuntos de datos. En un diagrama de dispersión, una correlation is evident if the trend line slopes downward correlación negativa es evidente si la recta de tendencia se from the top left to the bottom right corner of the graph. inclina hacia abajo desde la esquina superior izquierda hasta la esquina inferior derecha de la gráfica. negative reciprocals (p. 248) Two fractions or ratios recíprocos negativos (p. 248) Dos fracciones o razones whose product is 1. cuyo producto es 1. noncollinear points (p. 104) Points that do not lie on puntos no colineales (p. 104) Puntos que no están en la the same line. misma línea. noncoplanar points (p. 104) Points that do not lie on puntos no coplanares (p. 104) Puntos que no están en the same plane. el mismo plano. normal curve (p. 415) The symmetrical bell-shaped curva normal (p. 415) La curva simétrica acampanada curve resulting from a normal distribution of data. In a que resulta de una distribución normal de datos. En una normal curve, the mean, median, and mode are the same. curva normal, la media, mediana y la moda son iguales. null set (p. 6) A set containing no elements. The symbol conjunto nulo (p. 6) Un conjunto que no contiene for the null set is . elementos. El símbolo para el conjunto nulo es .

■ ■

O Glossary/Glosario obtuse angle (p. 109) An angle whose ángulo obtuso (p. 109) Un ángulo cuya measure is greater than 90° but less than 180°. A medida es mayor de 90° pero menor de 180°. 90° mA 180° open half-plane (p. 77) The region on either side semiplano abierto (p. 77) La región en cualquier lado of a line on a coordinate plane. de una línea en el plano coordenado. opposite angles (p. 182) Two angles in a quadrilateral ángulos opuestos (p. 182) Dos ángulos en un that do not share a common side. cuadrilátero que no comparten un lado común. opposite of the opposite property (p. 12) The propiedad del opuesto de la opuesto (p. 12) Lo opposite of the opposite of any real number is the opuesto de lo opuesto de cualquier número real es el number. For example, (n) n. número. Por ejemplo, (n) n.

Glossary/Glosario 741 English Español

opposite sides (p. 182) Two sides of a quadrilateral that lado opuesto (p. 182) Dos lados de un cuadrilátero que do not share a common vertex. no comparten un vértice común. ordered pair (p. 56) Two numbers named in a specific par ordenado (p. 56) Dos números nombrados en un order. orden específico. origin (p. 56) The point where the x-axis and y-axis origen (p. 56) El punto donde el eje de x y el eje de y se intersect in the coordinate plane. intersecan en el plano coordenado. outcome (p. 384) The result of each trial of an resultado (p. 384) El resultado de cada ensayo de un experiment. experimento. outliers (p. 87) Data values that are much greater or datos extremos (p. 87) Valores de datos que son mucho much less than most of the other values on a stem-and- mayores o menores que la mayoría de los otros valores en leaf plot. un digrama de tallo y hoja.

■ P ■

parabola (p. 520) The locus of points whose distance parábola (p. 520) Los lugares geométricos de puntos from the focus is equal to the distance from a fixed line cuya distancia desde el foco es igual a la distancia desde (the directrix). una línea fija (la directriz). A

B parallel lines (p. 119) Coplanar lines C líneas paralelas (p. 119) Líneas that do not intersect. coplanares que no se cruzan. D AB CD AB

parallelogram (p. 182) A quadrilateral paralelogramo (p. 182) Un cuadrilátero whose two pairs of opposite sides are con dos pares de lados opuestos paralelos. DC parallel. AB DC ; AD BC

perfect square trinomial (p. 492) A trinomial that trinomio cuadrado perfecto (p. 492) Un trinomio que results from squaring a binomial. resulta al elevar un binomio al cuadrado. perimeter (p. 206) The distance around a polygon. perímetro (p. 206) La distancia alrededor de un polígono. period (p. 628) The length of one complete cycle of a período (p. 628) La longitud de un ciclo completo de periodic function. una función periódica. periodic function (p. 628) A function that, when función periódica (p. 628) Una función cuya gráfica graphed, forms repeating patterns. forma patrones que se repiten. permutation (p. 403) An arrangement of items in a permutación (p. 403) Un arreglo de artículos en un particular order. orden particular. m

perpendicular lines (p. 119) Two lines that n líneas perpendiculares (p. 119) Dos líneas intersect to form adjacent right angles. que se intersecan para formar ángulos rectos adyacentes. Glossary/Glosario line m line n recta m recta n plane (p. 104) An infinite set of points extending in all plano (p. 104) Un conjunto infinito de puntos que se directions along a flat surface. extienden en cuatro direcciones a lo largo de una superficie plana.

742 Glossary/Glosario English Español

Platonic solids (p. 221) The five polyhedrons studied by sólidos platónicos (p. 221) Los cinco poliedros the Greek scholar, Plato. Each of the polyhedrons has estudiados por el griego Platón, y cuyas caras son faces that are congruent regular polygons. polígonos regulares congruentes. point (p. 104) A specific location in space having no punto (p. 104) Ubicación específica en el espacio que dimensions, represented by a dot, and named with a carece de dimensiones; se representa con una marca letter. puntual y se denomina con una letra. polygon (p. 178) A closed plane figure formed by polígono (p. 178) Una figura cerrada plana formada al joining three or more line segments at their endpoints. unir tres o mas segmentos en sus puntos extremos. Cada Each segment or side of the polygon intersects exactly segmento o lado del polígono interseca exactamente dos two other segments, one at each endpoint. otros segmentos, uno en cada extremo. polyhedron (p. 220) (plural: polyhedra) A closed three- poliedro (p. 220) Cuerpo tridimensional cerrado dimensional figure made of only polygons. compuesto solo de polígonos. polynomial (p. 468) An algebraic expression that is the polinomio (p. 468) Expresión algebraica que es la suma sum of monomials. A polynomial is in standard form de monomios. Un polinomio está en forma estándar when its terms are ordered from the greatest to the least cuando sus términos están ordenados según las powers of one of the variables. potencias, de mayor a menor, de una de las variables. population (p. 82) The total number of people población (p. 82) El número total de habitantes de una occupying a region or making up a whole. región que constituyen su totalidad. positive correlation (p. 406) The direct relationship correlación positiva (p. 406) La relación directa entre between two sets of data. On a scatter plot, a positive dos conjuntos de datos. En un diagrama de dispersión, correlation is evident if the trend line slopes upward una correlación positiva es evidente si la recta de from the bottom left to the top right of the graph. tendencia se inclina hacia arriba desde la parte inferior izquierda hasta la parte superior derecha de la gráfica. postulate (p. 105) A statement accepted as truth postulado (p. 105) Una declaración aceptada como without proof. verdadera sin prueba. precision (p. 202) The exactness to which a precisión (p. 202) El grado de exactitud al que se toma measurement is made. Precision is relative to the unit of una medida. La precisión es relativa a la unidad de measurement used; the smaller the unit of measure, the medida que se use; entre más pequeña es la unidad de more precise the measurement. medida, más precisa será la medida. preimage (p. 338) The original figure of a translation. pre-imagen (p. 338) La figura original de una traslación.

base base prism (p. 220) A polyhedron that has prisma (p. 220) Un poliedro que tiene two identical parallel bases and whose dos bases paralelas idénticas y cuyas Glossary/Glosario lateral face other faces are all parallelograms. lateral edge otras caras son paralelogramos. cara lateral arista lateral

triangular prism prisma triangular probability (p. 212) The chance or likelihood that an probabilidad (p. 212) La posibilidad de que un suceso event will occur. The probability of an event can be ocurra. número de resultados favorables expressed as a ratio: P(cualquier suceso) . number of favorable outcomes número de resultados posibles P(any event) . number of possible outcomes Un suceso imposible tiene una probabilidad de cero. Un An impossible event has a probability of zero. A certain suceso seguro tiene una probabilidad de uno. event has a probability of one.

Glossary/Glosario 743 English Español

proportion (p. 296) An equation stating that two ratios proporción (p. 296) Una ecuación que afirma que dos are equivalent. razones son equivalentes.

vertex vértice lateral pyramid (p. 220) A polyhedron with only face pirámide (p. 220) Un poliedro con una one base. The other faces are triangles that cara base y caras triangulares que se lateral meet at a vertex. base encuentran en un vértice. base rectangular pyramid pirámide rectangular

Pythagorean Theorem (p. 430) In any right triangle, the teorema pitagórico (p. 430) En cualquier triángulo square of the length of the hypotenuse c is equal to the rectángulo, el cuadrado de la longitud de la hipotenusa c sum of the squares of the lengths of the legs a and b. The es igual a la suma de los cuadrados de las longitudes de Pythagorean Theorem is expressed as c 2 a 2 b 2. los catetos a y b. El teorema pitagórico se expresa como c 2 a 2 b 2. Pythagorean triples (p. 433) Any three positive triples pitagóricos (p. 433) Enteros positivos a, b y c, integers, a, b, and c, for which a 2 b 2 c 2. para el cual a 2 b 2 c 2.

■ Q ■

quadrant (p. 56) One of the four regions formed by the cuadrante (p. 56) Una de las cuatro regiones formadas axes of the coordinate plane. por los ejes del plano coordenado. quadratic equation (p. 493) An equation of the form ecuación quadrática (p. 493) Una ecuación de la forma Ax2 Bx C 0, where A, B, and C are real numbers and Ax2 Bx C 0, donde A, B y C son números reales y A A is not zero. no es cero. quadratic term (p. 498) In a quadratic expression, the término cuadrático (p. 498) En una expresión term that contains the squared variable. cuadrática, el término que contiene la variable cuadrada. quartiles (p. 407) The three values which divide an cuartiles (p. 407) Los tres valores que dividen un ordered set of data into four equal parts. The lower conjunto ordenado de datos en cuatro partes iguales. El quartile is the median of the lower half of the data. The cuartil inferior es la mediana de la mitad inferior de los upper quartile is the median of the upper half. The middle datos. El cuartil superiores la mediana de la mitad quartile is the median of the entire set of data. superior. El cuartil central es la mediana del conjunto de datos completo.

■ R ■

random sampling (p. 82) Statistical sampling in which muestra aleatoria (p. 82) Una muestra estadística en each member of the population has an equal chance of que cada miembro de la población tiene una oportunidad being selected. igual de ser seleccionado. range (p. 49) The difference between the greatest and alcance (p. 49) La diferencia entre los valores mayores y

Glossary/Glosario least values in a set of data. menores en un conjunto de datos. range of relation (p. 56) The set of all possible alcance de una relación (p. 56) El conjunto de todas las y-coordinates for a relation. posibles coordenadas de y para una relación. rate (p. 204) A ratio that compares two different kinds tasa (p. 204) Una razón que compara dos tipos of quantities. diferentes de cantidades.

744 Glossary/Glosario English Español ratio (p. 202) A comparison of two numbers, a and b, razón (p. 202) Una comparación de dos números, a y b. a a represented in one of the following ways: a:b, , or a to b. Se representan en una de las maneras siguientes: a:b, o b b a al b. rationalizing the denominator (p. 428) The process of racionalizar el denominador (p. 428) El proceso de rewriting a quotient to delete radicals from the escribir un cociente eliminando los radicales del denominator. denominador. rational number (p. 10) A number that can be número racional (p. 10) Un número que puede a a expressed in the form , where a and b are any integers expresarse en la forma , donde a y b son enteros y b 0. b b and b 0. ray (p. 105) Part of a line that starts at one D rayo (p. 105) Parte de una línea que F endpoint and extends without end in one comienza en un punto y se extiende sin fin direction. en una dirección. real numbers (p. 10) The set of rational and irrational números reales (p. 10) El conjunto de números numbers together. racionales e irracionales. reciprocals (p. 27) Two numbers that have a product recíprocos (p. 27) Dos números cuyo producto es uno. of one. rectangle (p. 183) A parallelogram that has rectángulo (p. 183) Un paralelogramo que four right angles. tiene cuatro ángulos rectos. reduction (p. 348) A dilated image that is smaller than reducción (p. 348) Una imagen dilatada que es más the original figure. pequeña que la figura original. reference angle (p. 624) In the coordinate plane, the ángulo de referencia (p. 624) En el plano coordenado, acute angle formed by the x-axis and the terminal side. el ángulo agudo formado por el eje de x y el lado terminal. reflection (p. 338) A transformation in which a figure is reflexión (p. 338) Una transformación en que una reflected, or flipped, over a line of reflection. figura se voltea sobre una línea de reflejo. reflexive property (p. 34) Any number is equal to itself. propiedad reflexiva (p. 34) Para todos los números For example, a a. reales a, a a. regular polygon (p. 179) A polygon that is both polígono regular (p. 179) Un polígono que es equilateral and equiangular. equilateral y equiangular. rhombus (p. 183) A parallelogram that has rombo (p. 183) Un paralelogramo que tiene four congruent sides. cuatro lados congruentes. Glossary/Glosario right triangle (p. 150) A triangle that has one right triángulo rectángulo (p. 150) Un triángulo que tiene un angle. ángulo recto. rotation (p. 342) A transformation in which a figure is rotación (p. 342) Una transformación en que se gira rotated, or turned, about a point. una figura alrededor de un punto. row-by-column multiplication (p. 362) A method by multiplicación por fila y columna (p. 362) Un método which two matrices are multiplied together. Using this en donde dos matrices se multiplican. Usando este method, matrices can be multiplied together only when método, las matrices se pueden multiplicar únicamente the number of columns in the first matrix is equal to the cuando el número de columnas en la primera matriz es number of rows in the second matrix. igual al número de filas en la segunda matriz.

Glossary/Glosario 745 English Español ■ S ■

sample (p. 82) A representative portion of a population, muestra (p. 82) Una porción representativa de una often used for statistical study. población, frequentemente usada para el estudio estadístico. sample space (p. 385) The set of all possible outcomes espacio muestral (p. 385) El conjunto de todos los of an event. resultados posibles de un suceso. scalar (p. 359) The constant by which a matrix is escalar (p. 359) La constante por la cual una matriz se multiplied. multiplica. scale factor (p. 348) The number that is multiplied by factor de escala (p. 348) El número que es multiplicado the length of each side of a figure to create an altered por la longitud de cada lado de una figura para crear una image in a dilation. imagen alterada en una dilatación.

scalene triangle (p. 150) A triangle with no triángulo escaleno (p. 150) Un triángulo sin congruent sides and no congruent angles. lados congruentes ni ángulos congruentes.

scatter plot (p. 406) A method of visually displaying diagrama de dispersión (p. 406) Método que presenta the relationship between two sets of data. The data are visualmente la relación entre dos conjuntos de datos. Los represented by unconnected points on a grid. datos se representan mediante puntos conectados en una cuadrícula. scientific notation (p. 39) A system for writing a very notación científica (p. 39) Un sistema para escribir large or very small number as the product of a factor números grandes o pequeños como el producto de that is greater than or equal to one and less than un factor mayor o igual a uno y menos de 10 y 10 and a second factor that is a power of 10. For un segundo factor que es una potencia de 10. Por example, 496,000,000 written in scientific notation is ejemplo, 496,000,000 escrito en notación científica 4.96 108. es 4.96 108.

P secant (p. 441) A line that intersects a C secante (p. 441) Una línea que interseca circle in two places. D un círculo en dos lugares. CD is a secant of P. CD es una secante de P.

secant segment (p. 448) A segment intersecting a circle segmento secante (p. 448) Segmento que interseca un in two points, having one endpoint on the circle and one círculo de dos puntos y que tiene un extremo en el círculo endpoint outside the circle. y el otro fuera del círculo. sequence (p. 52) An arrangement of numbers according sucesión (p. 52) Un arreglo de números según un to a pattern. patrón. set (p. 6) A well-defined collection of items. Each item conjunto (p. 6) Una colección bien definida de artículos is called an element, or member, of the set. que se le llama un elemento, o miembro.

T X similar figures (p. 300) Figures figuras semejantes (p. 300) Glossary/Glosario that have the same shape but R Figuras que tienen la misma S not necessarily the same size. forma pero no el mismo tamaño. V W

T X, S W, R V; RT ST RS VX WX VW

746 Glossary/Glosario English Español simulation (p. 388) A model used to estimate the simulación (p. 388) Un modelo usado para estimar la probability of an event. probabilidad de un suceso. sine (p. 614) In a right triangle, the sine of acute A is seno (p. 614) En un triángulo rectángulo, el seno del length of side opposite A longitud del lado opuesto al A equal to: . ángulo agudo A es igual a: . length of hypotenuse longitud de la hipotesusa skew lines (p. 119) Noncoplanar lines that do not líneas alabeadas (p. 119) Líneas no coplanares que no intersect and are not parallel. se intersecan ni son paralelas. slope (p. 244) The ratio of the vertical change of a line pendiente (p. 244) La razón del cambio vertical de una (rise) to its horizontal change (run). línea (subida) a su cambio horizontal (recorrido). slope-intercept form (p. 245) A linear equation in the forma de pendiente e intersección (p. 245) Una form y mx b, where m represents the slope, and b ecuación lineal en la forma y mx b, donde m represents the y-intercept. representa la pendiente y b representa el intercepto de y. solution (p. 7) A replacement set for a variable that solución (p. 7) Un conjunto de reemplazo para una makes a mathematical sentence true. variable que hace que una frase matemática sea cierta.

sphere (p. 221) A three-dimensional C esfera (p. 221) Una figura figure consisting of the set of all points tridimensional que consiste del conjunto that are a given distance from a given de todos los puntos equidistantes de un point, called the center of the sphere. C is the center of the sphere. punto fijo, llamado el centro de la esfera. C es el centro de la esfera. spreadsheet (p. 30) A computer application that hoja de cálculos (p. 30) Una aplicación de simplifies preparation of tables. computadora que simplifica la preparación de tablas. square (p. 183) A parallelogram that has four right cuadrado (p. 183) Un paralelogramo que tiene cuatro angles and four congruent sides. ángulos rectos y cuatro lados congruentes. square root (p. 426) One of two equal factors of a raíz cuadrada (p. 426) Uno de dos factores iguales de number. A number a is a square root of another number b un número. Un número a es una raíz cuadrada de otro if a 2 b. número b si a 2 b. standard deviation (p. 417) The square root of the desviación estándar (p. 417) La raíz cuadrado de la variance of a set of numbers. varianza de un conjunto de números. standard equation of a circle (p. 562) The equation of ecuación estándar de un círculo (p. 562) La ecuación a circle with its center at any coordinate point (h, k) is de un círculo con su centro en cualquier punto (x h)2 (y k)2 r 2, where r is the circle’s radius. If coordenado (h, k) es (x h)2 (y k)2 r 2, donde r es the circle’s center is at the origin, the standard equation el radio del círculo. Si el centro del círculo está en el reduces to x 2 y 2 r 2. origen, la ecuación estándar se reduce a x 2 y 2 r 2. standard equation of an ellipse (p. 574) The equation ecuación estándar de un elipse (p. 574) La ecuación de Glossary/Glosario 2 y 2 2 2 of an ellipse with its center at the origin is: x 1. un elipse con su centro en el origen es: x y 1. a 2 b 2 a 2 b 2 standard equation of a hyperbola (p. 576) The ecuación estándar de una hipérbola (p. 576) La equation of a hyperbola with its center at the origin is: ecuación de una hipérbola con su centro en el origen es: 2 y 2 2 y 2 x 1. x 1. a 2 b 2 a2 b 2 standard quadratic equation (p. 524) A quadratic ecuación cuadrática estándar (p. 524) Una ecuación equation written in the form y ax 2 bx c, where a, b, cuadrática en la forma y ax 2 bx c; a, b, y c son and c are real numbers and a 0. números reales y a 0. statistics (p. 82) A branch of mathematics that involves estadisticas (p. 82) Una rama de las matemáticas que the study of data, specifically the methods used to collect, comprende el estudio de datos, específicamente los organize, and interpret data. métodos usados para coleccionar, organizar e interpretar datos.

Glossary/Glosario 747 English Español

stem-and-leaf plot (p. 86) A method of displaying data diagrama de tallo y hoja (p. 86) Un método para in which certain digits are used as stems and the mostrar datos en que ciertos dígitos se usan como los remaining digits are used as leaves. tallos y los dígitos restantes se usan como las hojas. subset (p. 6) If every element of set A is also an element subconjunto (p. 6) Si cada elemento de un conjunto A of set B, then A is called a subset of B. es también un elemento del conjunto B, entonces A se llama un subconjunto de B. substitution property (p. 34) If expressions are propiedad de sustitución (p. 34) Si son equivalentes, equivalent, they may be substituted for one another in las expresiones se pueden reemplazar mutuamente en any statement. For example, if a b, then b can be cualquier enunciado. Por ejemplo, si a b, la b puede substituted for a or a can be substituted for b in any reemplazarse por a o la a puede reemplazarse por b en statement. cualquier enunciado.

P R supplementary angles (p. 109) ángulos suplementarios (p. 109) 45 135 Two angles whose measures have a û û Dos ángulos cuyas medidas tienen MTNS sum of 180°. una suma de 180°. mMNP mRST 180°

surface area (p. 224) The sum of the areas of all the área de superficie (p. 224) La suma de las áreas de faces of a three-dimensional figure. todas las caras de una figura tridimensional. symmetric property (p. 34) The expressions on either propiedad de simetría (p. 34) Las expresiones en side of an equals sign are equivalent and can thus be cualquier lado de un signo de igualdad son equivalentes switched without affecting the equation. y se pueden intercambiar sin afectar la ecuación. system of equations (p. 258) Two or more linear sistema de ecuaciones (p. 258) Dos o más ecuaciones equations with the same variables. lineales con las mismas variables. system of linear inequalities (p. 276) Two or more sistema de desigualdades lineales (p. 276) Dos o más linear inequalities that can be solved by graphing. desigualdades lineales que se pueden resolver usando gráficas.

■ T ■

tangent (p. 614) In a right triangle, the tangent of acute tangente (p. 614) En un triángulo rectángulo, la A is equal to: tangente del ángulo agudo A es igual a: length of side opposite A sine A longitud del lado opuesto al A sin A or . ó . length of side adjacent to A cosine A longitud del lado adjacente al A cos A tangent of a circle (p. 441) A line that intersects a circle tangente de un círculo (p. 441) Una línea que interseca in only one point. un círculo en un solo punto. tangent segment (p. 449) A segment with one segmento tangente (p. 449) Un segmento con un endpoint on a circle and one endpoint outside the extremo sobre un círculo y el otro extremo fuera del same circle. mismo círculo. terminal side (p. 624) In the coordinate plane, the side lado terminal (p. 624) En el plano coordenado, el lado of an angle that is not the initial side; the terminal side de un ángulo que no es el lado inicial; el lado terminal is the side to which one measures degrees from the es el lado en el que se miden los grados desde el lado

Glossary/Glosario initial side. inicial. terms (p. 52) The parts of a variable expression that are términos (p. 52) Las partes de una expresión variable separated by addition or subtraction signs. que son separadas por signos de sustracción o adición. theorem (p. 114) A statement whose truth can be teorema (p. 114) Una declaración cuya verdad puede proven. probarse.

748 Glossary/Glosario English Español theoretical probability (p. 385) The probability of an probabilidad teórica (p. 385) La probabilidad de un event, P(E), assigned by determining the number of evento, P(E), asignada al determinar el número de resultados favorable outcomes and the number of possible outcomes favorables y el número de resultados posibles en un number of favorable outcomes número de resultados favorables in the sample space: P(E) . espacio muestral: P(E) . number of possible outcomes número de resultados posibles transformation (p. 338) A way of moving or changing transformación (p. 338) Una manera de mover o the size of a geometric figure in the coordinate plane. cambiar el tamaño de una figura geométrica en el plano coordenado. transitive property of equality (p. 34) If two propiedad transitiva de la igualdad (p. 34) Si dos expressions are equivalent, and a third expression is expresiones son equivalentes y una tercera expresión es equivalent to the second expression, then the third equivalente a la segunda expresión, entonces la tercera expression is also equivalent to the first. For example, expresión también es equivalente a la primera. Por if a b and b c, then a c. ejemplo, si a b y b c, la a c. transitive property of inequality (p. 77) The property propiedad transitiva de la igualdad (p. 77) Para that states: For real numbers a, b, and c, if a b and números reales a, b, y c, si a b y b c, entonces a c. b c, then a c. Similarly, if a b and b c, then a c. De la misma manera, si a b y b c, entonces a c. translation (p. 338) A change in position of a figure traslación (p. 338) Un cambio en la posición de una such that all the points in the figure slide exactly the same figura tal que todos los puntos en la figura se deslizan distance and in the same direction at once. exactamente a la misma distancia y en la misma dirección.

t transversal (p. 120) A line that transversal (p. 120) Una línea que intersects at least two coplanar lines in m interseca por lo menos dos líneas different points, producing interior and coplanares en puntos diferentes exterior angles. produciendo ángulos interiores y Line t is a transversal. exteriores. La recta t es una transversal.

base TRbase trapezoid (p. 188) A quadrilateral leg base angles leg trapezoide (p. 188) Un cuadrilátero that has exactly one pair of parallel cateto ángulos cateto que tiene exactamente un par de sides. de la base lados paralelos. Glossary/Glosario PAbase base tree diagram (p. 385) A diagram that shows all the diagrama de árbol (p. 385) Un diagrama que muestra possible outcomes in a sample space. todos los resultados posibles en un espacio de muestra. trend line (p. 406) A line that can be drawn near most línea de tendencia (p. 406) Una línea que puede of the points on a scatter plot that shows the relationship dibujarse cerca de la mayoría de los puntos en un between two sets of data; also called the line of best fit. diagrama de dispersión que muestra la relación entre dos conjuntos de datos. triangle (p. 150) A polygon formed by three line triángulo (p. 150) Un polígono formado por tres segments joining three noncollinear points. segmentos que unen tres puntos no colineales. trinomial (p. 468) A polynomial with three terms. trinomio (p. 468) Un polinomio con tres términos.

Glossary/Glosario 749 English Español ■ U ■

unit rate (p. 204) A rate that has a denominator of tasa de unidad (p. 204) Un valor que tiene un one unit. denominador de una unidad. unlike terms (p. 468) Terms in which the variables or términos diferentes (p. 468) Términos en que las sets of variables are not identical. variables o los conjuntos de variables no son idénticos. upper quartile (p. 407) In statistics, the median of the cuartil superior (p. 407) En estadísticas, la mediana de upper half of the data. la mitad superior de los datos. ■ V ■

variable (p. 7) A symbol, usually a letter, used to variable (p. 7) Un símbolo, comúnmente una letra, represent a number. usado para representar un número. variance (p. 412) For a set of numbers, the mean of the varianza (p. 412) Para un conjunto de números, la squared differences between each number in the set and media de las diferencias cuadradas entre cada número en the mean of all numbers in the set. el conjunto y la media de todos los números en el conjunto. vertex angle (p. 160) In an isosceles triangle, the angle ángulo de vértice (p. 160) En un triángulo isósceles, el opposite the base and adjacent to the two legs. ángulo opuesto a la base y adyacente a los dos lados. vertex of a polygon (p. 178) The point at which two vértice de un polígono (p. 178) El punto donde dos sides of a polygon meet. lados de un polígono se encuentran. vertex of a polyhedron (p. 220) The point at which vértice de un poliedro (p. 220) El punto donde tres o three or more edges of a polyhedron intersect. más aristas de un poliedro se intersecan.

2 vertical angles (p. 115) The 13 ángulos verticales (p. 115) Los angles that are not adjacent to 4 ángulos que no son adyacentes each other when two lines uno al otro cuando dos líneas se 1 and 3 are vertical angles. intersect. Vertical angles are intersecan. Los ángulos verticales 2 and 4 are vertical angles. congruent. 1 y 3 son ángulos opuestos por el vértice. son congruentes. 2 y 4 son ángulos opuestos por el vértice.

vertical line test (p. 57) A test used to determine prueba de verticalidad de línea (p. 57) Una prueba whether or not a graph is a function. It states: When a que se usa para determinar si una gráfica es una función vertical line is drawn through the graph of a relation, the o no. Cuando una línea vertical se dibuja a través de la graph is not a function if the vertical line intersects the gráfica de una relación, la gráfica no es una función si la graph in more than one point. línea vertical cruza la gráfica en más de un punto. volume (p. 230) A measure of the number of cubic units volumen (p. 230) Una medida del número de unidades needed to fill a region of space. cúbicas necesarias para llenar una región de espacio. ■ X ■

x-coordinate (p. 56) The first number in an ordered coordenada de x (p. 56) El primer número en un par pair. The x-coordinate determines the horizontal location ordenado. La coordenada de x determina la ubicación

Glossary/Glosario of a point in a coordinate plane. Also called the abscissa. horizontal de un punto en un plano coordenado. También se le llama la abscisa. x-intercept (p. 245) The x-intercept of a line is the x- intercepto de x (p. 245) El intercepto de x de una línea coordinate of the point where the line intersects the x-axis. es la coordenada de x del punto donde la línea cruza el eje de x.

750 Glossary/Glosario English Español ■ Y ■ y-coordinate (p. 56) The second number in an ordered coordenada de y (p. 56) El segundo número en un par pair. The y-coordinate determines the vertical location of ordenado. La coordenada de y determina la ubicación a point in a coordinate plane. Also called the ordinate. vertical de un punto en un plano coordenado. También se le llama la ordenada. y-intercept (p. 245) The y-intercept of a line is the intercepto de y (p. 245) El intercepto de y de una línea y-coordinate of the point where the line intersects the es la coordenada de y del punto donde la línea cruza el y-axis. eje de y.

■ Z ■ z-score (p. 413) The number of standard deviations calificación z (p. 413) El número de desviaciones between a score and the mean score. estándares entre una calificación y la calificación media. Glossary/Glosario

Glossary/Glosario 751 Selected Answers 752 Selected Answers 33. 8 27. 8 25. 31. false 23. true 21. 29. false 19. true 17. 1 re1.{ 13. {e}, n true 11. 9. subsets, one3-elementsubset,andtheemptyset. three1-elementsubsets, three2-element eight subsets: 7 0 ,3 ,7 }2.{,5 3.{}3.33.true 35. 3 33. {1} {1,9} {3, 5}31. 25. false, 29. 37. {0, 1,2,3,4,5, 6,9} {0,1,3,5,7, 9} 23. 27. {1,2,4,5,7,8} 21. 7 23.6, 39. 32 37. 3 as 5 re4.tu 9 irrational, real 49. true irrational, real 47. 53. true whole, integer, rational, real 45. 51. false 43. 13. 8 11. 33nickels 9. 6 1. Lesson 1-1,pages6–9 Chapter 1:EssentialMathematics a,rn a,wn 1 {c 11. {ban,can,fan, 9. man, ran, van, wan} {ban,can,fan, man,pan,ran, tan} 7. 5. {1,2,3,4,a,b, c 1. Lesson 1-3,pages16–19 1. Review andPracticeYour Skills,pages14–15 37. Answers willvary. 35. 33. 21. 17. false 13. true 11. 15. 15 9. 7. 5. false 3. false 1. Lesson 1-2,pages10–13 {1,2} 27. or 1 Volga 31. 7 32 27. Selected Answers 1} 1} 1,1}3. , {10},{15},{10,15} 6 02 3.25 9 {x 19. 23. 02 3 2 42 1 ,5 ,9 3. {1, 3,5,7,9} 1345 35. 32 32 32 34567 1 1 9 284million 29. 212 N 3 7 9 21. 1 19. 4 17. Mackenzie or2,194 2 2 2 3 9 true 39. 5 {x 25. is arealnumber andx a}, 41. 6 3 2 37. 29. 1 1 1 .{1,2,3,4,a,b, c 3. } 1 x 0 x 3 1 0 e, n {t,e},ne, 15. 0 0 0 is arealnumber, and 9 6, 39. 3 P 31. } { .1 .N;thereare No; 7. 11 5. 1 0 . 15. 5.5 13 13 13 22 3 { 13. } 1 039. 10 1 3 – .8, 5. 5 }orP { 1345 23. 6 m 4 126 million 2 1 and 1 6 1 2,635. c 2 1 3 5 { 15. } 0 i 1 3 0 43. 3 41. 2 3 5 8 35. 6 33. 0.75 .6, 7. 8 5 false 25. 3 1 orx 3 1 false 41. 1 2 } 1 }, {t,e, n},{t {b, u,g 1 2 – x c, h c, 3 8 43. 9 9 19. 17.{}} 4} 2} } 6 R }, 12 ftandtheareais8 43. 23. 45. 43. 41. 3 0 ,4 ,6 }3.{,8 7 39. 3 37. {1,8} 35. {0,3,4,5,6,7} 33. .{ 1. Review andPracticeYour Skills,pages24–25 1. Lesson 1-4,pages20–23 1. Review andPracticeYour Skills,pages 32–33 Store Sampleanswer: 5. 11. 38 19; 16; 8; 3. 2L Entertheformulas for 14 theperimeter, the value 4for L. 7; 4; 2; 1. Lesson 1-6,pages30–31 47. 1. Lesson 1-5,pages26–29 3 . 5 . 7 473.193.75calories 39. 34.7 37. 8.4 35. 41. 0.1 33. 3 4 ,1,1,2,... 5 { 35. .} . {4,8,12,16,20,. 33. 3 . 5 4 25. 0.4 23. 5 57. 0 55. 15(.2.2.$1.22.$7.22.1,6, 25. $273.42 29. 23. 2,7,12 $317.52 27. 21. (1.5)(8.82). of hoursworked, Ben’s pay isequalto8.82(40) 1 e,rudteaonsadad $5 Yes, roundtheamountsandadd: 11. 13. 3 1 ,5 ,9 5 0 ,7 }6.27.5% 67. {0,1,7,9} 65. {0,2,3,4,5,8} {1,3,5,7,9} 61. 63. {0,2,3,4,5,6,8} 59. .{ 9. 3 8 13. 9 26 21. 22.60 19. eaiennmlil f4 7 0 9 e 1 938.91 41. Yes 39. {0} 43. 37. negative non-multiple of4} 3 o3.fle3.fle3.fle4.true 41. false 39. false 37. false 35. 43. No 33. 17. 13. 49. 2 13. $24 18 3. 21.84 3. 4.93 11 3. 27 c, o, m,p, u,t,e, r p, u,t,e, r 5 04.3 9 851. 38 49. 38 47. 20 45. 3 321.76 t15. 7362ft 13. 1312 49. 21 8 3 1 8 1 2L 54.{c, l,e, a,n,y, r 45. 15 15 02 62 62 25. 02 9 8 5 55 45. 1 .0 3 85.7.4 55. 48 53. 9.605 51. 1345 * 15. 5 5 0.5 andarea,L 43. 15. 24 4 4 ¡ 17. 4¡F 15105 }3.{ . 15. 3.9 15. 3 51. 4 3 1 3 4 1 5 2 7 . t2.1 1 {1,2,5,7,8,9} 31. 16 29. 5.7ft 27. 1 2.98 3210 1 0 0 2 2 3 1 27. 46 5. 1 , 5. 1 e, r e, 17. . .369 o 152ft No; 9. 3.6 7. 3.6 11. } 29. 6 27 . 9. 5.1 7. 32 9 52.202.525. 5 23. 29. 200 455 21. 27. 15 19. 0 17. 0 2 }5. 2 1 453. 24 45. .133.65in. 7. . 18 9 021. 40 19. 21.84 4417. 24.4 3456 1 8 5 3456 1 * , L 5 3 10 9 Letting 19. 15. * 7 { 47. } 1 00 20 17. 12.04 x , 0.5. The perimeter is Theperimeter 0.5. .49. 8.64 64 05 1 o 22 no; 31. 10.56 x 2 1 4 is anatural number ora .{ 7. , 20 16 5 3 2 2 3 g, j,p, v, z 1 9 321. 43 19. 8 p, u,t,e, r 1 1 about20ft 31. 115 0 31. . 1 2 11. 1.2 1 55. H 2 268101214 1 2 3 0 1 6 00 $8 6 r655.12 53. or 6.5 9 4 , {0} 30.91 .1.65yd 9. 85.0 57. 18 41. 3 the number } 11. 500 } 2 $2 ( 50 4 H 61.5 11 67 $9 3 1 40) 2 11 25 2 Selected Answers 753 b 1, 0, 1} 13 3, $13,150; $14,965; $16,961.50; $19,157.65 ; $11,500; 10, Selected Answers 2, 0, 2} 21. 49 4), (0, 2), (2, 0), 7, 1 4 OUTPUT 15, 15 31. No 33. Yes 7 9. no; domain: 3 17 17. 7 c ; 15, ; 4, 1, 2, 0, 1}; range: { 35. $230 37. {0, 6, 8, 14, 20} 15. (4, 2)}; domain: {2, 0, 2, 4}; range: {4, 23. 17 25. 48 27. 1 19. {(2, 29. 500 INPUT ; 5, 10, 15 27. 3, INPUT INPUT INPUT x 5. { A INPUT 7 7 5 x 7 2 D y B 2 4 2 9. 0.125, 0.0625, 0.03125 2 4 y C B OUTPUT OUTPUT OUTPUT 4 2 2 4 2 4 7 OUTPUT INPUT 4 1 * INPUT A 6 C 2 , 44 5 INPUT 2 15 D 7 1024 3 160, 320 3. 23, 33, 45 5. 10,000 INPUT 0.10 (INPUT) 44 15 , 6 7 1 11. 13. 17. 15. Lesson 2-2, pages 56–59 Lesson 2-2, 1–3. Skills, pages 60–61 Review and Practice Your 1. 80, 7. 39. 14, 18, 20} {0, 3, 5, 6, 10, 13, 43. 41. {0, 3, 6, 8, 10, 14, 20} 3, 6, 8, 14, 20} {0, 11–13. 7 6 2 1 y 3 12 10 14 10 5 8 m or 2 43. 38 7 6 15 1 1 1 c m 29. y 69. 7 0 2 5 1 8 35. 35 11. 11. 45. 16 13. m 29. 2.15 1 9 4 m 35. both equal 10 25 5 5 53. c r 2 a 3 3 15 9. 23. {6, 12} 25. 67. 10, 10 x 1 45. true 47. 2000 10 33. 17 8 135 55. 34 57. 27 or 3 d 7, m (all real numbers) 9 -1 17. 0.00043 19. 3.6 in. 1 x d 7. 21. 3 576 9. 1 2 19. $1500$785.31, $944.21, $1115.03, 21. $637.50, $1298.66 5 65. 4 g and 10,000 27. 9.3 51. 21 , 1 4 31. 3 10 m 37 5 4 1 3456 6 1 3456 1 3456 1 1 9 cm 6 1 or m r 19. 1 34567 1 34567 3 0 1 3456 0 0 17. 4346 19. 9 21. 64 23. 96 e 486, 1458. 7. 12, 17, 23 64 7. 0 0 0 , 21 49. 1 63. 1 3 29. 1 13 41. 1000 25. m 57. 46,000 59. 0.0000278 1 11 1 1 6 2 35. 12 37. 640 39. 1 41. 2 2 x 3 2 b 2 25 4 16 51. 225 53. 11. 125, 216, 343 13. He added 6.2 5. 15. 6.052 4 c 2 0 2 18 m 1 3 a 6 3 2 , 0.000039 33. 2.592 3 4 c 7 3 5 1 2.75 15. 3 3 10 4 4 4 4 4 , 125 cm 61. r 3 47. 4 10 23. 4 5 12 5 10 5 5 1345 39. $9.00 41. 30.48 cm 43. 33. 12 3. 52 52 b 62 02 62 62 62 10 8 12 8 11 2 1 1 d r a 8 27. 2 x 6 m 1 1 1 33. 31. 29. 27. 25. 23. 5. Multiply 3; by 162, 9. 21, 31, 43 rather than 5.2.rather 15.17. $300; $450; $1012.50; $1518.75 59. 37. 28 39. 49. $231.50 51. $292.60 17. 27. Lesson 2-1, pages 52–55 1. Add 4; 1, 5, 9. 3. 3; Subtract Chapter 2: Essential Algebra Chapter 2: Essential Algebra and Statistics 55. 3.92 • 10 31. 1. j 3. c 5. d 7. l 9. e 11. false 13. true 15. Chapter 1 Review, pages 42–44 Chapter 1 Review, 37. 47. 25 49. 13. 5.9 21. 31. 3.9 Lesson 1-8, pages 38–41 Lesson 1-8, pages 1. 43. 27 in. Lesson 1-7, pages 34–37 Lesson 1-7, 1. 16013. 3. 284 5. 25. 45. Selected Answers 754 15, 25. 21. 8 19. 13. 17. 5 100 7 $170.00 37. $170.00 35. 7. 187 47. $168.75 33. 11. 19Ð25. .1 3. 14 1. Lesson 2-4,pages66–69 3 1. Lesson 2-3,pages62–65 1 47. 12 45. 3 Answers will vary; 43. Selected Answers 62.1 29. 12 27. 16 519. 25 03.6, 35. 10 n 44 n 2 x 027. 40 4 6 15 2 6 4 2 2 4 M y 95. 26 .15 $60, 5. 1 3. 3 y 88 C 5 2 2 1 49. 8 . 21. 0.4 4 2 1 x x 8 4 3 7 9 14.40 41. 11 39. 0 37. 6 7)13. (72) 9 II 49. B 4 8 67. 56 9. A 8 6 4 y 8 n 1 5 17. 7 15. 2 4 6 4 x 44 L D y 1 3003.16,000 33. 13,000 31. 3 35.9 53. 90 51. 23 3 5 1 3 0.7, 2 3 .425. 9.34 23. 9 x 4 2 J n 2 4 1 n .4.0.6 45. 3. y K 10 30 50 70 23. 0 9. 26 13579 . 29. 5.6 12 16 20 24 28 32 36 40 44 48 52 56 60 4 8 2.5 x x 88 c 123456789 4 1 1 11. 3 10 43. ZYXWVUT ZYXWVU, 41. 170 39. {3,4,7} 0, 1,2},R: {2, D: (2, 7); (1, 4),(2,7), (0,3),(1,4), 37. not afunction {0,6,12,18}; R: 156 {0,3,4}, D: 33. 35. 0 29. 31. 25 27. 5 22 15. 9 8 4 p 4 8 35.12 55. 13 1 25.5 31. 2 136, 17, y S $101.25; 4 5 n , n 10 ZYXWV, x 25 24 6 , 10 1, 7 5. 4.5 3. 51. 100 49. 96 47. 27 45. 216 72 43. 39. 13 Answers may vary. 41. 37. 29. satisfy theequation. 1 27. Any real number will solution setis{allrealnumbers}. 3 25. 9. 5. 1. Review andPracticeYour Skills,pages70–71 1. Lesson 2-6,pages76–79 10 3. 6 1. Lesson 2-5,pages72–75 57. 55. 5 17. 4 15. 8 44 70, 5 17 5 5 5 2 3 3.9 53. 12 16 3 3 3 65. 4 2 3 44, 4 15 6 4 4 2

2 1 9 21. 2 19. 2 4 6 2 y 2 4 6 2 4 6 8 2 0 1 14 y y 4 2 4 6 y 1 35 1 35 2 1 35 y 18 35 10 1345 47. ; x 11 . 1 13.$97 5 The 35. $29.75 33. 11 31. 3.5 c x x x 7. x 5 2.6 55. 19 17 1 13. 3 11. $1.75 9. 11 16 23. $177 17. 19. 7 13. 15. 13 11. 45. 39. 27. 51. 33. 3. 246 7. 61. 3 2 63. 59. 3 3n 23. 1 2 2 4 6 5 1 25. 3 6 21. 3 64.243. 47. 2 36 41. 36 65.3, 53. 16 135. 81 4 1 5 5 y n n 8 3 4 2 9 631. 26 29. 10 3 3 13 9 65. 4 2 2

1 11, 2 4 2 4 6 8 6 10 y y 1 35 1 35 4 03.112 37. 70 4 1 x n 3 4 8, 29, 4 ; 49. m 102.3 n 19 x 44 x 31, 2.2 4 1 5 n 42 7 3 2 9 Selected Answers 755 2 5 2 4, 5, x x x 22 13.2 6 Selected Answers 2 y y 2 2 2 2 4 2 4 3. median7. 5. 1.9, 2, 1 390Ð399 9. $2.90Ð$2.99 11. 7415. 13.than greater 100Ð109 19. 17. 26 5 25. 21. 0 23. 16 10.8, y 2 2 98 77. 24 4 2 2 4 44 44 24 8.4, (6, 6)}; D: {6, 3}; R: {1, 6}; it is a Yes, function. 71. 3 73. 75. 79. ; {(3, 1), (4, 6), (5, 1), 3. 38 5. 51.9 2 5 4 3 3 1 1 1 x 65. 63. 2.4, 2.7, 3.0 67. 1.212121, 1.2121212 1.21212, 51. 55. 59. 6 represents 1 a score of 16 on a scale of 0Ð100. x x x x 1 3 5 y 2 2 2 6 4 2 y y y 1 2 4 6 4 2 4 2 2 2 y 2 4 2 4 2 4 2 4 PER STUDENT 3 2 2 2 2 0 1 2 3 4 5 60 70 8 9 5 NUMBER OF ABSENCES 44 44 44 44 Aptitude Test Scores Aptitude Test Absences Tally Frequency 16 2 788 3 234888 40 5 0256679 6 0012569 7 1145 86 69. Lesson 2-8, pages 86–89 1. 61. Lesson 2-7, pages 82–85 1. 49. 53. 57. 3; 3 2 6.2 27, 29, 7 6 0 3 25 4; 1024; 16 15. 7 1 c 26 e d a p z 1 6 ; 1 ; 2) ; ; ; ; 27 12 2 5n 0 x 0 k 28 2 29 1 5 3 0 0 2 6 6 x g 3 22 30 12 ; y 27 d 4 2 67 1 4 9 9 29. 3(n 18 h 47. 43. 35. 39. 13 13 2 10 44 n h 11 0 0 , 3 3; 16, 19, 22 41. rule: 1 2 12 21. 4 35. Students should discuss 3 0 25. 13 4 1 1 210 3 2 1 y 14 x 1 2 x 21. 4 23. 12.5 25. 6 2 1345 1345 5 2 2 15 x 7 3 2 n 4 7 1 3 1345 1 34567 0 0 8 4 6 3 y 3 y 6.2 hx 2 33. 4 2 4 2 0 9 5 2 3 5. 0 7. 20 9. 3.6 11. 84 13. 2 4 4 3 02 4 7 6 42 y 42 10 2 3 12 x 12 1 2 2 4 2 7 1 2 4 7 27. 11 31. 11 22 44 44 8.5 y m n c 24 45. and compare the solutions as they appear on both a appear on both and compare the solutions as they line and a coordinate plane.number 37. rule: Review and Practice Your Skills, pages 80–81 Review and Practice Your 1. 9 3. 23. 4096; 16,384 39. rule: 17. 45 19. 19. 11. 9. 243, 729, 2187 n 41. 29. 31. 27. 13. 15. n 17. 33. 37. Selected Answers 756 7. 13. 11. 76.5,75,70 5. 240,235,235and210 3. 7. 84,81,77 1. Review andPracticeYour Skills,pages90–91 25. Answers willvary. 19. 60.00Ð79.99 17. 21. 21 15. Selected Answers 98 81 25578 7 6 0235588 5 1333555667 4 00158 3 2 17 Time SpentonHomework 5 5 01256788 8 23 7 6 22 5 2 210000055588 1 88 20 3Ð4 3 5 7 231Ð240 12 221Ð230 211Ð220 201Ð210 oue Frequency Volumes

Number 12

201-210 0 4 8 458 58 4 0 0

211-220

221-230 5 5 231-240 17 min. 1 y 5 7 represents y 5 20 3 Q,U, Y 67,95,123 23. 21. mean: by 3h 19. increased mode: increased by 3h; 13Ð15 17. median: increased by 3h; 23 15. 5 1 represents201mL. x .2120 211Ð220 211Ð220; 9. 3 5,231Ð240: 221Ð230 : 7, 12,211Ð220: 201Ð210 : .4 n 51.52.1 11. 13. 43and45 9. 23. x 5

3 . 35. 4.8 29. 33. 41 27. Frequency 10 12 14 16 18 20 22 24 26 28 30 32 34 36 0 2 4 6 8 – – 01 51 20–24 15–19 10–14 5–9 0–4 Number ofMoviesSeeninOneYear Number ofmovies 5 5 y 15 03.8 31. 10 5 25–29 x 57. 37. 33. 25Ð31. 21. 17. {2,3,4} {1, 0,2},range: 16, 13. 7 61.1 1 72.0.1 23. 17 21. 10 19. 16 17. .c3 .l7 .a1.1, 11. a 9. h 7. l 5. e 3. c 1. Chapter 2Review, pages94–96 2 9. 5 7. Graphs willvary. 5. different scale size onthevertical intervals 3. thehorizontalscaledoesnothave uniform Yes; 1. Lesson 2-9,pages92–93 55. 43. 51. number ofhits. twice thelengthofother, itdoesnotshow twicethe withzero—although onelineis increments starting 53. 7 1 44 44 44 3 1 36 1 3 32, 64,multiply by 2 31 y 2 2 4 1 4 2 2 011 10 9 8 7 5 2 2 4 6 U 2 4 y y y 2 x Q N 2 2 P 56 23. 1 x M T x x 2 S 0 y 6 4 2 9 341. 23 39. 5 2 45. 43. 49. ; R 2 4 x y 35. higher thanmediansalary group manager andwillbe ofpresidentand the salaries itisinfluencedby mean; 61. about29.1,30,22 59. 24 ; 150 6 g 5 ucin domain: function; 15. 2 3 2 5 x 4 3 3 1 44 47. 6 x 5 7 26 27. 29. 7 25. 3 235. 37 12 33. 19. 4 11. 2 4 19 4 2 1 II 31. I 29. 27. II 25. . 9 1 2 41. 8 39. 2.5 4 1 . 31. 1.1 2 y 3 2 , 2 1 1 1 6 x-axis 3 15. 7 13. , divideby 4 14 9 x 2 7 0 2.5 Selected Answers 757 and AXB 43¡ 0.5 12 TXU 9 6 5 2 1 2 N 9. H 1 4 176¡, C

D A

, M 90¡ X F are not opposite c x L N V

; B D Selected Answers AB R , 2; 19.5, 9.75, 13.75 XU C C 0 ; 1. B L , 85-87 82-84 79-81 76-78 73-75 70-72 mVXU The fourteenth figure will be a rectangular of 210 arrangement with 14 points points, along one side of the rectangle and 15 points along the other. 4, and 0 Interval Tally Frequency Interval Tally D 3 1 13. will vary. Answers 1 1 . is a right angle, A mTXU is the ; cannot tell. 37. 2.5 B 2 V are not equal in measure, into 2 M 3 23. 35. n , so it is not possible to XV, so it is not possible B Now use Now 243, 729, 2187 43. rule: a of 4 A 12 ; 3; 5. 119¡; 61¡ 7. H 5 mTXV mWXV F MB. UXV (n) , 6 f 1 4 K 3 6 8 3 1 1 J ;TXV. false. 35. is No information divide NB. 7 E 0 0 and , N 8

D

11

5. 108¡ 7. 144¡ 9. 14 11. 28 13. false , AN

each side 3. 66 C 9

B 1 2 and MN 3. point 10 D 3 3 TXU 10 mYXW as the midpoint of Z B 11 2 4 J X are complementary, and are complementary, L, M, and the midpoint N 90-99 80-89 70-79 60-69 50-59 40-49 3. 5 12 LM Interval Tally Frequency Interval Tally 14 41. rule: M does not bisect D A 7.5; 62.5, 55, 47.5 45. rule: UXV 19. 90¡31. 21. 54¡ 49¡ 33. 23. 139¡ 25. 49¡ 27. false 29. 128 Points rays; false. 33. Since that XZ to indicate given 39. 11. 146¡23. 13. 62¡ 142¡31. 25. Since 15. 121¡ 19¡ 27. 17. 45¡ 14 29. 19. E and S 49 21. 118¡ 7. 22 9. 153 11. 17. 21. Review and Practice Your Skills, pages 122–123 Review and Practice Your 1. Lesson 3-5, pages 124–127 1.5. figure: Next ; sixteenth figure: triangle with 16 dots on 19. Lesson 3-3, pages 114–117 Lesson 3-3, 1. point 118–121 Lesson 3-4, pages 1. 90¡students’ drawings. 3. Begin with the 53¡segment bisector construction shown 5.in Example 1. 97¡ Because point M midpoint of A 7. Check four segments of equal length: segments four AL 15. 47¡. Since identify the segment bisector construction times to find the midpoint more two of is an obtuse angle. XY Therefore, XU 9. 51¡ 11.19. 39¡ will vary. Answers 21. 13. yes 141¡ 15Ð17. (or 90¡; XZ 80¡; x x ), 13 mQTU 180¡; 10 5 5 YX 3200 35. Post. 2 ; 1. Postulate MOR 17 19. Think of S (or y 100¡; y 5 mVWZ 5 5 mRTS XY and 49. 83; 85; 85 51. Outliers: 59 and 62; clusters: 78-94; gaps: 78 62 and between U, V, U, V, Z; 90¡; ). is justified Each answer mXWZ 90¡; x ; Post. 3 39. 176 41. 75¡ 5 5 ZY 1 90¡; y mUTR W 34 and NQ (or 3 1 27. 1 3 , V 23. 1 18, 8 9. false 11. true W 4 x x mXWV , Y mQTS PN V 5 5 47. , Y mXWY ), and YZ 10¡; W ); 4. Postulate 9. 5 11. 6 13. 56 y y 4 33. x 5 5 VR 5 40,000 39. 1521 41. 2.4 180¡; 33. 104¡ 35. 90¡; , U 180¡ 31. SR V 12 (or y 3 2 1 (or , U 1 2 3 25 and 9 17. Y RV 1 5 mQTR 5 MOQ, 125¡ and NOR, 145¡ 15. 72¡ 23. 115¡ 2 31. U ), RS by Postulate 3. Postulate by 3.7. 34 5. R points 90¡; 13. 12¡25. 15. 149.5¡ 84¡ 27. 17. 162¡ 1¡ 29. 19. 48¡ 21. 97¡ 23. 54¡ Review and Practice Your Skills, pages 112–113 Skills, Review and Practice Your 1. 5 3. 6 5. 60 7. Lesson 3-2, pages 108–111 1. 120¡; obtuse7. 79¡ 3.the pairing with geometric of real numbers figures in a 120¡; obtuse 9. will vary. Answers to Both postulates refer systematic way; of taking the absolute value 5. both involve 180¡; straight real numbers. of two the difference 11. 13. 25. 67¡508 27. never 37. 29. 41 31. 1 33. Lesson 3-1, pages 104–107 Lesson 3-1, pages 1. answers: There are three possible Chapter 3: Geometry and Reasoning Chapter 3: Geometry 45. 53. Yes; Brand that 22 people preferred show graphs both cookies. Bill’s preferred X cookies and 30 people 15. ZX 29. the end of each leg as a point. legs, has four When a table points.the ends of the legs represent four If the legs are and the points are noncoplanar, the four lengths, of different wobbles.table the ends of the has three legs, When a table legs represent three points. 2 guarantees Since Postulate the length of the legs three points are coplanar, that any does not wobble. the table and so does not matter, 21. 25. mUTS mYWZ mVWY 37. Selected Answers 758 1 23.72 33. 72 31. adjacent. angles arenotnecessarily Complementary angles whoseexterior angle sidesform aright if two anglesarecomplementary, thenthey areadjacent angle,right thenthey arecomplementary angles areadjacentwhoseexterior sidesform a thegiven Write definitionastwo conditionals: 29. of oppositerays, but angles. theanglesarenotvertical counterexample inwhichthesidesof Hereisa rays, anglesisfalse. thentheanglesarevertical rays angles,two anglesare vertical thentheirsidesform opposite thegiven Write definitionastwo conditionalstatements: 27. ie ndfeetpit.21. lines indifferent points. transversal ifandonlyitintersectstwo ormorecoplanar Alineisa Biconditional: points, thenitisatransversal. a lineintersectstwo ormorecoplanarlinesindifferent Ifalineistransversal, thenit Conditionals: if intersects two or morecoplanarlinesindifferent points; 19. length. only ifitdividesthesegmentintotwo segmentsofequal Apointisthemidpointofasegmentifand Biconditional: equal length,thenitisthemidpointofsegment. ifapointdividessegmentintotwo segmentsof length; then itdividesthesegmentintotwo segmentsofequal Ifapointisthemidpointofsegment, Conditionals: 17. the given statementanditsconverse arefalse. Iftwo Converse: Both lines donotintersect,thenthey areperpendicular. 15. statement anditsconverse aretrue. Iftwo anglesarecomplementary, Converse: Boththegiven then thesumoftheirmeasuresis90¡. 13. true. Itsconverse is Thegiven statementisfalse. are coplanar. Lesson 3-6,pages128–131 J, K, IfpointsJ, Converse; 11. 7. False. base. Ifanerrorischargedto madeabadthrow tofirst thentheshortstop the shortstop, 5. formed areequalinmeasure. bisected by aray ifandonlythetwo adjacentangles anangleis measure, thentheray bisectstheangle; by aray intotwo adjacentanglesthatareequalin ifanangleisdivided angles formed areequalinmeasure; Ifanangleisbisectedby a ray, thenthetwo adjacent 3. itispossible thatthetwo linesarenoncoplanar. False; 1. 1 Sampleanswer: 11. Sampleanswer: sameassecondfigure 9. 7. 10unitslong the interior 3. assecondfigure, sameorientation but withtenlinesin 5. 10unitsvertical 19unitshorizontal; 1. Review andPracticeYour Skills,pages 132–133 Selected Answers h g stu.However, ifthesidesoftwo anglesform opposite is true. 1 t 2 9. A BEF C opposite rays. whose sidesform two pairsof anglesastwo angles define vertical For to thisreason,itisnecessary D B and t, Q p L q are collinear, thenthey 23. A 1 and ,X P, stu.However, is true. 25. 2 form apair is false. C If two X, Y If 4. .Given: 9. 3. 6. 5. 4. 2¡2.1¡ 0¡2.7,9¡2.29¡,119¡ 29. 33¡, 23. 7¡,97¡ 27. 5,120,000,000 21. 15¡,105¡ 0.0000000059 25. 0.000397 15. 19. 123¡ 70,200,000 21,000 13. 17. 0.0000000146 11. 7. 3. 2. 2. Prove: 5. Answers willvary. m1 3. ofequality property 9 4¡ 2 1 6¡2.164¡ 23. 164¡ 21. 148¡,32¡ 19. 17. and onlyifthey angles. intersectto form right Two if linesareperpendicular then they areperpendicular. Iftwoangles, linesintersecttoform right angles. form right Iftwo linesareperpendicular, thenthey intersectto 15. nls esn3 rn.Po.o nqaiy Statement4: m ofinequality; Prop. trans. Reason3: angles; 1. Statements parallel linespostulate; given; 1. Lesson 3-7,pages134–137 5Ð11. and Eva—San Diego Pedro—San Francisco; Carina—Dallas; Ned—Miami; 3. 1. Lesson 3-8,pages138–139 1. Statements op to comp. .Given: 7. 3 If 13. Prove: k m1 m3 m1 2 is a right angle 6. def. of right angle ofright def. 6. k angle 2 isaright m2 lines ofperpendicular m1 def. 2. m1 angle 1 isaright Prove: l k 1 at lr x x x x x o x o x o x Seattle x Santa Clara Pittsburgh Des Moines m, AB l m, 5 m ;Saeet 1: Statement: m3; m k l k k k l F 0 .substitutionproperty 5. parallel lines postulate angle ofright def. 4. 3. 90¡ m2 90¡ 3 3. trans. property ofequality property trans. 3. m3 post. parallel lines 2. m2 m2; ;Rao :gvn esn2 e.ofcomp. def. Reason2: given; Reason1: 2; m D 3. 2(AC m m l l m , , k l ), thenC H E oySe ol Mao Molly Srey Cory m 5 o x x x 5 l .cre.anglespost. corres. 4. .given 1. C A .given 1. 7. def. of perpendicular lines ofperpendicular def. 7. Reasons Reasons is themidpointofA m m 5 k scm.to 1 iscomp. B G k m2 3 2 1 1 2 3 1 13. ;transitive m3; 2 and B true,false . 19, 7 3 is Selected Answers 759 ; , ; 11 115¡, P RQP H 8 12, 10, ; , B is a 155¡ 5, QTP, S is an G 7 S 6; P UVT, UVT, T FBC R VUT , C Q x ABC 2 4 F 1 S D 12, lines; right RSP, Q 3 Selected Answers ; 2 17. isosceles triangle 19. 21. ABD 7, ⊥ N 6, 10, R y SRT PRS; P 5; 4 2 RST ; SAS postulate; 8 2 4 M F 34 NOM; SAS postulate 28 , 2 RSQ, 90 5 H 90 T R 2 56 3 ; given; P 44 scalene acute U Q 4 56 H 10, 124 124 8, F TUV, TUV, H 56 4, 90 7, QRS F 90 T ⊥ 28 2; 34 13. 2; H 9 , S 3. true7. 5. The altitudes are concurrent cannot be determined lines. J 6 11. cannot be determined 13. true 15. true 17. false T is a perpendicular bisector of Q is an altitude of PQR; ; 3 1 V 15. H S S S 1 PRS; 21 33. 0 35. 10 TSR x F 1 is isosceles; R R 9, 11, 8, T ⊥ A R 40 K 2 G XYZ , PQR F y 4 5 U 2, or ; are right angles. 25. D 27. VTU, VTU, 50 90 4 2 J V 2 4 QRS ; CPCTC 3. 12 5. 3 7. 45 9. are two There 50 H 90 15 31. 2 T m G C B 9, 11, 12, S 44 40 right isosceles QTR 29. XZY G R RPQ; R lies on the bisector of QRP; 1 JL F RTS J S I 9. 19. The three distances are equal. sides that are perpendicularthe two (the legs) are two 21. In a right triangle, altitudes of the triangle. true that a side of a It is never connects triangle is also a median because a side always verticestwo of a figure. 23.responses: will vary. Answers Possible base angles. angle must If each measures 70¡, the vertex measure 40¡. 11. altitude of PQR; A 17. always 19. sometimes 21. R Review and Practice Your Skills, pages 168–169 Skills, Review and Practice Your 1. 8 cm 3. 46¡ 5. Lesson 4-4, pages 164–167 1. Review and Practice Your Skills, pages 158–159 Skills, pages and Practice Your Review 1. 9511. 3. 23 5. 40 7. false 9. false 15. 160–163 Lesson 4-3, pages 1. median of PQR; and m 3 7; 13. 1 6 7.“included angle”) be (must false 17. 9. false false 19. 15. true true 21. 71 23. 28 25. 112¡ Z ; 1 6 X Y DBE mDBE. x D and C 5, 2 and y 4 2 2 4 6 90¡ 2 F B A 424 E equality mH 61 and 27. 140û MNK; SAS postulate 17. 3. property of Transitive 4. SAS postulate Reasons 4. SAS postulate 3. vertical angle theorem Reasons 2. definition of vertical 26¡; Z QRS; given; angle bisector; Y x K 6 90¡ 2. Definition of right angles ; 1. given ; 1. given Z B 4 Y are right angles. D C Y B Y bisects mG ; XYZ y T are right m Y Y¡ intersect C B 2 4 4 2 CBD R X B E J E ; 74 and 25. are vertical angles, then mABC are vertical angles, false, truefalse, 33.California; Stephanie: Marco: Florida Wisconsin; Sue: 64¡; XYZ 2 CBD CBD ; ; and Y m ; mode: 8 C S 90¡; B Y and 1 2 4 R B ; reflexive; SAS postulate B X C 11) or (7, 15) scalene, obtusescalene, right isosceles, T A 62 and ABC and B B R L Q B B D mF are vertical angles. angles ECB; ASA postulate 7. ABE m ABC R A at point B. ABE ABE B A A angles. m T 5. 11. vary. Proofs may proof is given. A sample Given: 9. (7, 13. 104¡ 15. 71¡ Prove: 2. 4. 3. vary. Proofs may A sample proof is given. 3. 4. Statements 1. 1. Statements Lesson 4-2, pages 154–157 1. Lesson 4-1, pages 150–153 Lesson 4-1, pages 1. 45¡13. 3. 26¡ 5. 153¡ 7. 71 9. 63 11. 38¡, 76¡, 66¡ Chapter 4: Triangles, Quadrilaterals Chapter 4: Triangles, and Other Polygons 6, 3 and 29.shaded square a 31. If ABC Chapter 3 Review, pages 140–142 3 Review, Chapter 1. 115. 3. 8 e 17. 5. 13û f 19. 7. 110û g 21. 9. 68û j 23. 11. 6 planes 13. no median: 7 3. R 2. 19. never 21. sometimes 23. 52 25. mean: 7 15. Selected Answers 760 ie ttmn utb re .59 1 19 11. 9 9. 5 7. given statementmust betrue. The given linethroughapointoutsidetheisfalse. toa assumption thattherecanbetwo linesperpendicular statements inStep2 P, m2 angles,definition ofright m1 m1 intersecting lines, sincem since stu.25. BC, istrue. It follows thatthedesiredconclusion, be false. angle the topangle hypotenuse, isthelongest unequal anglestheorem,thesideoppositethatangle, the Bythe angle isthewithgreatest measure. Therefore, theone right cannot have anobtuseangle. canhave triangle Aright angle, onlyoneright andit 29. Lesson 4-5,pages170–171 21. 1 acuteisosceles 31. assume thatm Inparticular, inthefiguretoright, line. through pointP 5. two; 3. can Assumethatthetriangle 1. .6;123 4 .9¡7 0 .4;15 2 28 42; 135; 45; 9. 90¡ 7. 90¡ 5. 64¡ 1 3. 11. 112 68; 1. Lesson 4-8,pages182–185 20 72 21. 11. 40 132 19. 9. 60 129 25. 60; 30; 7. 17. 36¡ two different typesoffaces, 53 pentagonsandhexagons. 15¡ 5. 31. Althoughthefaces areallregularpolygons, thereare 15. 23. 136 7.5m 2880¡ 3. 29. 13. 101 28 1. 27. false 25. Lesson 4-7,pages178–181 0 15. true 23. no 13. false 21. yes 11. Answers willvary. 9. Assumethey donot Assumethey are 5. 3. equilateral. Assumethatagiven isnotisosceles, triangle but 1. Review andPracticeYour Skills,pages176–177 2.56 39. between 5ftand9 3. 5. between 3 ft and15 1. Lesson 4-6,pages172–175 17. otlt.Therefore, theassumptionAB postulate. 15. h hretpt otlt.Similarly, if pathpostulate. the shortest than alongB BC, thenthereisapathconnectingpointsB be true: oneofthesetwo statementsmust ofcomparison, property then theremust beapathconnectingpoints is shorter than is shorter Selected Answers m Step 1: C P D (n K and 8 5 M F m1 , ;1 ; , P n;cnrdcoy as;true false; contradictory; one; Y; X; s; r; 90¡. By the transitive property ofequality, By thetransitive property 90¡. .By the correspondinganglespostulate, m2. AB n E 0 35. 60¡ 2)180 M 8 5 n F 3 AssumethatAB 23. O Assume thattherearetwo lines , 1 10 , are intersectinglines. , M C 11 17. 2 1 m2, itfollows thatm AC L ;1 that isequalinlengthtoB B O 27. approaches 180¡ 29. right scalene right 29. approaches180¡ 27. perpendicular tothegiven perpendicular 0 3 whenthemeasureoftop 33. 60¡ C , M 8 5 1 8.9 41. B 7. V l ; this also contradicts the shortest path thisalsocontradicts theshortest ; f C and W (n) N BC X , 3 re1.fle1.false 17. false 15. true 13. r otaitr.Therefore, the are contradictory. , , N Y A U , B nesc.7 Answers willvary. 7. intersect. n or V O Y , n Z A and and 2 AB ie 1 whenthemeasureof 31. side. 10 , C l. 19. X , 12 Step 2: Z C U (n n be anobtusetriangle X D W AC each passthroughpoint 0 and 90¡ AC Step 3: not .ys1.n 3 yes 13. no 11. yes 9. Y , , A )3.3.71 37. 1) Bydefinition of n. W D 9 0 19. equal inmeasure. By the BC; Y AB Then,by the BC. , 7 2 27. C Y The lasttwo Z thiscontradicts ; AC If , B AB AC W x and AB and Z , BC z m 11 C X x AC BC, C 10 W 21 P other AC is must that 12 11 14 n nyoe 7 quadr 17. only one. hasthreemedians,a triangle whereastrapezoid has of thefigure, whereas themedianofatrapezoid doesnot; hasoneendpointthatisalsoavertexmedian ofatriangle midpoint ofasidethefigure. ignl ietec te.2.2.¡2.6¡2.45 27. 100cm 67¡ 31. 25. 60 28.5¡ 29. 23. diagonals bisecteachother. vary. 19. mV mF parallelogram Draw Sampleresponse: 25. 4. 2. it follows thatA arecongruent, triangles ofcongruent corresponding parts oan 2 ,4 ,6;rne {4.5,6.5,8.5,10.5,12.5} range: {2,3,4,5,6}; domain: 29. to show that Thegoalis both diagonals. 6. 5. 3. A 1. Statements .1 .35. 3 3. 16 1. true 13. Lesson 4-9,pages188–191 24 11. 9 9. 360¡ 7. 18¡ 5. 17. 60¡ true 3. 15. 143¡ 1. Review andPracticeYour Skills,pages186–187 and BEA ASA postulate, therearetwo triangles: pairsofcongruent it isknown thatAB Because theparallelogram-side theoremhas beenproved, 1 and3; so therearefour pairsofanglesthatareequal inmeasure: anglesareequalinmeasure,transversal, interior alternate e;ys o o2.n;ys e;ys e;n;no no; yes; yes yes; no; Given: yes; yes; yes; no; no; 29. yes; no; 25. no; 27. no no; yes; yes; 3 Given: 23. Yes, thefigureisasquare, and every squareisaparallelogram. 21. opposite angles. theanglesthatareequalinmeasurenot No; 19. or 1 isosceles 21. and thatA 27. B DE A B ABC A m6 m5 ABCD a with basesA Prove: supplementary. Prove: ABH ABG C B B D Possible likeness D C and Itfollows that B . D 0¡7 . .91.713. 7 11. 9 9. 3.6 7. 105¡ 97¡; Therefore, point BE. 8.8; and C C D, ormB saprleorm .given 1. is aparallelogram. C A ; mB ADC m8, or6 m7, or5 ABCD ABCD and DEC, andBEC and A CDA 2 and4; bisects B mU A b D tr ABCD D a D E apez GEF, FEH, and bisects B mC B B 6.8; is atrapezoid is aparallelogram. C 115; and C mD C oid B Whenparallel linesarecutby a . DAB and ilater E CD 97¡; D Eachhasanendpointatthe : c udiaea 3 o e;yes; yes; no; 23. , quadrilateral , orAE Bythedefinitionofparallelogram, . CBH GBC D x D b A ;and 5 and7; C mD and C 75¡; al bisects are by atrans., thenalt. Iftwo 3. 8 7; mW . 133; , 0 m3.103.43 35. 100 33. 900 cm 65; E DC AD 9 tr 19. mD and and and is themidpointofboth Possible differences: 8 c A d DE, andthatD A 5 4 .CPCTC 6. .ASApostulate 5. .reflexive property 4. definitionof 2. Reasons GED C Because DEA. 3 5 Answers may 15. 83¡ DEH apez Therefore, by the CB. 1 37; 32.Yes, 21. 83 and measure. int. D 75¡; d AB oid s E mT 6 and8. A 3 mE , quadrilateral C 1 yes; 31. 2 43 lines arecut are 7 bisects 6 E C B 83¡; -ogram in 105¡; A B B A E D C , . Selected Answers 761 2 LNO; 2 and ABC; 2. is 4 times 2 0.318 qt 23. 45 SA and v 235.5 m 15. 6300 in. LMO 2 3 27. 6 29. 3 15. the area of 7. at least 230 ft Selected Answers f 2 .26 9 2 7. 452 ft 2 5 A 2 19. a) 28 EFD; Remaining e 2 acute isosceles right isosceles 2 and x 67.1 m; . 5. a coplanar line x . 3. pyramid; Triangular L 3 1 13. 735 m D 2 2 O F ABC 5. 126.5 m 0.262 5. 5. 222 in. P 2 A

5 5 2 33. and 2 and 65 7 M F times as great. 21. 1 4 5 0 2 y y 7. 1 9 ; BCDF intersecting faces 5 F 5 5 31. 21. 45 23. 2.9 25. 15. a cylindrical surface 19. a square is E 48 37. 10.9 39. 39.5 3. 396 ft 11. 476 in. 3. 336 m SA B C 2 2 and 2 0.40 0.24 3. 0.1 9. unlikely 11. will vary. Answers Most B A C A LNO; edges; no parallel will vary. Remaining answers 5 B 5 2 5 33 35. 5 0 6 1 2 1 as great; b) long, at least 150 ft wide 9.167.14¡ 7740¡, 172¡ 13. 11. 5760¡, 169.41¡ 4680¡, 15. 7200¡, 171.43¡ base include intersecting faces Sample answers dimensions of the Palaestra and the total map or actual and of the Palaestra dimensions ruins. area of the 29. 31. 33. intersecting edges E Lesson 5-6, page 224–227 1. 158 cm 9. 166.4 m Lesson 5-4, pages 216–217 1. 12,150 ft Skills, pages 218–219 Review and Practice Your 1. 17. 1:50023. 19. 1:2 21. Lesson 5-5, pages 220–223 1. prism; Triangular bases answers will vary.answers include parallel Sample answers edges halfway between them between halfway 7. prism; hexagonal 11. 8; 12; and vertices is 2 more than The sum of the faces 18 of edges.the number rule: Possible 7. students will answer “likely.” students will answer 13. 320 m the base 17. about 24,727.5 mm intersecting edges O 13. 2 postulate 36 in. ft per day 17. No. That 1 4 13. about 0.785 s QZY, SSS P 3 5 00 9 19. likely 21. likely postulate supplementary angles 10 25. 96 in. 2 5. 40 cm 7. 4.8 cm 11. 2 2. of trapezoid definition 3. corr. Reasons 6. definition of 2 ) has more area than the 2 1 3 2 XYZ 27. The map or actual 2 3 7. 9:1 9. 1 9. 1 6 204 ft 3 2 5 27. Assume if a triangle is 796 ft 180¡ 5. property substitution 180¡ 4. addition angle . 6 961.625 yd 3 2 C A 25. D D A , which is 7. 1 9 A 4 5 11. It triples too. 13. about 144 ft 29. 832 31. 22, 2 33. 0.0004 1 2 and 3 1 1 3. 11 cm; 10 cm 2 B 0.05 m 33. 8000 billion qt 35. 2 mi/h 2 ). 27. yes 29. yes 31. yes 33. yes DAB mDAB mADC mDAB 17. . Luis entered 3.14 for Irene used 2 5. BET, SAS 19. 2 2 1 4 15.9 ft and A and C is a trapezoid 1. given 94.2 in. 23. 124.95 yd; D 3. 27.93 mi key on her calculator.key 21. will vary. Answers B C AES P 0.5 m; 6 3 1 A mEAB mEAB ABCD A with bases mADC are supplementary ADC 21. 35 23. 60 25. 9. about 62.8 m 23. Sample answers: not including space, Area of wall etc.; doors, windows, and price number of cans of paint covers; needed based on the area one can of paint of painters involved.painting speed and number 25.circle (r The the 3. square (625 ft obtuse, then it can have a right angle. then it can have obtuse, 29. angle of an isosceles triangle angle bisector of the vertex Assume the is not an altitude of the triangle. 31.35. no 45¡ 33. 37. 115¡ 19 39. 110¡ 41. 38 43. 20.5 in. 45. 4 m Lesson 5-3, pages 212–215 1. 27. Review and Practice Your Skills, pages 210–211 Skills, Review and Practice Your 1. 1213. 3. b 0.3625 15. 5. c 7030 17. 7. $1.79 1 gal for 40:9 19. 9. 7:5 11. 5:6 21. Lesson 5-2, pages 206–209 1. 10 m; 7 m Lesson 5-1, pages 202–205 1. 32 c 3. 3500 mL 5. Chapter 5: Measurement 1. c17. 3. i 5. l 7. g 9. b 11. 18 13. 27 15. 51 Chapter 4 Review, pages 192–194 Chapter 4 Review, 1. Statements actual probability is 15. answer: Possible about 0.009 or 23. about 0.56 or 35. 1:1043. 37. 30:1 39. 1:1000 41. 200 L barrel 35. 5 37. 6 39. 6 15. 3600 ft 11. 3223. 13. 2:5 25631. 25. 15. 1:3 0.004 27. 17. $0.06 per copy 6 29. 19. 4-L vase lb 21. kL 2. 4. 37. 48¡; 70¡; 62¡ 5. 31. 9 33. 5 35. 8 6. Selected Answers 762 Review andPracticeYour Skills,pages228–229 15. pyramid isone-thirdthevolume oftheprism. 16 cm Cutting4-cmsquaresgives thegreatest volume— the$0.40can 25. 23. separate shapes andadd. Tetragonal systemiscombinationof 21. findvolume of andtwo squarepyramids; rectangular prism Itistripled. 19. Cheops issmallerthantheareaofbaseCholula. eutn iesosadvlmsi al.2.36.9ft; 80 ft 27. resulting dimensionsandvolumes inatable. 9 1 164.9cm 31. 29. pyramid; triangular 6edges 27. 4vertices; 4 faces; 12edges 8vertices; 6 faces; 9 ie slre2.6525. 21. 9timesaslarge 19. 9. 7. Answers willvary. 5. 1 vertex. faces andedgesareundefinedfor cones, oblique cone; 3. 6faces, 8vertices,12edges rectangularprism; 1. 11. 1. Lesson 6-1,pages244–F247 of Equations Chapter 6:LinearSystems 2:5, 11. l 9. k 7. d 5. 19. j 3. e 1. Chapter 5Review, pages234–236 340m 9. 1309mm 1. Lesson 5-7,pages230–233 7. 3 .0 15. 0.005m 13. Selected Answers m V 9 1 y 2 2 4 3 1 0 3 0 1 256ft 21. 9 45i. 8.22in. 14.5in.; 29. .udfnd5. undefined 3. 4x 3840 yd 16 cm 3 6, .1 7 8478in. 27. 0.215 3 1 about254m 11. b 9 6188.9mm 39. about226cm 35. 13. 2 .3561cm 3. 3 49. 2 4 cm C 7 n nwr Areaofbase Oneanswer: 17. 3 300in. 23. 11. 2x y4 m 15.42 m; 3 1024 cm 3 2 2 13 3 3 3 3 1 .6c .1570cm 7. 6cm 5. m 3 177.1in. 33. h 1 2 1 3 1 2 i 0 2 3 Thevolume ofthe 13. 1 36in. 41. y A (0, 4) , 1 1 b 3 34 23. 5 rectangularprism; 25. 3 1 3 slope 2 7 135cm 37. Listallcutsandthe . 1 3 y 14.13 m 7 1306.2m 17. 272ft 15. 3 240cm 13. 13 5 1 5 2 , 2to5 x P(4, 1) m ga 2 in l x 2 3 2 17. 2 3 2 5 3 45. 1 30 3 slope 43. $3000 41. 39. 33. 29. 27. 11. 15. 1 11 e b5.4m/ 5 $1.67perjar 55. 4mi/h 14, 53. 57. $1.19perlb 62mi/h 51. 49. andtheslopeisundefined. vertical No, sincethereisnochangeinx,thelinemust be 47. 3 ;ys25. yes 2; 23. 1 323. 23 21. .13. 1 1. Review andPracticeYour Skills,pages 252–253 slopeofL 29. 27. 11. 1. Lesson 6-2,pages248–251 so L N y y m m 17. 2 9 2 5 is not perpendicular to is notperpendicular ,

6 5 Weekly Earnings, $ 2 , 2 4 2 9 45.4, 59. 14 100 200 300 400 500 600 6x P 5 6 undefined, undefined, y EN 3 B A .4, 3. 4 5 x 268 13. 6 4 1 1000 35. N LI 2 4 6 7 3 5. y 5 2 Weekly Sales,$ 1 35 4 m C B 7, 2000 19Ð21. ; 4 1 B 4 3 9 4 3 b b 3000 7 1 1 26, 61. 4 4, and slopeofE .nihr7 ete 9. neither 7. neither 5. 13 x .09. 0 7. b 3 1 4000 0 5 ete 7 o1.parallel 19. no 17. neither 15. oe31. none none 1 3 a, (0, 2) 44 y 2x 3y6 slope 1 x 13. y-intercept E 0 I . 22 2 3 1 48cm 31. 6 x 4 2 5 P 2 4 66.15, 63. 26 I P(1, 1) y y 37. 3 m 1 8 3 m 1 m 0 6 4 1 ; 2 4 6 r 44 5x y 2 1 35 4 3 x 22 m 3 5.25cm 33. 8 3 4 2 4 2 4 15 4, (0, 2) y y 3x2 x slope 3 4 1 1, x 2 Selected Answers 763 1, 7 1 3 3) 12 m , 12 8 2x 1 2 1 9 13 13 0, b x x 2 y 3 2 , 1 0, x x 1 2 5 4 Selected Answers 8 45. 7) 9. (2, 17. bagel, $0.55; 3x y y m y 2 7 y 6 17. 530 11. 7. (2, 9408 19. 1975 21. 1 29. 1, 3) 13. Choose the 7 49. 45. 4, 5) 25. 15 and 18 15 4x , 2 15 61. (45, 36) 6 5 3 23. x 1 3 23.0.77 about 25.0.97 about 27. 190,000,000 29. 6,520,000,000,000 300x , 3 4 4 3 5) 35. no solution b y 72 33. y x , 3x x y 3 2 y 2) 5. length: 24 cm; width: 15 cm 1 1, 1) 11. (4, 3) 13. 2) 41. 1 43. 5, 1) 15. 1, 2, 1) 31. 29,000,000 10 2 65432 y 33. (0, (4, 2) (4, 7) m 15 20 3 7.5 3. 2 15. 7 21. 1 27. 4 ()()() 0.05 9. 26 47. , 5 510 x x 5 2 3 2) 27. (1.5, 0.25) 29. 4) 33. (8, 8) 35. lines (no solution) parallel y 7 2 1 2 36 59. x (2, 3) 0 1 2 5 6 2 4.5x x 60 months 9. ( 3 11 1 2 y y y y y y 37. (9, 4) 39. (4, 19. 25. 13. 7; food, 3 personal care, solution 15. $10,092.5021. 19. no peach, $0.35 19. (1, 1)25. (3, 21. (2, 0) 23. (2, 1) 33. 35,500;37. 15,828,000,000 35. 15,300; 2,940,000,000 39. 41. 43. pages 272–273 Skills, Review and Practice Your 1. (15, 3) 3. (3, 2) 5. 31. Lesson 6-5, pages 264–267 1. (1, 2) 3. (1, 23. (1, 1, 2)27. 25. 12 3 quarters 9 dimes, 15 nickels, 29. 36 31. Lesson 6-6, pages 268–271 1. (4, 5) 3.7. (3, 1) 7 5.15. 43 children 13 adults, (2, 4)19. 17. (2, 3) wheat, 950 acres; 250 acres 27. barley, 21. (10, 21) (3, 9) 29. 23. ( ( Review and Practice Your Skills, pages 262–263 Your Review and Practice 1. 7. (4, 0) 9. (1, 2) 11. (5, 7. 11. (0, 2) 13. (7, 31. (3, b variable that will be easy to isolate in one of the equations. that will variable 15. $1.19, $0.79 17. 13. 51. parallel57. 53. perpendicular 55. x 3 x 2 3 1 1 4 y

9 – (2, 1) x (2, 2) 9

1

2 7 2 1 3

x x y 7 , 3 4 1 3 5 15 x 9 4x 2y y 9

y 3 1 pay 4 2 4 2 13 1 3, 2 4 2 4 1 4 7 1 4 9 3 y 5 5x 1 22 y 1 3 5 y

y 3 – 2 y

43.

47. perpendicular b x 3y 1 b b b 2 8 2 x

32 and 6x 4 8 8 , 44 1 , , 39. 1, 4 6 Solution (2, 1) 2 3 b x 1 4 44 2 3 1 3

3 5, 9 63. Solution (2, 2) 2 , 5 17. y 20x 5 1 1 3 2 3 sales, sales, 1 2 , 15 27. , 11. y 9y 3 5. 2 2 5 5 5 b 1 1 5 , x m 2, y y m m m m 1 4 25. x x ) 11. x 42 1 1, 0 ( 2 49. parallel 51.53. neither undefined 55. 57. 41. 37. 45. 25. 29. 21. 23. 19. 17. 33. 1 4 , 8 1 m 7x where 1 8 23. 2x 4x 2y 4 ) x y

x x 2y 5 x F, x 2y 3 y y 4 4 2 1, 0 x ( y 4 2 2t 3 4 4 22 15. 4 61. d 2 3 44 1 3 5 1 3 5 1 3 5 y y 3x + 6y 3 y P 23. Solution y 6 4 2 6 4 29. {2, 3, 5, 6, 7, 8, 11, 12} 31. {4, 9, 13} 6 4 2 0.01px 1 1 1 4 6 4 6 4 6 No solution b x 2 1 3 3 3 3 3, 3x y 2 21. 99. 5 5 5 x y m y y 7. (3, 2) 9. Lesson 6-4, pages 258–261 1. yes 3. 19. Lesson 6-3, pages 254–257 1. 65. undefined, 0 67. 15. 33. {1, 4, 9, 10, 13, 14} 35. 31. 13. 7. 59. 18 25. 27. 96 cm Selected Answers 764 y solutions ofy 7 Thesolutionsetofy 17. 13. 41. 37. .ys3. yes 1. Lesson 6-8,pages276–279 det 5. 3. 1. Lesson 6-7,pages274–275 .n 11. no 9. 5. 58.4in. 11. 129in. 9. 41in. 7. Selected Answers 35D 25D 2 3 2 4 5 4 22 5 5 3 x 6; 4 2 3 7 22 3 4 1 2 4 0.25M 0.35M D 1 y 21. 5 y y 2 1 4 1 y x 2 4 6 8 2 4 y x 1 2 3 4 P 5 d; y y 1 35 4, x 2x y 4 x 1 23 3 50.35 25 250 230 y 2 6 M 4 3; x P 4 .19. 3. det ; 2 3 y x x x 300 mi 7. x det ; 50.25 35 A 39. 15. 2x 44; 4 4 47. neither 45. 3 perpendicular 43. 49. 51. 3 (3, 53. 3 A x x 3Solution: 23 y 22 y y y 3 doesnotinclude 0; 4 10 20 4 2 1357 1 3x 10 2 4 4 8 6 2 0Solution: 10 )5.(2, 55. 1) y y 3x 1.5x y M D 5 y 1 x 43 19 x 4 P 1 6 x 10 250 230 2 2 3 2 2; , 2 2 x x 3 8 1 5 1) 3 , 5 6 7 82.4800 29. 78 27. 23. 75. ouin 5 oslto 7 4 )5.(5,0) 59. (5, (4,2) (3, 63. 57. 69. (8,3) nosolution 61. 55. solutions 49. 33. 29. 25. ( 15. (2.8,0.8) 21. 13. (6,9) 11. (1, 1. Review andPracticeYour Skills,pages280–281 y 4 4 )3 1 )5 7 )7 ( 7. (7,8) 5. (1,3) 3. 5) 4 4 4 )7.(6, 71. 1) 4 2.5x 22 4 2 2 2 2 2 6 4 2 4 2 4 2 6 4 2 y 2 y 6 4 2 y 6 4 2 4 2 2 6 8 4 2 4 6 2 468 y y y 15.(,0 3 infinitelymany 53. (5,0) 51. 11 2 4 2 4 2 46 2 46 )6.(2, 65. 4) 4 3 3 (1,2) 73. 43) x x x x x x 31. 23. 25. 1 aall4.perpendicular 45. 43. parallel 41. 39. 37. 35. 47. 27. y m m m y ,5 7 e 9 yes 19. yes 17. 2, 5) 10 4 4 4 4 6 8 3 2 )6.(2, 67. 4) y 7 5 7 5 5 ,2 9. 1, 2) 2 2 2 x 2 , , 3, 6 4 4 x 2 2 4 2 b b 261 y 2 6 4 2 4 6 4 2 b y y 13 7 2 46 2 4 4 2 4 11 13 11 0, 4) x x x 3 7 0 x Selected Answers 765 are 6 7 4 E 5 6 58.5 29. 6 4 5 and 1 2x , 56 mi 5 4 47. is half the length 2 27. 5 B x y Selected Answers X 1 2 7 4 , it follows that , it follows R L 25. . 35. 6 37. 21. 51 in. 8 x y 27 cm 4 2 3 : 1 7 30 : 3 25. 3 27. 5 ft 9. Corresponding x 0 3 x 1 2 3 40 mi 37. 23. x c 21. 40.5¡ 49.5¡ and in. 17. will vary. Answers or 9 D. Because 7 1 4 4 9 3 2 8 x E. the triangles are Therefore, 4 :AL. Because : D, there are 2 pairs of congruent RY y 0 in. 21. 15 ha 23. A 3 1 1 2 in. 9 by B 43. undefined 45. 19. 5 9 2 25. 11 is half the length of A :AK 3 2 3 21. B 1 2 15 cm 51. 1 12 dm 55. 21 2x 41. x x x 17. 0.036 19. 1 2, and D 5 3 , and A 4 3 y y Y R 23. yes 25. no 27. 5 29. 65 One possible answer involves two rhombi with different rhombi with different two involves answer One possible angles. 19. Lesson 7-5, pages 316–319 1. 4.5of similar triangles are in the same proportion as 3. 3.3corresponding sides. 5. 7. so RW similar, given; 3.2 definition of altitude; Altitudes 9. triangles are The given Review and Practice Your Skills, pages 304–305 Review and Practice Your 1. no15. 3. yes 5. yes 7. 24Lesson 7-3, pages 306–309 9. 51. 11. 12 ft 10011. 3. 13. 0.5 m 1.25 cm 180 Columbia, about 1 13. 5. 10 mi 40 mi 15. 7. 18 mi 32 mLesson 7-4, pages 310–313 17. 9. St. 1 in.; Lawrence, m 7.5 1. no both the pole for angle with the ground the same size form 3. yes;and tree. AA Therefore, 5. yes; AA 7. of the sun The rays pages 314–315 Skills, Review and Practice Your 1. km 240 11. 3. in. 12.5 0.02 ft 12 ftby 13. 5. 40 cm 21. 52.5 mi AA yes, 15. 7. 15 mm 23. 5.55 yd no 17. 9. 4 ft 25. 1027 mi no 19. 18 ft 27. Chapter 7: Similar Triangles 7: Similar Chapter pages 296–299 Lesson 7-1, 1. yes13. 3. 2.1 yes23. 15. Sample answer: 5. 100 : 988 10 2 17. 7. 630 $900, $1200 19. 9. CDs 1400 no 21. 11.39. 7.5 lb no 49. 1 300–303 Lesson 7-2, pages 1. yes 3. 100 5. no 7. 6 angles are between corresponding sides.angles are between 11.13. 4.5 in. 3 : 4 15. 7 of 23. 17. 53. 6 31. 6 33. 960 cm 35. 29. about 8 h are not writtenratios in the same order. The correct 31. 54¡ 36¡, proportion is either 33. The terms in the two both right angles, similar by the AA Similarity Postulate.similar by 9.1 Yes; because angles. applies. The AA Similarity Postulate 11. always 13. sometimes 15. 2 5 10; 142.272 4 4 1 12 5 y x 1 4 2x x 2x 50 15; 1) 37.1) $1.25 41. 25; Mario, y x 11 y y y y 21. x 23. should sell 15 They and 10 sweatshirts. T-shirts 25. Plant 1100 acres of Iceberg and 2500 acres of Romaine to yield a profit of maximum $845,000. 27. 29. 25.5 31. 23. 25. 21. 15. 29. 7 m 13 m by 31. (3, 4) 33. 78¡ and 102¡ 35. (3, 39. (2, 40 Danielle, 17. neither 19. 45. 15 47. 22 x x x x 100 x 4 2 (0, 6) y 50 y 4 2 4 2 y 2 4 4 2 y 4 24 24 y 28 at (5, 3) 2 22610 4 4 50 4 100 0 cars and 75 planes gives maximum profit of $2625 Max P 13. 1. i 3. e 5. l 7. a 9. j 11. Chapter 6 Review, pages 286–288 Chapter 6 Review, 9. 140 at (5, 15); maximum 60 at (0, 10) minimum 11. 2); 26.5 at (20, maximum 3 at (0, 4) minimum 13. will region that the feasible insure These constraints quadrant.be confined to the first This models constraints world. regions that can occur in the real and feasible 15. (0, 8), (4, 0), (0, 0) 17.19. 12 at (0, 6) minimum Lesson 6-9, pages 282–285 Lesson 6-9, 1. no7. 3. yes 5. (15, 0) 225 at maximum 43. 27. Selected Answers 766 length isisosceles,Theorem, thetriangle sobothlegshave BytheBaseAngles for thethirdangle. leaving 45¡ angle, witha45¡ triangle Mingformed aright Yes; 5. .253 .31.8613. 8.6 11. 3 19. 7. is isosceles. 6 3. 15. 2.5 1. Lesson 7-6,pages320–323 RX 1. Lesson 8-1,pages338–341 10.5 15. no Chapter 8:Transformations 13. yes 11. i 9. b 21 7. 21. j yes 5. 19. e 12.5c 3. 17. g 1. Chapter 7Review, pages328–330 aproportion, Shecanwrite such as 3. Answers may vary. 1. 4.5 19. 27. 46.5m true 37.4in. 9. Lesson7-7,pages326–327 17. 25. 20in. 130¡ 33 7. 15. 23. 27m 21cm 5.12 5. 13. 21. 6ft 4in. 3. 11. 24.5m 1. Review andPracticeYour Skills,pages324–325 2and10 modes: 9.5; median: 10; mean: 25. .(.,85 .(,2 11. (1,2) 9. (5.5,8.5) 7. 7 0c 9 e,A 1 . 3 483.10 35. 24.8 33. 3.8 30ft 31. 39. yes, AA 4.0 29. 37. 10cm 27. have You now ofsimilartriangles. are correspondingparts WX:KB 13. 6.125xy 11. of similartriangles. Selected Answers G : G BE AB WRX 44 33c 15. 33.3 cm Sotheheightoftreeisa b. 1 D F D F w 3 17. Congruent base angles mean the triangle baseanglesmeanthetriangle Congruent 17. WR:KA, becausethey arecorresponding parts RY RY 4 E E 2 4 6 8 2 1 E y 8 0 : KAB AL and solve for 2 D F 2 5 7 , 1 5 G RW RW 1 x ySSSmlrt otlt.Then, by Postulate. SASSimilarity 3 5 , : 3. line ofsymmetry. opposite side, theline isa onthe image ofthepart side ofalineisthereflection ofthefigureonone Ifpart 5. 21. 3 AK. 4 3 2 1, w, thewidthofpond. 1 3 6 9 R 10 , 7 19. 6 17. 3 25m 25. 52.5mi 23. 1 1, 16 , YW 1 1 4 0 3 A, becausethey : 3 0:36 20: 13. XY b. 2 3 23. , 2 3 7 3 , ZW 2 5 7 2 3 , 3 4 4 1 : XZ 5 3 in. .1.1 19. 10 23. 17. corresponding slopesis1. Triangle 8 13. theproductof product ofcorrespondingslopes is1; Triangle the 5 Theslopesofcorresponding sidesareequal; 11. 15. Triangle 6 9. 5. rotation. thesecondwas a180¡ rotation; Thefirstwas a90¡ 3. 1 Lesson 8-2,pages342–345 7 h lpsaeeul 9 52.1 3 2 23. 18 21. 27. 15 4 19. 25. Theslopesareequal. 17. 15. 11. 9. 7. 64 H 5 6 (9, 1) E 2 4 6 8 8 A A 2 4 6 A 42 y

y (2, 7) (1, 4)

= (6, 4) y C

25. x 2468 6 B K D A 2 246 1 F (5, 6) 4 I 9 31. 5 29. 2 B 6 4 2 B D D (5, 1) 2 4 6 B 3 2 D C (2, 4) y 2 C C (1, 1) F J x x 4 2 7 neie lp 29. undefined slope 27. 2 4 slope side H H 13. y (1, 1) 2 7. (4, 4) E (4, 4) 6 K x K 468 thecorrespondingslopesare ; 2 4 BB AA CA BC AB I I A CB 2 1 (5, 1) equal. (5, 1) I (8, 4) (8, 4) 33. J J 4 x 3 1 A y D F 32 , C C B x G 7 1 B , B 4 3 H 21. BC , A 3 I 7 6 C A 3 1 Selected Answers 767 x 24 y 4 2 2 8 10 2 x 4 R’’ 6 Selected Answers S’’ y x x x B R B 20 B’’ 10 Q’’ C Q x A A’’ P’’ y B’’ S P’’’ 7. y x 24 y x C’ B’ C’ C’’’ S’’’ P 21 D’’’ x Q’’’ A A’’ B’ y 27 y C A’’’ R’’’ 3. 4 times as long A’ 23 29 y A’’ A’ C’’ R’ B’’’ D D’’ B’ C D Q’ C 19 25 A’’’ A C’ S’ 28 C’’ AB B’’ D’ P’ B’’’ B 246810121416 y 8 6 4 2 12 10 2 5. 17. 19Ð21. 23Ð25. 27Ð29. 1. square Lesson 8-3, pages 348–351 x L’’ N’’ y x y x 10 K’’ x K’ x B’’ M’’ F 9 C’ x y M’ y x Q’’ Q’ 14 D S’’ S’ S 7 NN’L’ B’ 13 A’’ M F F C’’ y A’ 1 2 M’’’ L E E 5 E C K A’’’ P’ PQ P’’ y R R’ R’’ 15 B’’’ D y D A R’’’ P’’’ K’’’ D 11 6 E 3 C’’’ B F L’’’ N’’’ S’’’ Q’’’ 13Ð15. 9Ð11. 5Ð7. Review and Practice Your Skills, pages 346–347 Skills, pages and Practice Your Review 1Ð3. Selected Answers 768 1 e;dmi:{3, domain: yes; 31. Lesson 8-4,pages352–355 9. .Scalefactor: 9. 5. 1. Review andPracticeYour Skills,pages356–357 1. 5 e 7 e 9 oain2.A 3 SAS 23. AA 21. rotation 19. yes 17. yes yes 15. 13. Possible answers aregiven; 11. reflection over y-axisandtranslation 5unitsup Answers willvary. 9. 5. Selected Answers 10 12 16 4 6 8 2 0 2 0 4 8 10 12 66 66 2 4 6 8 y y y M E 44 44 2 2468101214 4812 B 2 2 46 6 4 2 6 2 4 6 2 4 6 G ML y y F JK 2 5 1 2 8 ; Center ofdilation: C A 10 16 H ,2 } ag:{2, range: 2, 3}; x x x x x the right. and atranslation 8unitsto reflectionover No; 3. 7. ag:{ 2, range: yes; 29. {2, domain: 81m 102km 25. 27. 60km 54m 21. 23. 48ft 19. 4 timesaslarge; 6squareunits; units; 96square square units; 1 .51.31.24 17. 3 13. 1.25 11. 7. 3. 66 E 44 -2 F(5, 0) B 10 2 -2 0 2 6 8 4 6 4 y 2 4 6 2 4 6 0246 8 2 y 1, 0,1} y G 1, 0,1}; 2 1, 0,1} 46 F 4 1 x-axis as large x 8 A C 10 x H x 3 P2.N 27. NP 25. NP 23. 3 3 13. 23. Answers willvary. 21. 11. 27. 7 23.75 39. 12 37. 33. BA 3 1. Lesson 8-6,pages362–365 19. 15. 3 1. Lesson 8-5,pages358–361 31. 5 cl atr ;cne fdlto:origin centerofdilation: 3; Scalefactor: 25. 17Ð19. clockwise rotation90¡ reflection acrossx-axis; Sampleanswers aregiven. Answers willvary. 15. 11. Q’ x A(BC T R’ 4 13 pget 330 150 70 1 1 1 Spaghetti Whole milk White bread 17 aoi on 010330 150 70 Count Calorie evn 1 1 1 Serving 43.2 43.105. 6 14 26 5 1 15. 3 2 1 2 Q’’’ Q 3 ) 2 875 894 P’’ , P’ 3 8 13 1 y R R’’’ y 0 (AB S’ 18 5 3 y 19 31. 2 R’’ 965 930 2 5 11 )C S’’ P’’’ y =x .N .N .[6]1.NP 11. [163] 9. NP 7. NP 5. 4 P AI 1 29. 7 P1.1 19. NP 17. 1 13. S’’’ S evn Calorie Serving 5 0 ra Milk Spaghetti bread Whole White x 1011 45 R 17. 969 13 12 x 1 21Ð23. 3 10 9 3 0 10 13 11 S 3 4 4 4 33 13. 5 2 980 949 7 16 11 1 1 ; .2 7. 3 4 IA S Count 3 C’’’ -10 0 5 2 13] 11 [20 25. 11 3 5 11 35. 1 33. 29. 9 R -8 23 39.5 7 4 1 22 B’’’ AB 1 [28] 21. 2 B’’ 3 -6 A’’’ C’’ A 10 5 2 -4 A’’ 4 y A’ B B’ C -2 11 11 7 3 2 -4 -6 -2 21 4 2 0 ;yes y 10 x 4 C’ x Selected Answers 769 x 3 x 7 4 4 , M’ 4) C M 1 2 4 7 5 3 1 L’ L y 15 7 6 4 2 2 4 6 x, (4, x, (4, 2) 2 2 11 3 B’ C’ N N’ 4 Selected Answers 24 68 11. 20 y 6 y A’ AB D 62 9 6 4 2 4 D’ 5 14 2 1 1 4 1 13. 6 17. 3 4 y-axis 25. center dilation with 25. 2 x 2 4 x 15. (4, 4), line 17.y (2, 4), line 3 23. C’ 4 15. 0.75 17. 0.75; 375 19. Of R’ B’ B 4 8 x 12 9. 1 3 29. 7 4 7 3 12 y 6 , 18 4 3 S’ R y 4 2 2 4 4 7 3 7 15 QS Q’ y 16 4 2 13 10 6 4 2 2 4 6 A’ A 3 1 7 3 8 20 424 2246 2 D’ 2 1 28 DC , 3 33. 14 7 2 1 2 19. yes 21. at origin and a scale factor of 2at origin and a scale factor 27. c; b; a 29. Chapter 9: Probability and Statistics Lesson 9-1, pages 384–387 1. 0.7vary. 3. 20 times 11. 1), 3), (C, 2), (B, 3) (B, 1), (A, 1), (A, 2), (A, 3), (B, 2), (C, (C, 5. 13. 0.18 7. 0.55 9. will Answers 27. 31. Advanced: $326, Beginning: $490 7. 13. 372–373 Lesson 8-8, pages 1. A: $1602.50; B:B: $1748.25; $571.25; C: C: $2344.50 $586.2511. 10,080¡ 3. 5. A: 6300¡ $465; 7. 4860¡ pages 374–376 Chapter 8 Review, 9. 10,800¡ 1. k11. 3. f 5. e 7. i 9. g 15. 19. answer: Possible then translation x-axis, reflection over 4 units right 21. 3 23. past days when weather conditions were similar to those conditions were when weather past days of the time. 25% it rained tomorrow, predicted for 21. experimentally 23. theoretically 31. 2 54 13 19 2 4 1 19 3 7 7 12 22 7 3 91 5 y 2 73 17. 0 y 8 1 9.5 66 1, 4 55 1; 12 51. 2 9 5 20 1 5. 20 70 7 18 x 1 9.5 16 11 3 34 3.5 5 2 50 23 x 8 5 68 Rotation 3 0 15 29. NP 31. 39. 8 37. 12 16 6.5 8 Translation 4 3 10 10 4 8 3 43. 57. 8 4 4 9 3.5 4 x 7 14 4 3 23. 3 22 49. 3. 7. 62 42 15 A’’ B’’ 2 4 5 20 5 3 0 1 11. 15. y C’’’ 119,500 309,000 B’’’A’’’ 1 3 1 0 650 290 62 5; 58 50 2 C’’ 78 12 63 34 27. , y D A’ D’’’ 2.4 Rotation 5 3. Translation 0 2.4 63 17 1 2 C 55. 3 41. 16 12 1 D’’ 61 x D’ 70,000 35. 4 8 21 0 181,200 B’ 0 0.4 9 C’ y 47. 1 B A 5.5 6 3 3 6 18 15 y 122 166 38 14 9.5 3; 1 8 14 26 , 1 3 0 1.2 4 21. 1.5 8 0; 0 1 24 11 12 90,200 22 2 1 233,400 10 45 25 28 68 84 68 1 0 4 276 168 2 4.4 3 12 15 x x 9 7 4 25. 41. (1, 3) 43. (2, 3) 45. 5) (6, Lesson 8-7, pages 368–371 1. 67. no affect 65. yes; 59. 61Ð63. 53. 45. 33. 39. 13. 9. 5. Review and Practice Your Skills, pages 366–367 Your Review and Practice 1. 37. 35. 19. 2 Selected Answers 770 fet h te.27. affects theother. events canoccuratthesametime, but neitherevent Independent exclusive events cannotoccuratthesametime. ay .Aseswl ay .Cag ie4t:“IF Changeline4to: 7. X Answers willvary. 5. Answers will 3. vary. 1:5(18ofthe90possible numbers) 1. Lesson 9-2,pages388–389 25. 29. 15. 1. Review andPracticeYour Skills,pages400–401 33. 15. 1. Lesson 9-4,pages396–399 11. 1. Lesson 9-3,pages392–395 29. 15. 23. 1. 17.5 21. 15 19. Review andPracticeYour Skills,pages390–391 0 17. undefined 15. ubr.2.0543.4033. 400 31. 0.594 12isamultiple ofboth 37. 29. SampleAnswer: 27. numbers. 21 25. 3 )(,H;(3, T) (6, T) (3, H)(6,H); (2, T) (5, T); (2,H)(5,H); (1, T) (4, T); (H,H)(T, H)(H, (1,H)(4,H); T) (T, T) 37. 39. Answers willvary. 35. Selected Answers 5 4 3 1 4 1 3 5 2 8 4 1 0 9 00041. 10,000 39. 500 8 3 4 1 9 2 9 2 3 2 .4 THEN 44 2 0 31. , 400 3. 17. .15. 1 3. 3. 13. 31. 17. 17. A 2 A 3. 2 1 7 3 C 2 1 D 4 4 8 9 2 6 1 2 1 3 1 1 7 1 4 92 1 8 y 7 S y C 0 C 2 5. 5. 19. 5. 15. 19. 1 2

33. 19. 2 7 3 5 S 1 B 1 number ofpiecespaper 2 20 7 3 B 2 1 B 5 4 number ofpiecespaper 3 1 3 Answers willvary. 33. x 7. A 1 2 6 1 1 1 ”9. 1” 6 0 1 21. 4 7 19. 1 17. 9 7. 6 7. 1 4 27. 21. 3 35. 21. 5 1 1 29. x 3 6 1 3 6 9. 16 3 7 4 1 9. 2 1 6 1 6 4 1 3 2 23. 2 2 9. 1 2 7 6 1 13. 3 11. 2 P P S S 3 23. 23. 6 5 37. 6 1 1 5 3 1 3 11. 5 6 y 6 2 5 2000 35. 320 11. 5 1 2 5

9 5 8 R 21. Q Q R 11. 2 8 25. 8 3 1 61 0 1 4 2 5 Mutually 25. 25. x 0 1 2 1 0 13. 8 3 6 1 7. 39. 2 1 7 9 4 1 3 0 23. 13. 13. 27. 3 1 1 5 6 9 25. 27. 2 2 7 9. 2 6 1 2 5 3 3 5 3 1 6 6 3 3 2 2 1 6 1 fies 23. They equalthetotalnumber of items. 21. They arethesame. 19. 7 os3.does 39. does 37. Divide 7!by 2! 17. Yes, whentherearedatavalues far from the median. 15. 10points Sampleanswers aregiven; Answers willvary. 7. scatterplot 13. above 25%. Thereisagreater range ofbatting 5. 11. averages intheupper25%ofitsplayers thaninthelower 67Ð68in. Artichokes 3. 9. about130lb 1. Lesson 9-6,pages406–409 30 7. 32,760 permutation; 5. 11. 20 combination; 15,504 3. 9. 120 1. Lesson 9-5,pages402–405 61. 41. .j3 .c7 .g11. g 9. b 7. c 5. f 3. 17. j 1. Chapter 9Review, pages416–418 2 8; 3. 0 0; 1. Lesson 9-7,pages412–415 31. Answers willvary. 29. positive 27. 9 23. 1 210 11. 21. 10 3003 9. 19. 17,297,280 6840 7. 17. 840 15 5. 15. 25. 4 8 3. 13. 60 1. Review andPracticeYour Skills,pages410–411 1 27. [11] 25. one. Theright 23. Theonewiththehighermean 21. totheright. is farther Answers willvary. Answers willvary. 17. 19. Answers Answers willvary. willvary. 13. 15. 256; variance: 30; mode: 16 40; standard deviation: median: 38; mean: 11. ueostms 21. numerous times. Repeat theprocess or notallnumbers arerepresented. Record whether select numbers from1to3five atatime. Usetherandom number generator torandomly to eachtoy. ilvr.51. Answers will vary. 49. Mon., Tue., {Sun., Wed., Sat.} Thur.,Fri., 47. 2 4 3 1 9 2 6 4 3 28 36 Value of house (thousands) 5 140 150 160 170 180 190 200 1 9 osbease:Assignanumber from1to3 Possible answer: 19. 32 43. 1 2 3 4 5 6 7 8 9 10 1112 13 171920 1 23456789101112 141516 18 4 9 8 1 2 2 2 2 1 3 61 0 2! 20 1 8 53. 4 7 2 1! 45. {HH, HT, {HH, TH,TT} 45. 13. .2; 5. 57 Age ofhouse 7 8 3 9 1 5 1 7 141¡ 27. 51¡ 25. 1! 15, 23. 55. 2 14 46 1 600 !1.8!or40,320 17. 1! 9 5 4 3 7. 9 58, 29. 5 20 Sampleanswer: 1260; 15. 25. 57. 3 1 0 0 215 60; 1 3 1 2 3 15. 1 13. 00 1 94 4 1 27. 59. 33. 8 1 99 .2310 9. 8 5 1 9 120 29. 00 5 2 5 0 35. Selected Answers 771 2 m; 4.2 m and 2 4 x 29. mm 19.8 ; 2 C 11) 9. (3, 5) 3 Selected Answers 0 12.5 19. 6 cm C 18 48 64 34 56 15 43 1 14– 101 5–13 6 21. 1 23. 5 7. (6, 2 Under km 13. 44 in., y 19–25 : 2 3 25. 352.99 ft 65 Over 5, 7 84 76 32 11 x represent the measure of the represent Under 5 5–13 14–18 19–25 26–39 40–64 Over 64 26–39 ft 17. 46 19. 125 150 2 ; can represent the larger angle. can represent 40–64 x 25. 4 x x 19. 6 Since the triangleSince the 30¡-60¡-90¡ is a length of the side triangle, the 30¡opposite the half the angle is length of the hypotenuse. 0 6 km, 203 3. 1 2 1 2 by AA similarity. by ft, 42 1 2 Persons 3 Persons 4 Persons 5 Persons 6 Persons 7 or more in.; 14.1 in., 14.1 in. 3. 3 2 23. 17. 2 82 20 25 41 29 16 25 6.5 17. x) 123 23. 186.5 in. 3 6 9 1 1 Mortgage CAD 2 6 Misc. Food . 4 0.5x 2 y 5 cm, 22 cm 7. 5 in., 10 in. 9. 18.5 ft, in., 10 CD 21. 15. 13; ft 11. 103 3 2 6 45 30 45 0.5(90 5 Car in. 15. 42 E, because both are inscribed angles that 67 4 3 3 4 3 1 1 2 Mortgage Food Car payment Utilities Credit card Transportation Savings Misc. x 2 CEB Savings Credit card Utilities Trans- portation x x x 19. 1.5x 27. 442 31. 11.0 ft 18.53 A intercept Lesson 10-6, pages 448–451 1. 315. 3. 3 5. 30 7. 6 9. 10 11. 12 13. 9 cm 1. 10 Lesson 10-5, pages 446–447 1. 5. 15. 9.5 msmaller angle. Then 90 17. Always; x for this equation can solve You let 440–443 Lesson 10-4, pages 1. 140 the then intersect inside a circle, secants (or chords) 3. 49 one-half the is equal to formed measure of each angle 5. arcs.sum of the measures of the intercepted 50 7.13. 40¡ 9. 50¡ 11. If two Skills, pages 444–445 Review and Practice Your 5. 11 25. 21. 124 23. false 25. 27. 4752 21. 2 m 529 2 2 11. 32 d 11. 6 7 21. 12 2 3 5. Because 21. 62 . yd; 8.5 yd m, 2 m; 1.7 m, 9. 28 h 4)] 2 ; Therefore, w 3 2 19. 157 or about 43.3 cm w (3 3 2 61. no 63. yes d 2 6 45. 2 47. 10,000 cm 27. 0.17 29. 0.155 y l 7. 5 41. true 43. false; possible l 5 3 5 m; Wat Kuhat Temple, m;Temple, Kuhat Wat 2 ) 7 2 2 3 72 47 y 17. 112 49. 51. 2 53. 24 11 4900 and )(18 27. 29. 4 31. 2 33. 10 cm; 14.1 cm 9. 2 2 h Basketball Team Ratings Basketball Team h 2 39. 34; about 5.8 5 2 2 and y 25. 27 27. 29. 20 31. 2.4 m w 2 15. 222 47. 210 h 2 in., 8 in.; 6.9 in., 8.0 in. 3. 62 57. 36 59. 2352 2 18 37. 26 m 39. 13.6 in. 41. 65 yd 43. 30 cm 40 50 60 70 80 90 l d 2 3 2 3 23 w 1 3 2 3, 4, and 5 form a Pythagorean triple, they formed a right formed a Pythagorean triple, they 3, 4, and 5 form triangle. 45. 26 33. Temple, Bakong 2 m 11.cm 10.6 13. 25 d 25. a formed the workers because The system worked triangle rope that had sides measuring 4 3 rope lengths, [12 and 5 rope lengths, lengths, 35. 13. 15. 4.58 17. 8.54 19. 9 Lesson 10-3, pages 436–439 1. 43 446 1. 7.2813. 3. 45 5.29 5. 31.62 7. 31.62 9. 5 Review and Practice Your Skills, pages 434–435 Skills, Review and Practice Your 1. 9.9 m9. 3. 7.9 cm 8.6 ft17. 11. about 4.5 yd 5. 11.3 ftbelow. about 17.3 ft 19. 13. 6.7 7. yescm 9.4 21. 15. Yes 6.4 cm 23. See the figure Lesson 10-2, pages 430–433 1. 3.32 3. 9.22 5. 2 23. 242 Lesson 10-1, pages 426–429 Lesson 10-1, pages Chapter 10: Right Triangles Right Triangles Chapter 10: and Circles 37. 18; 31. numbers 60 whole 35. 33. positive l 35. 3 37. 2 39. 7.5 cm counterexample (2 counterexample 5. 5.8 ft 7. 10 23. 25. 49. 140 Selected Answers 772 Review andPracticeYour Skills,pages452–453 3 23 23. 9 53.3 3 hc tdns circlegraphs. Check students’ 35. 33. 4%. 33%, andJapanese: 35 41%,French: 31. 22%,Spanish: Percents should beItalian: 55 29. 5. 1. .d3 .l7 .c1.3 11. c 9. i 7. l 5. b 3. 15. d 1. Chapter 10Review, pages458–460 17. 40in. 13. 7. false 5. Lesson 10-7,pages454–457 3 .,132.10.25,3.2 25. 1.7,1.3 2.9,1.7 23. 21. straightedge todraw adodecagon. Hecanconnectthese12pointswitha points onthecircle. Atthispoint,thereshouldbe12equallyspaced the circle. hexagon, thepointwherethesebisectorsmeet andmark bisectorsofeachtheothersides perpendicular the Thenhecouldconstruct a vertex ofthehexagon. radius equalto thedistancefromcenterofcircleto Hecouldusea their intersectionsasthecenterofacircle. bisectors oftwo different sidesofthehexagon, anduse Mike couldtake thecopy, findtheperpendicular 19. Selected Answers upgrade Repair/ Food Favorite FlavorofIceCream access Internet 2 Technology AnnualBudget 3 Howe FamilyBudget Strawberry Chocolate 19% 7 5m1.1. n 1 6 21. 13.1in. 19. 15m 17. cm, 43 36% Utilities Salaries Vanilla 26% m2.6ft, 25. cm Insurance Mint Chip Mortgage 12% Other equipment New Research Cookie Dough in thecircle. ahexagon Theninscribe 2 in. Draw acirclewithradius of 3. 7% Soccer Volleyball 1 e 3 no 73 23. 25. no yes 19. 4 21. false 11. true 15. 17. 11 false 9. 13. 4 7. 21i. 21in. 12.1 in., 7 m,27.6m 27. 2 5 Fall SportsAthletes 7 9 11 39. 2 37. 41. 43. 392 Lacrosse t2.62 27. ft 2 2 3 845 13. in., 21in.; 117 m Football Cross County 10.8 3 2 1 2(3a 11. 7. 17. 39. .11 7. 5 12uv 35. 31. 9 25p 29. 5 5x 35. 1 .64.1.04.154.4.36 49. 47. 175 45. 14.70 43. 8.66 41. 5.8bc 5 3x( 45. 9 2t 19. 7r 14x 21. 49. 5 36c 65. 7 13j 27. 45. 3x 3 9x 13. .2x 7. 31. 27. 11. 3xy 1. Lesson 11-2,pages472–475 814 51. 3v 25. 5x 1. Lesson 11-1,pages468–471 Chapter 11:Polynomials 3 7b(2ab 23. 3(2x 1. Lesson 11-3,pages478–481 13r 55. 8ayz 39. 31. 28s 25. 12n 17. 6x 1. Review andPracticeYour Skills,pages476–477 3ts 51. 2b 43. 9 12x 59. Cheetahs. Gophers, Keshawn, for theGoats, andLevon for the 3x 3 3xy 2 11 r s y 2 (7r 6 y(5x x A 12x x 18l 3m e p 4 5 y 8 y 2 a (n1) x t 3 4 h 2 9 2 2 y ( 3 z 2 3 2 3 b 2 (3a 5 3 3 2 6 2 4 5 13 k 2 f q 79. 10y 2 2 .12 3. d t 7xy 7xy 2 1 2 1 5m 21. 5 ) 3 4 13. 2 (3x x 9 4x 39. 3 1.7b 3s 5 2 b(6ab)2 w m n 8 3 h(t 20t 3 2(3ab ) l y 2vw 5x 6x 11x 7 2a 47. 2 32s 9p 3 )3. 3) g 3 10rs 3 5(3p 13. 4b) 6byz 3 4x(3 43. 2x (3j e 2 3 3.2 53. 3 2 19. 2y) 6x 7 12x 27. n 2 7x 2 3p pq 3 9a 23. 3 .16 3. 5 9r 25. 5c) 27c f 3 2 7 2 x 51. 8v x 2t 3 4800p 53. 3 19. kl 3m 17. )43. 2) b) 637. 16 2 2 y 1 3 6.3 33. 4 31. 5 19x 35. 3 3x qr .1 n tall,8figurines 18in. 9. ) 6 10w 4 ) 3x 7); 3 w n 5. 2 y 8x 13. 18l 5 8a(8b 35. ) 5m 5 d 11.7x 11. 21 21s 43.4 3(2ab ) x 20cyz 6x (5m x n 2 4 2xy 5jk 2 2 8y 9 15x 49. 4 2 3b(2ab)6( b(3ab) 22 in. 2 5 rs n(13mn 2 2 7p 10 ab 2 5 5a 15. 3 m 23. 4v 61. 9. 3 2 3 25. x 2 9 8e 29. ) 12x 7); 30x 4x 2 6 10 4p 7 6b 27. 2 5 17c 15. xy 2 2 2 3 n 57. 2 2y q w 2 (2r .7x 7. np)5.6 x 2xz 2n x 16p 21. 5 4l 4 1 3x 41. 2 18x 6x 2 4 2 4 )6( 132 6x 5 Jarius plays for the 55. 3 ab 4 y 3 2xy 33. 15. 7q) 4m 29. ) 3 75. 2 3 4abe 33. q 9 33x 29. 2 xz 3 15ax 33. 2 7 7r 37. 42m a 2 2 2 2 f 2 05 6x 5. 10 4 3) 22x 1 60hk 41. 12p 5 21. 25) 4 ab 3 2 2 7 12x 37. qr 15x g 15 15x y 7 25x( 37. 5c) 9 3x 19. 6a 2 2 4 28x 21x 2c 20p 3 31.2x 17. 13 y ) 7x x(2 4x 2x .94.$2.17 45. 9.19 4.2a 430 17cd 2 9 xy(ax a 3 5 2 2 (3x z 4 53. y s n (6b 1 4x 11. 1 3 5 63. 3y 23n w(v 8ef 10 2 15. 2 2 4 9. qr t 15 7 11b 47. 3 2 4 5 3 2 2 3 9k 23. 5xy 2 5 b 22x 2 y 4a )2 10bx 2 3 6x f 3) a 2abf y 15x 7x g 2z 180h 6x 4 2 6d 4 3xy 4x 7r 12p x) 3 4x 2 11 2 2 2 2 4 3 3 a y 6 2 s y y a bxy ft (3b 2 y 3 5 11x 10 3 20cx q 2 24b t abg 2 7x 28x 3 z 4 11 2y) 2 9 ) 2xy 2 2 c) Selected Answers 773 2 xy 2 k) 18 18 ab , 1) 3 )(h b) y y 18 6x j 2 3 and 6)x 31. 7) b 3) a) 21. 9, 7 bx 2q) 2 9v) a 6)(c 10) 2z) a 6) 3 3x (3 3x 1) 11y) 6)(x 5) 12) x 2) 39. 3xy(x 4) v) 3 ) 45. No. Only Selected Answers , 16y 3 4) a a)(1 8g) 4)(3x 3) 2 2 2 x 4r 2 1) 1) 69. 5x 3 x x x c)(x ) y a 2)(x 29. 2 10)(x 2q)(7p 3) 5. (2 3 2t 5)(x 9v)(4u 2 y 3 1)(4g 2)(3y 3)( v)(w 19. 5b, 2b 3 2x 1b. (x 3b. will vary. Answers 2g 12)(k 12)(w ) 4)(x )(s b 2 yz 2 2 3g)(f 2 y 3) 13. (c 11y)(15x 2t y 1) (x 2 3)(2z 2 1)(6b 2 2 , b c)(b 5. 6 and 1 7. b 2 (d x 30x 2 2 x(x ) 77. (w x xy n 2 n b 2 2 1 27. 1 2x a 2)(c ) 29. (x y n y)(x 11n) 49. (1 n 2 3z) 25. (x 2 4ef y ab ) ) 45. (7p 17y b 2f z ) 41. (4u abxy 1) 53. 3x(x ) 49. (6g 7y) 2 abxy 7t by ) and 2b 2) 61. y) 21. (3x 1 2s) 17. (1 )x 2 3d b) 65. 4xy 4q) 35. (k 2r y x) 13. (2x 2) 57. 4y) 37. (w 1 2 b 2 )3.( , 2y n 2 24) 39. (f 7) 43. (s 2) 9. (w 7) 17. 7y, 5y xn x n (g d 2 14xy bx 2 73. 3 11. (c 2) 73. 2 29q 2)(a )(1 25. )(ax )(5s )(a 2 a y abxy 2abxy )(c 2 2)(x )(1 11n)(8m )(x b)(a q)(r 7y)(2x 2)(x z 1 by 7t by xn (n n)(w x 4)(x 2 6q)(p 1)(h 4)(q 7a) 3r 3ay 3)(x 4y)(x 3d 3)( n 2 2 3 2 2 b)(c 2y) 41. (x y (a x x 2 2 (k 2 2 2 2 2 and FOIL FO I L L FOI x 2 x a a 1, 2; 2; 2, 1, 3; 3, 2; 3; 2, 1, 4; 4, 2; 3, 3; 2, 4;1, 5; 5, 2; 4, 3; 3, 4; 2, 5;1, 6; 6, 2; 5, 3; 4, 4; 3, 5; 2, 6;1, 7; 7, 2; 6, 3; 5, 4; 4, 5; 3, 6; 2, 7;1, 8; 8, 2; 7, 3; 6, 4; 5, 5; 4, 6; 3, 7; 2, 8; 8, 3; 7, 4; 6, 5; 5, 6; 4, 7; 3, 8; 8, 4; 7, 5; 6, 6; 5, 7; 4, 8; 8, 5; 7, 6; 6, 7; 5, 8; 8, 6; 7, 7; 6, 8; 8, 7; 7, 8; 8, 8; y 5a. (ax Lesson 11-7, pages 498–501 1. 3 and 7 3. 4 Lesson 11-8, pages 502–503 1a. (x 43. 1, 1; 2, 1; 3, 1; 4, 1; 5, 1; 6, 1; 7, 1; 8, 1; 45. 0.1875 47. 0.5 Skills, pages 496–497 Your Review and Practice 49. cm 10.5 1. (5 2y)(x 71. 16x(3x 79. (2x 3a. (ax 67. 6x 15. (p square trinomial; 100 37. 5s(s 11. (m 19. (x 63. 4(a 55. 27.5%63. 57. 99¡ 13% 65.71. 59. 46.8¡ 10.5% 67. 61. 37.8¡ 6.25% 69. 22.5¡ 33. (p 23. (w 9. 75. 2s 37. (h 7. (y 23. 10f, 3f 15. (x 41. (q 27. (2 51. 5x one pair of factors will satisfy all conditions. one pair of factors 47. (1 31. not possible 33. (6 35. (x 39. (c 47. (8m 43. (5s 55. 3(x 51. not possible 53. (15 59. 3a(x ) ) ) r 2 2 3 2 s 3 1) ) 2 q 2 m 7h) 2 2r 4 y 15f 2 3 54n ) b 5s) q 40x y 2 p) 3 2x 23ab 66x 12p 2 3 mn )(6r 6a ft n s (x 2 4g fg 2 6) 2 2 4 2yz 4n ) 6 1 4 p 9 3 or a 2 52x 2 2 2 2 2 (3rt 2x) 5q 4) ) 37. 2.4 2 ) b r 2 lm 51mn qr 6) 7. none 9. )(2x 3 25f 3x 2z 3 2 2t 2 2 y 3d) 16z 3t a 2 2 ef k) 9 1 51. 64p 8 4a 18s 2 5 3 0 7 30x 2 24x 3w 35. 25x 2 3 20p 5e)(2f 39. 3a ln 5mp 1 17x 2y 10k 15qr (2mn m 7 7) 2 4) n) 2 15 4 (2 2 2 12 47. 2 3 3 6)(3r 2v)(3u 67. s)(r 2 n r 8wz y)(3x a 2s)(r 1) 17. 18p(pq y 2 59. 6.2 in. 2 2 3 31. 30x 2 l 3 6 24z) 11. 5x gh 3) and (2n 4 1 2 q 4c)(2b x 8x) 35. It is a perfect x 9 45. 8y 21. 5 4 2p 1 2 5z)(v 15. (2x 2 25mn 3. 2 43. p 37jk (r 2 11x 20x p 15xy 8 4x 2c 2 17y 17. 2eg w m)( 24 4 35. 4e 2 25g) 77. 15rst a 4 xy 2 59. 2 qr 53. 3 6x ) 85. 16x 16 7 5. (3r 6 2 b (17x b) 81. 2(4x 2 2 29. 2 2 49. 81x 89. ) 31. (3d 2 15) 5. 2 2 25 55. 8r 2 29. 2 2q k bc 3 2 ) 11. (y 8x)(y 2 y 2 71. 32 28 10bd 3 3 ) a 4t ) 43. 50 45. 50 47. 55 2 ) 25. 18m 20np b 2 3y 3) or (m 4a 5t 14x 2 12 2 ) 15. (4q n 2 9x y 15d 4 g(12 2 2 a v 4 1) 3c 5n) 23. (5t y ) 11. squares; of two the difference 2 ) 35. 3r z x 5c 3d ) 27. (y v 2) 29. 4mnp(2 2 10pq 3 u 2 5 ;( 35q 2z)3.(9 ab x(7x 3 z 2l 3s 4h) 19. (9w 2 3) 65. 7b )7.( 2bc 8s 5pq )9. 8 25. 7j x 2 2 19. none 21. none 23. (6 57. 7b 2x 36 43. 64x 53. 15 7.120 8x 13. 6pr 5m 8t b 3 16 33. j 64x 3s) 21. 2x(2x 51. 396 cm 5 39. 9x 53cd uv 6 33. 2x 2 9) 75. q 2 )( 2b) 15. 5b(a b)(2a 3. (m 11a 3 45. 2y 2 18y 2 2pq 37bc 27pr k 3) 13. (6 15x )(8u 6) and (n xy 30 40 30 7ab x p 3 12ac 10x 11) q)(2r 3c)(2b g)(7f v 3y) 3. 3m)(2l 8)(3y 2 (6a 5)(2x 2 2 (t y 15ad 2y)(3x 8x 21x 22x x 4 64q 3 2 x y t 3)(s 3n)(3r 2 2 b 2 2 5 5) b 4 20 15 47. 2 3 41. 2 2 2 2 (2j 13x 25 2 2 2 2 3)(p 33. 42c x x 56 51. 2 53. 12 55. 6 x 3 2 2 a(28bc 1 2 p 21. (k 128pq 27. 2abc(3a 79. 8a Lesson 11-6, pages 492–495 1. (s Lesson 11-5, pages 488–491 1. (3w 57. 1. 4(2x Review and Practice Your Skills, pages 486–487 Review and Practice Your 55. 49. 143 in. 23. 3x 27. 24b 31. 37. 5x 11. 19. 45p Lesson 11-4, pages 482–485 Lesson 11-4, 1. 3ac 19. 15s 69. 20x 4ab 30b 73. 6( 31. 13. 12(3a 17. (10r 61. (7x 45z 39. (2m 23.(1 3uv 9. (8u 25. (x 16 37. 4mp 87. 48p 63. 25. none 27. 4( 83. 49a 41. 2p 41. 3a(2a 49. 2 7. 5. (5r 29. (5p ( 5. 6x 15. 4a 9. (m 33. 3j 13. (2a 17. (3e Selected Answers 774 xmlswl ay (n examples willvary; 3 (48 43. 9 (f 39. 5 (p 35. 1 (b 31. 17, 11,7,4, (72 95. 9 (ab 99. 7 (p 27. 1 (b 91. 1 (5r 41. 3 (d 23. 9 (a 19. 7 (x 87. 7 3x(2v 37. 3 (m 13. 3 (x 83. 3 (2r 33. 9 (3x 29. (x 7. 9 3 ) 3 ) 2 ) 2 )2.(,1;(,6;(3,1); (4,6); (4,1); 10,15,16,24 21. 23. 17. (2,5) (3, 6) (2,1); 6,2,15,5 (3,5); (3,1); 15. 19. 3,12,1,4 13. 9 (a 49. 3 3a 33. 5 (x 75. 5 18x 55. 37. 16x 9 11x(1 29. 9 (x 79. 7. 5 7s(m 65. 3 (1 53. 25. 9 12d 19. 5 57. 55. 5 66.64 67. 16 65. cefcetmlile y1 .81.3.51.3 13. 1.8 34.75 17. 11. 4 8 15. 9. as ay-coefficientmultiplied by 1. Inasingle-variable thinkoftheconstant trinomial, True. 7. 5 (5r 45. .(x 1. Review andPracticeYour Skills,pages504–505 (3x 5b. 1 20v 41. 7 11. k 9. a 7. g 5. c 3. i 1. Chapter 11Review, pages510–512 239 45. 5. (5,3) (5,4); (2,3); (2,4); 3. 3,18,1,6 1. Lesson 11-9,pages506–509 16x 59. (ax Specificexamples willvary; 49. 3 13a 13. Selected Answers y ; 2 2 m 32x 78 27x 2 6 2 2 2 71. 1 nwr ilvr.5.5 53. Answers willvary. 51. b(3a 2 4)(x 6)(x 3 3 2)(f 12y f 14)( 5)(a 11q)(p 2 4c)(b 12q)(p 24)(b 8)(d 8)(a 3y)(1 9)(m 2 1 4x(4 61. .(f 9. 9)(r 3s)(10r 2s)(t 5)(8z 1)(9x 4n 4)(7x b x)(1 m)(1 3)(ab y 4y 3b 30f ; 21. 2 2 13vw 7 24.6 49. 12 47. 9x )(x w)(3v )(a 4x 2 x 4w 2 )9 (w 9. 5) )3 (d 3. 1) 4 1 (c 41. 24) 2 6b 24k 2 7 6x 57. 59. 8 5 3x 15. 56x 9 4r 39. 2b 1 4x(3a 31. y) )2.(m 25. 7) )2.(p 21. 6) 2 2 )4.3x 43. 2) 7, 10 )1.(c 15. 6) 4 5 (4a 85. 14) g)(7f 5 (x 45. x) 3 (a 33. c) 5 (9m 55. 3y) )9.(f 93. 3) 7 (2x 47. 4u) 12y 7 (p 97. m) 7 (3 77. 11b) 3x )3.(z 31. 2) 25. 1 (d 51. b) 7 (x 37. 7q) )11 (x 101. 1) 9 (r 29. 5q) 3x 8 2 5 (8m 35. 5s) 21w 131f 9y y 2b 1 11, mi 9 (2x 39. 2w) 9 (5m 89. ) )8.(13 81. 7) 1) 2 3 5 63. 15) 2 ; y 2 3 2 52.2x 23. 15 67. ) 9x 2 35. ) 2 761. 17 112xy 1 (6x 11. 3g) x)(n z 2 35 6x 17, 12rs 2 3)(w 3 (3a 43. 87.(w 73. 18 6)(d 1 2 48xy 3d 27. 9)(p 5)(c 3x 8g)(f 6n)(m 2)(x 9b)(a x 3 x c 4)(2z 8)(d 3e 27q)(p 28, 2 )(c 7 2 s)(r x) 7 3n 17. 3 5b 1 630 51. 6)(x 8)(x b)(a 4n)(9m ; b 6m)(2n 9s 7 27x 27. 2 )1.(x 11. 7) )(4a 2 )5 (x 5. 7) z 63. 8 11n)(5m 1 10 n x 20x 3)(8m a)(13 2 (3df 2 4) 10c )1.(t 17. 4) 1)(x 2 4 7 Specific 47. 24) 59 y)(bx n 9g) 5b)(2a 16d 8c) 2b) 8) 1 5n) 6xy 2s) 27x 3) 2 8) 2 0.59,28, 103. 12) 3c) 4y 12x 5)(x 0; 6n 3q) 7 2 ) 4)(5x y(3 96.81 69. 99 2 b 3 5fg 16 x 4n) x 7p) 3) 2 ) a) 4 yz 5) 3 176 53. 2 y) 2xz 11n) 1 14)(x 1 13n ; 3b) 2 2) 2 or 8)(x xy) 5)(t 4gd 4) abx ) 11 2 3 5 4) 2) 2) 5 (a 65. 1 (r 61. 5 (4a 75. 7 (3x 57. onadadhsamxmmpit 7 2y 27. downward andhasamaximum point. 1 (3k 71. 9 3b 29. 3 Anequationinwhicha 23. 7 8f 19. 18ft Thegraph shiftsdownward. 17. 15. Astheabsolutevalue ofa 13. graph becomeswider. upward 11. 7. 3. axn 15x 1. Lesson 12-1,pages520–523 Chapter 12:QuadraticFunctions 5. 3. (2,21) 1. Lesson 12-2,pages524–527 44 44 44 2.5 2 2 15x 2 n 2 2 10 12 8)(r 3 2 4 6 8 2 12 16 2 4 6 8 4 8 b 5)(3x 5)(3k y b)(7a 2b )(a y y 1.5 a 2 25 2 2 2 x y 2 )6.(g 63. 2) 5 1 1 x 31. 3 , 4 b x x 0.5 7 (ax 67. ) )5.(x 59. 5) )7.(2 73. 5) 9 31 13 2b) 6x 2axn 5 4 x 0 )5. (0, 2) 2 0 )9. (0, 0) 2 1 3 5 7

y 3d x 30x 1 (0,0) 21. 2 3113 n 2 2 11)(g s ;(3 2 3 ;thegraph opens 0; , 7 n 55 56.(3s 69. 25 3y)(x x )(ax 4d 44 5t)(2s 4 3 3 ; 2 x 5)(3x 180 140 100 4) 60 20 1 35 25 15 73.11.3 33. 17 5 n 2y) ) x-axis y y 3t) 13 2 3 2 decreases the a 5) 2 2 2)(s x 2 x x 4y 9x axn 2 (0, 0) 4) (0, 1) 8 Selected Answers 775 2 6 z) 2) x 1 x ; 9 4 0, 1 4 x(w 2, 1 3 9 x ) 2 , 4 x 9 4 ) 7, x 1 3 y(9xy 1 4 2 x Selected Answers 1 3 5 3 3) 41. x x 3 2 x 3x 5 x 2 31. 0, 11 33. 45 7 11. x 12 17. 6 or 5 19. 2 2 x IV x I 37. 5 , 1, x h x x 1 2 15. 3) 47. 3x , 0, x x 9 4 2, x y 0, x 5 2x 4, x 5 c (2x . 27. x x 2 b a 5 25 13. (x 81 17. (x x 21. 2z) 2 29. x x 3b) 39. 3mn(n x 1 4 5 y

7 3. no solutions 5. 5 1 2 2 35. 10 9. 0 25. 25) 81) 3 4 5 c 3y ) 2 9. lengths cannot be negative 5 4 31. 1 4 y 43. x x x 7b) 45. 5x 5 x x ; 7 8 h x x 10x 18x x 3, 3, (2x 5 7 8 3, 6, 3 4, 0, 4x 2 y 10, 2 , 3 , 2 2 2 5 3 4 1 4 2 c x x x x x x x 13. no solution8 or 1 15. 21. 0, the other is always 11 sec 23. 13 sec 25. One solution is 33. 35. 200 37. 9( 29. 15. (x 19. (x 23. Lesson 12-3, pages 530–533 1. 7. Lesson 12-4, pages 534–537 1. 29. 31. 33. 35. 27. 43. 9(4a 49. 3x 11. (x 7. c x x bx 5

1 2 5 2 1 3 y = x 2 y ax 1 4 y 5 5 5 5 bd 2 x y 5 x ; ; 6a 1) 1 3 5 7 8 3) , c 3 1 3 3 , y-axis 33. 1 4 5. downward 7. upward x 13. (2, x x x 27. 8a x 1 4 2 21. 70¡ 2 y = 3x 4 7 5 , 8 3 4

y 5 5 1 2 6 y = x 2 12s

10123 5 y 5x 1 17. (0, 1); y 50x y y y 5 3 5 5 8 6 4 2 5 2 5 25. (1, 2) 27. 5 2 5 2 x 5 4 18s 4x y 5 138545813 7 3 3 5 8 112 5 5) 11. 2 5 4); 4 , 6) 11. (0, 3 4 x y y 2 19. 15. (1, 29. 100x 13. no 15. yes 17. no 19. no 21. 9. (0, 1. each x-value. for There is only one y-value 3. Review and Practice Your Skills, pages 528–529 Review and Practice Your 31. 35. 9. (3, 7. 23. at about 45¡. is reached range The maximum 25. 6s 23. Selected Answers 776 7 6a 47. 12bc 3 2(m 43. 5 35a 55. 9 (x 19. 43. 3 o atrbe3.2(3 (2x 35. 37. notfactorable 33. 9 (3m 39. 45. 3 15. 4 13. .fle3 re5. 11. true 3. solutions false 1. Review andPracticeYour Skills,pages538–539 59. 37. 9 (x 29. (10, 15. Since( 38yd Answers willvary. (1,1) black: 18yd; 3.2units 25. 7. 58yd,purple: 13. 18yd,red: green: 13.9units 23. 26.7units 5. (0.5, 11. 17. (1,0) (4,1.5) 3. 9. 7.1units 1. Lesson 12-6,pages544–547 2 1. Lesson 12-5,pages540–543 39. (1,3); 35. 23. 33. 31. 5 (a 35. BrooklynBridge,2.9sec. Bridge, ofForth Firth Garabit Viaduct, 5.5sec; 33. Tunkhannock Viaduct 3.9sec; Harbor Bridge,3.3sec; 6sec Sydney 31c. Verrazano Narrows Bridge,3.6sec; 3.0 sec; 144ft 31b. ilb h aepstv ubr 27. will bethesamepositive number. 3x (y 23. Selected Answers 2 h x 77 c x 2 3 2; y 2 7 2 3 1 , y x 2 1 25. , 3 5 ,827. 0,8 25. , 2 ) x 6cd 4 7 2 121, 2 m,b 2 3 4)(3x .)1.aot47f 1 about234ft 21. about467ft 19. 0.5) b)(2a ; 3 6, 37 18x 7)(5x 2 12a 1 214 61. 4n)(2m x 4 2 n .0 .1 5. 0,2 3. 11ab ,215. 1, 2 x (y 47. 2 )(4m h 1 9c 51. 1 2 1 y 2 2 3 y 81) )3.2( 31. 2) 3 2 7 4(2a 37. 3b) 4ab 13.4sc4.18in. 41. 4sec 39. 11 5 10in. 45. 6 m 41. 6 37. 1 )3.(4 39. 3) , 4 10123 2 x ) 2 1 6b 2 3 2 2 1 8a(3 41. 5n) n x , thesumofsquareddifferences x c 5 2(3x 45. ) 2 7 4 17. 5 12.(x 21. 81 3 8374 63. 7 ,1 9 40f 1.3sec 31a. 6400ft 29. 1,11 27. 12c 8b x x 7 60x 57. ,229. 6, 2 5 x 4 3 4 x 2 b ,47. 3, 4 1, 7 , 2 1 x x 20; 9 8ab 49. 7 2 , 2 2 8 3 9 5, 19. 5 3 12x 53. 4 y)(2x 14 ,343. 4, 3 3)(3x 5 x .2 9. 2,7 7. 7 (x 17. ; 3y)(4x 5 2 2 x x y b)(2a 1 ) 11 in. x 65. y 2 13. 5 )(x 62xy 5x w 4 3 x 2 3y) b)(a 4) 5 4ad 2 3 (x x 3y) 2 29.no 1 1 0, 21. 7 b) 4 in., 4x y 2 7 ( 47. ) 4 y y 5 12y 2 ) x 2 1 67. 2x b) 20 in. x 2 29 4) x ) 2 2 1 0,7 11. 2 r 2 4 5 215 and 2 2 8 in. 3 2) 2, 4) 4 3 5 1 (a 11. itret soeo h ons 5. y-intercepts asoneofthepoints. easier tosolve thesystemofequationsifyou usethe However, you may findit located onthegraph willwork. 7. 35. 1 25 21. 1 (x 11. 31. 7. 3 . 25. 8.5 23. 51. 1. Lesson 12-7,pages550–551 45. 39. 31. 5. true 3. true 1. Review andPracticeYour Skills,pages548–549 1. Lesson 13-1,pages562–565 and Relations Chapter 13:AdvancedFunctions 15. d 9. c 7. a 5. (0,0) k 11. 3. i 1. Chapter 12Review, pages552–554 3 [w( 23. 5uis5.1 5 75.725.1. 1 4.3 61. 13.6 59. 7.2 57. 17 65. 55. 1.2 13 63. 53. 15 units 47. 39. 9. 5 . 6 2017. 12.0 16. 7.8 15. 2 y 13 x y x m 7 33. 27, 7 x x m y .,244.( 49. 2.9, 2.4 1 2 3 2 112 , x x 1, 9. , (8,4) 3 2 y 2 1 2, 2 2 )2.20,(9, 23. , (12,6) 9) (2, (1, 8)(a x 2 6 4 2 ; 2 5 47. 4 2 x 2 5 52)] m 7 y 2), 2x 4x 2 y 93 (x 3. 49 2), 29 2, ( 7 o1.n 21. no 19. no 17. 2 11. y 3 2 41. )1.(a 13. 3) 2 3 ,73.1 37. 1,7 35. 3, 7 d x .Ys Any threenon-collinear points Yes. 3. 5 29 (5 9. 12 2 2 41. d x 4) 10, x 3, 53. x x 5 4, 25. 2 7 0 )29. (0,0) 27. . 33. 8.5 2 x 4x 7037. 17.0 7 4 5 ,549. 3, 5 x ) 98uis5.(6, 51. 2), 19.8units 2 1 4 3 (x 13. 144 43. 2 , 7 8) y , 3 (1,3) 13. 123 1 4 a 33 2 27. 2 2 7 2 2 3 2 41 8 6)(3a 3 m 1 )2.9,(1,9) 25. 1) 144 ; 2)(3a 9 . 1 5.1 21. 7.3 19. y 1 2 3 4 x 7 2 y 13. x 7. 5 4 y 2 3 29. 7 4 5 5 7 45. , 1 55. 25 4) x 2 5 x , 55. 1, 2 3 0.5, 3 , 5) 9, 7 4) , 2 3 43. x 4 1 2 2 1 4 3, 1 7 2 x 1 , ; x d 11 ( x 4 y 41 5, 2 2x 2 2.5), x 7.1 , (0,0) 1) 5 2 2 3 3 2 22 4 Selected Answers 777 0, x 1; x 1764 0 135 2 2 2 y x a 3 1 1 3 0; 49y 10 19. 1 Selected Answers 3 y 2 x x 5 1. If 0, x 9. 36 13. 2 2 x y b x x 5 2 2 x a 1 17. 5 5 x y 2 ) 16 5 a. 7 k 5 2 y y x 3 b 8 5 5 ; y 2 5 5 y ( a 8 x 16 8 5 16 2 2 ) 8 5 5 x h 2 a 1; 16 x 8 21. ( 2 2 x a 7. an ellipse uses the sum of The standard equation for to the foci;the distances from a point on the ellipse the of these uses the differences hyperbola a equation for distances. 9. 11. 7. Review and Practice Your Skills, pages 578–579 Review and Practice Your 1. parabola 3. circle 5. is standard form The x 11. 15. 1 2 2 5 4) (0, 0) 2) 36 12y 0, that 51. (y 5 c 2y 2 , 28y 89.1; 4 7 U 8(y 1) 2 2 4225 x 39. 1 2) is the y- 13 y 2 23. focus 2 2 and 3 2 (3, 4) x 2 (y x 2 33. 3 2) 0 and k (3, 0) r 3 4 1 c 2 5 4 3 2 9 4 17. 1 81 29.1) 3, (2, 169y c 25. 6, 3) 47. 0 49. 39. parabola 6, 2 8y 2 1 2 16 9. y 23. (x r y 4 11. (0, 5), r 9) 33. (0.25, 11.875) 2 2 10y 2 2) 4ax 9) 45. 3. 25x 5. No; a circle is not an ellipse. of an ellipse are different The foci points. x 3 4 2) 27. (1.5, 3.75) 2 0.375, 8.5625) 39. {2, 5, 8, 9} 0 x 9 2 49 49. (x 1 x ; directrix y is ; directrix y is (y y ; directrix y is (1, 0) 17. false 19. false ; directrix y is 3 2 9 4 37. 3 1 15. 4 2 5 4 1 2 3 3. (0, 2), y 21. 20(y 24 (3, 4) 13. 3) 81 or (x c 1) 0, 0, 0, 0, y 9. (0, 4), y , (0, 1); directrix is 28y 4 2 6.25) 31. (0, c 4 2 x (y 4ay 7) 37. ( 2) y 3y 2 5, 27 ; directrix y is 2 3 2 2 2 3 4 2 4 -coordinate of the center, and k is the x-coordinate of the center, 2 x x x r x r h x 97.( 0, 13. (0, 1), y Lesson 13-4, pages 574–577 1. 1. circle 3. point 5. parabola 7. 2; 8 and Lesson 13-3, pages 572–573 29. focus 25. focus 27. focus 19. Review and Practice Your Skills, pages 570–571 Review and Practice Your 1. 1. (0, 3), y coordinate of the center. 3. when h 11. no solution 13. 2; 6 and 1 15. 2; 53. 566–569 Lesson 13-2, pages 27. is, when the center is at the origin when the center is at the is, 5. (x 35. 41. undefined 43. 11. 31. (0, 0) 33. (0, 3) 35. (0, 6) 37. 49. {2, 5, 8} 41. {6, 7} 43. {9} 45. {1, 3, 4, 6, 7, 9} 47. 7. 41. parabola 43. circle 45. 21. focus 31. focus 29. (1.5, 35. (2, 25. (x 47. 15. Selected Answers 778 9 16x 19. 25. 23. 21. 5 91x 15. 13. 35. 1. Lesson 13-5,pages580–583 17. itwillstretch1.75in. added tothespring, 9 ietvrain31. $5.41 directvariation directsquarevariation 22. 29. 27. $1.23; 21. $0.03; directvariation 20. 25. $0.13; 19. 23. 1 53 3 01.No, Paige’s conclusion iswrong. 15. 40 13. Using thedirectionvariation form, y $5.31 11. Selected Answers y x A 0.25x 2 2 2.598s 3 5 5 5 5 49y 100y 4 13 3. 5 5 2 2 5 5 1.3 9 052.10 21. 1035 19. , 210.438 5 2 5 y y y 5 5 784 y y 7 .93.1.34.1043. 180 41. 13.23 39. 8.49 37. 101.9x 17. 9100 2 .$0 .8 i9 450 9. 80mi 7. $500 5. 125 5 5 x 5 5 3 x x 4 x x 57 2 kx, if14lbare 25y 33. 2 x 225 2 2 3 2 3 7. 19. where bothvariables arepositive. Quadrant Iistheonlyquadrant and nonegative costs. 15. 1. Review andPracticeYour Skills,pages588–589 17. 1. Lesson 13-6,pages584–587 31. 29. 27. 25. erae.1.4nwos13. 4newtons 11. decreases. inverse function,asonevariable increases, theother Studentsshouldmentionthatinan Answers may vary. 9. 5 .92.1.02.1 1 20.5 31. 11 29. 13.60 27. 5.39 25. aito rp saqartcfnto.5. variation graph isaquadratic function. adirectsquare Adirectvariation graph islinear; 3. y x y y y m y decreases iftheconstantofvariation ispositive. 5 4 1 6 x 8 0 7 Inreallife, therearenonegative people 17. 405 x 6 2 5 kst x PA 313 A 31 1 13 AA MP A .3 5 5 x .$.0ec .1 ues7. 12lumens 5. $1.80each 3. 9. 5 33. 21. 5 19. y 5 5 y 5 5 y y y y r 4 9 x 5 5 7 .123. 3.11 kwxy x 5 5 11. y 21. x x x .413. 2.14 t p v s k w a k kr 2 15. 3 10.20 23. y y I y 3 2 48 x R k 3 Selected Answers 779 4 n 4 6) x x x x 15m 42 x x 4 47. cm 6.3 2)(t y y y y 2 y n) 41. b 2 2 4 4 4 4 2 2 6 4 2 2 4 2 2 4 15 3 3 Selected Answers y a 40 30 20 10 2 8 6 4 2 2 2 2 2 6 14 12 10 1 2 424 2 424 4 424 33 424 2 increases. This graph n)(m b 2 2 a 3. 7. 4 15. 11. , which is not a real number 1 3 3 16 ab x x x 31. 25 33. the form, In radical x 3 x x decreases as x 10) 39. (m x y 6 y 45. m 268 410 y 6 4 2 1 3 y 6 2 8 40 30 20 10 y y 8 6 4 2 2 4 6 8 x 40 30 20 10 2 2 2 2 2 8 6 4 4 6 3 4 4 14 12 10 2 2 4 29. 2)(s 4 2 4 424 6 6 424 2 84 8 6 62 424 5 10 7.9. 1 1 11.13. 3 7 15.computers about 8329.2 million 19. 17. $3522.72 about about $7877 of y graph 21. about $12,204 23. No. The because the radicand is negative.because the radicand 35.37. (t (s 43.x 4 Skills, pages 598-599 Review and Practice Your 1. 5. 9. 13. expression would be would expression increases as x decreases. 25.27. up 2 units translation 3 2 x x x , 3 2 101 6 x 2 2 75 33. y 10 10 13 x y y x 8 6 4 2 4 9 2 b 5 3 1 2 4 1 3 5 1 , 13 y 2 2 x 5 2 y 105, 7 5 3 1 8 4 35 16 12 1 44 1 44 45. 2 a 5 3 3 424 31. 7. 39. 3. 11. 7 2 15. x x x , 3 1 2 x x 1, 13 y 4 60 43. 305 ft 7 5 3 1 9 21. of the solution set shows The graph 4 13 1 3 y y 37. 1 y y 8 4 3 1 b 4 1 3 8 4 40 30 20 10 3 1 9 2 4 8 2 48 1) 29. 4 120; 19. 3 5 , 424 3 88 2 1 a 55 7 C(00) points above the first parabola and below the second and below the first parabola points above parabola. 23. will vary. Answers 25. 2 5. about $25,828 1. 1 3. 5 Lesson 13-8, pages 594-597 35. 17. 13. 9. 27. (1, 5. Lesson 13-7, pages 590–593 Lesson 13-7, 1. 41. Selected Answers 780 55. 4 49. 24 51. 47. 60 45. 41. 39. 7 o 729 log 17. 21. 2 119. 17. .log 1. Lesson 13-9,pages600–603 .61.91.log 13. 9 11. 6 9. Selected Answers 3 about 4 23. 5 424 44 8 9 1 625 424 2 22 44 6 O 2 4 2 2 4 4 2 2 4 4 2 4 2 20 40 60 80 4 y y y .log 3. 4 4 2 2 4 y 2 y 9 1 19. 3 8 6 4 2 2 4 6 8 x x x 8 y 32,768 x 2 246 x 5 1 12 7 43. 7 about33,687,150 57. 53. 0 y focus (0,1),directrix 37. ) ais13.focus 35. y (0, 5),directrix 5), radius 1 4 1 ( 31. 144 1) 9 (x 29. about$33,636 27. about$992 25. 5 log 15. 5 2 21. .216 5. 9 8 x 424 424 3 center(1, 33. 4 1 1 1 00 2 2 224 1) 4 2 2 4 $5962.59 2 4 6 x 2 2 4 6 4 y y 10 y 6 1 4 4) ( 2 6 y 3 2 x x x 3) .6 7. 3 5 ( y 2 39. 35. 31. 9 (x 39. 3 (x 13. 5 (x 35. ,0,0,0,0,0 3 10 43. 1,000,000,000,000,000 5 36x 25. parallel tothex-axisanddoesnotcontainvertex. 23. 45. .l3 .c7 .i11. i 9. d 7. c 5. j 3. l 1. Chapter 13Review, pages604–606 57. (4,-1) 55. 23. .rgttinl .fle5. false 3. triangle right 1. 10.7 11. Review andPracticeYour Skills,pages622–623 20¡ 23. 3.0 9. 32.8ft theanglemust beacute. (0,1); Sometimes; 21. 31¡ 31. 29. 7. 150.8in. 40¡,50¡,90¡ no 19. angles: 55¡ 27. 36.5; hypotenuse: 5. 10,832.8ft 15. 17. 34¡ 35¡ 3. 13. 21.6 1. Lesson 14-2,pages618–621 31. 13. 1. Lesson 14-1,pages614–617 Chapter 14:Trigonometry ai fhih odsac o a 0) 7 29. 1 27. ratio ofheighttodistance(ortan10¡). 9 (0,1),y 19. 3 6663.53.73.44.10 41. 4 39. 7 37. 5 35. 46,656 33. 1 5 2 2 y x 1 1 5 4 4 1 43 3 2 2 22 3. 15. 2 O 5.533. 156.25 2 5 Dividetheheightoflighthouseby the 25. 3) 1 4) 5) y y y 1 1 3 2 ylog 2 2 2 3 2 1 5 100y 10 20 30 40 4 3 1 3 5 7 9 y2 2 y x y ( .034 .129 .022 11. 0.2126 9. 1.2799 7. 0.3746 5. 53.(x 33. 25 y (y y x 7 .9 .51.02 1 about32.1¡ 21. 0.29 19. 1.05 0.69; 17. 3 (0,2); 33. 1 5 7 29. 3 27. 3 25. 1 2 21. 1 4, 2 xy 2 2) x 3) 61.3 0 )1.(0,5), 17. 3,(0,3) 15. 36 6027. 3600 4 2 2 1 y 2 x x of Thedomain positive realnumbers. real numbers andtherange is all 7 Thedomainofy 47. ubr.4.2a 49. numbers. numbers andtherange isall real 1 16g 51. x 93.(x 37. 49 2 9 20 59. 90 37. 62 41. 56.25 1 log 41. 5 log 45. 3 log 43. 49. y 5) y 4 3 2 2 log 3 16y 43 1 4 2 or 100times y x 17 8 7. 5 1 2 2 ( 1 16,807 31. 2 35. 2 32,768 x 6 1 5 51. y 2 289 553. 25 25 1 029. 50 5 3 is allpositive real 3 Theplaneis 23. 16 12 7 y 3) 4 8 1 6 2 1) 9. 2 y 15 2 7 0 47. 4 2 43. 2 0, 5 3 or 24 64 ( 2 5 y y 1 2 5 1 12.25 2 11. 2 8 a 55 7 ; x x y 5) 320 is all y 5 4 2 2 1 4 3 4 36 2 5 5 Selected Answers 781 18 1 1 2 x p, the 4 5 33x 2 2 sin 8x 540 40 15. 2 1 2 nx x 2 units. 2 4 3 3x 1) cos y Selected Answers 180 37.14¡ x 4) m y 13. 2 1 23. 360 19. 600¡ raised 3 units. raised x 1 3 5 x 2)(x 81 21. 6x 51.3 ft 23. about 94.0 m 2 x x 3 180 4 7 3)(x 47. 66.0¡ 49. 51. 0 2 3 sin 2 x 8 sin 2x 6 7 sin x y cos 2x 8 sin y 3 2 540 y 2 1 2 raised or lowered p or lowered raised

3 y y nx 5) 39. 3( 29. 16 19. 4x 85 72 25. 3.23; 1.80 27. 42.36; 6.51 8) 90 180 270 360 2 685 y sin (x 90) 3 cos 90 180 3 2 720¡ m , and the graph is the , and the graph , the amplitude is m raised 2.5 units.raised 13. yes; 5 15. no 0 26x 11x 1)(2x n 15. 17. 60¡, 300¡ 19. 120¡, 240¡ y 36 8)(x y 2 1 1 2 1 2 85 2 2 785 4 sin 3x 9. 4.67 11. 3.75 13. 3.77 15. graph of y graph 21. 0¡, 360¡ y-values.and minimum 23. the maximum between Half the difference 25.31. 2 360¡37. 27. 33. 120¡, 2, shifted 1 unit up 120¡ 9¡ 39.41. 29. 35. 180¡, 5, shifted 2 units up 36¡ 360¡, 2, centered on x-axis 43. 45. 53. 55. 60¡, 120¡ 57. 30¡, 330¡ 59. 45¡, 315¡ Review and Practice Your Skills, pages 632–633 Review and Practice Your 1. true 3. false13. 5. 7. 9. 11. Lesson 14-5, pages 634–635 1. 483.2 ft 3. 15¡ 5. pages 636–638 Chapter 14 Review, 1. j 3.17. d about 30.5¡ 5. 19.25. h 55¡ 1 21. 7. 27. 31. f period 9. l 11. 29. 31. 40.537. 33. (2x 133 35. (2 21. Sample answer: 17. answer: Sample The graph is the graph of is the graph The graph period is 25. 27. of the equation y the graph For 33. yes; 8 35. about 2.8 mi 17. 3x 41. (x 23. 6x 11. period 120¡; 4; amplitude of is the graph the graph y 2 2 3 2 3 x 48 2 2 2 2 2 2 2 2 3 225¡ 0.8; 2 2 2592 4y 270 The period is 90¡. x 23. 1 25. 27. 29. 31. 33. 19. 15. 11. D 2 2 x x x x x x 485 ft 2 2 81y 2 360 lowered 1 unit from the lowered 2 2 2 y sin 3x x 45¡ and 2 x sin 9. 90 17. 13. x 630 0.58 15. of the angle The sum y x y 2 R y sin x 3 180 y sin x 1 3 1 405 53. 32 5. y sin x y sin 4x lowered 5 units. lowered y cos x 450 540 1 2 450 90 180 270 360 90 180 270 360 90 180 270 y sin x 1 2 0.50; tan 120¡ 9y y 0.75 31. 66¡ 33. 32.9¡ 35. about 24.8 y S y y y y 1 1 2 1 2 sin 2x 4 2 1 1 1 1 1 360 1 360 1 2 2 E 2 y 21. 43a. the equations on the same set of axes. Graph Points of intersection of the curves represent solutions of the system of equations. 43b. 45. 150¡, 210¡ 47. 60¡, 240¡ 49. 3 37. 0¡, 180¡, 360¡ 39. 90¡ 41. 35. The graph is the graph of is the graph The graph 3. Lesson 14-4, pages 628–631 1. period 1. 3. Lesson 14-3, pages 624–627 Lesson 14-3, pages 13. cos measures of a trianglemeasures is 180¡. right If one angle is a angle, its measure is 90¡. know you the sum of the Therefore, be 90¡. must angles other two the measure of know If you to can use this information you acute angles, one of the measure.find the missing 17.23. 36¡ 0.57 19. 25. 24.0 0.57 21. 27. 60¡ 0.82 29. sin tan 7. 51. 5x origin. 5.of period 180¡; amplitude 2; is the graph the graph 7. 9. Photo Credits

Cover (tl)Digital Vision/Getty Images, (tr)Steve 285 Getty Images; 292 Doug Martin; 293 Krongard/Getty Images, (bl)Nathan Bilow/Getty (t)Horizons Companies, (b)Getty Images; 297 299 Images, (br)Dana Hursey/Masterfile; Endsheet File 303 Getty Images; 306 Doug Martin; 307 312 Getty photo; iv File photo; vii Courtesy of United Nations; Images; 319 Courtesy of Kodak; 321 Getty Images; viii Masterfile; ix Getty Images; x Doug Martin; 327 Aaron Haupt; 334 335 Getty Images; 343 xi xii Getty Images; xiii Horizons Companies; Courtesy of Six Flags Amusement Parks; 344 Doug xiv Courtesy of Six Flags Amusement Park; xv Mark Martin; 350 CORBIS; 360 Getty Images; 362 Ransom; xvi Aaron Haupt; xvii Len Delessio/Index Courtesy of Six Flags Amusement Park; 365 371 Stock Imagery; xviii xix xx Getty Images; 1 Mark Getty Images; 372 CORBIS; 380 Getty Images; 381 Ransom; 2 3 6 Getty Images; 8 Mark Ransom; (t) (c) Getty Images, (b)Mark Ransom; 384 Getty 9 13 15 Getty Images; 19 File photo/Courtesy Images; 388 Brent Turner; 392 Geoff Butler; 395 United Nations; 22 28 Getty Images; 29 Tim Fuller; Getty Images; 396 Aaron Haupt; 398 through 409 34 37 Getty Images; 41 CORBIS; 48 49 52 Getty Getty Images; 414 MAK-1; 422 Aaron Haupt; 423 Images; 54 Masterfile; 55 Ross Hickson; 59 Getty 426 Getty Images; 429 Geoff Butler; 433 Getty Images; 65 Laura Sifferlin; 69 Getty Images; Images; 435 KS Studios; 438 through 451 Getty 74 Doug Martin; 81 Getty Images; 83 Digital Vision; Images; 457 Foto Search; 464 Len Delessio/Index 84 85 86 87 Getty Images; 88 Aaron Haupt; Stock Imagery; 465 (t)Tim Fuller, (b)Getty Images; 89 93 Getty Images; 100 Geoff Butler; 101 through 472 File photo; 473 Dynamic Graphics; 475 480 115 Getty Images; 118 Aaron Haupt; 125 128 Getty 481 Getty Images; 482 File photo; 484 Mark Burnett; Images; 130 CORBIS; 138 Getty Images; 146 (l) 488 KS Studio; 495 through 517 Getty Images; 524 Getty Images, (r) CORBIS; 147 153 Getty Images; File photo; 527 Getty Images; 532 Masterfile; 535 156 Doug Martin; 159 through 199 Getty Images; Doug Martin; 536 Getty Images; 543 Christina De 204 CORBIS; 206 209 211 213 Getty Images; Musie/Getty Images; 547 through 565 Getty Images; 214 CORBIS; 217 Getty Images; 225 Mark Ransom; 567 CORBIS; 568 Getty Images; 571 NASA Marshall 226 227 CORBIS; 229 Getty Images; 230 CORBIS; Space Flight Center; 576 581 582 584 Getty Images; 232 240 Getty Images; 241 (t to b) Curt Fischer, 585 NASA-JPL; 586 through 617 Getty Images; 620 Tim Fuller, Aaron Haupt, Dominic Oldershaw, Doug Martin; 624 File photo; 627 Stephen Webster; Getty Images, Aaron Haupt; 247 Getty Images; 628 Getty Images; 631 CORBIS; 634 Tim Fuller; 644 250 Matt Meadows; 253 255 257 Getty Images; through 651 Getty Images; 652 (t)Aaron Haupt, (b) 258 Doug Martin; 261 Rod Joslin; 264 File photo; Getty Images; 653 Getty Images 266 267 270 Getty Images; 273 CORBIS; 279 282 Photo Credits

782 Photo Credits Index

■ ■ exponential decay, 595–596, 598 Angles, 425 A exponential functions, 594–598, 600 acute, 109 AA Similarity Postulate, 310 exponential growth, 595–596, 598 adjacent, 109–110 Abscissa, 56 exponents, 34–41, 464, 594–598 alternate exterior, 120 Absolute value function, 63 factoring, 465, 478–481, 498–501, alternate interior, 120 Absolute values, 12 506–509, 530–533 arcs and circles and, 440–443 Acute angles, 109 focus, 566, 574 base, 160 Acute triangles, 150 f of x notation, 57 bisectors of, 115 Addition, 4 FOIL process, 483, 502 central, 440 associative property of, 21 functions, 56–59, 62, 516–517, 520, complementary, 109 closure property of, 21 594–603 congruent, 154 commutative property of, 21 geometric means, 299 corresponding, 120 estimation with, 20–23 hyperbolas, 576–577 defined, 108 identity property of, 21 inconsistent systems, 258 of depression, 619 inverse property of, 21 independent systems, 258 drawing, 102–103 with matrices, 358–361 independent variables, 57 of elevation, 619 matrix, 359 inequalities, 48, 76–79 exterior, see Exterior angles of polynomials, 468–471 inverse square variations, 585 exterior of, 109 solving systems of equations by, inverse variations, 584–587 identifying, 102 268–271 iterations, 52–55 included, 155 subtraction and, 518 joint variations, 587 inscribed, 441 Addition property like terms, 73, 468 interior, see Interior angles of equality, 66 linear functions, 62–65 interior of, 109 linear inequalities, 76–79 of inequality, 76 measuring, 100 linear programming, 282–285 of opposites, 21 obtuse, 109 logarithmic equations, 601–602 Addition/subtraction method, 268 opposite, 182 logarithmic functions, 600–603 Additive inverses, 21 of polygons, 178 monomials, 468, 472–475 Adjacent angles, 109–110 polygons and, 178–181 Algeblocks, 62, 64, 66, 72, 268, 478, multiplication property of equality, reference, 624 492, 500, 534, 536 67 right, see Right angles Algebra, 52-81, 244–285, 468–603 multiplication property of of rotations, 342 absolute value functions, 63 inequality, 76 segments and, 114–117 addition property of equality, 66 parabolas, 520–523, 566–569, 607 straight, 109 addition property of inequality, 76 perfect square trinomials, 492 supplementary, 109 addition/subtraction method, 268 polynomials, 466–515 of triangles, 149 algeblocks, 62, 64, 66, 72, 97, 268, proportions, 296–299, 559, 581 types of, 108–111 478, 492, 500, 534, 536 quadratic formula, 540–543 asymptotes, 576 quadratic functions, 518–557 vertex, 160 binomials, 468, 482–485, 488–491 quadratic inequalities, 590–593 vertical, 100, 115 coefficients, 468 ranges, 57 Angle-Side-Angle (ASA) Postulate, completing squares, 534–537 rationalizing denominators, 428 148–149, 155 compound inequalities, 17, 241 substitution, 34, 264–267 Aphelion, 561 conics, 572 systems of equations, 258–275 Applications, Real World constant functions, 62 systems of inequalities, 276–285 Advertising, 19, 74, 92, 473 constants, 274, 468 terms, 52, 73, 104, 296, 468, 498 Aeronautics, 536, 543

dependent systems, 259 trinomials, 468, 492, 498–501, Agriculture, 285 Index dependent variables, 57 506–509 Air Traffic Control, 620 difference of two cubes, 503 variations, 580–587 Amusement Park Design, 341 difference of two squares, 483 Alternate exterior angles, 120 Amusement Parks, 336 directix, 566 Alternate interior angles, 120 Animation, 155, 344 direct square variations, 581 Altitudes, 164–167 Archeology, 204, 206, 208, 214, 221, direct variations, 580–583 defined, 164 226, 232, 233, 475, 547, 634 domains, 56 of similar triangles, 317 Archery, 533 ellipses, 574–577 Amplitude, 629 Architecture, 111, 119, 162, 165, equations, 7, 62, 66–69, 72–75, 240, Angle Addition Postulate, 109 171, 174, 184, 223, 303, 306, 242–291, 550–565, 574, 579, Angle bisector construction, 118–119 323, 424, 426, 431, 436, 449, 601–602 Angle Bisector Theorem, 115 455, 457, 565

Index 783 Art, 116, 127, 171, 174, 183, 191, Data File, 13, 29, 31, 37, 59, 68, 89, Measurement, 40, 41 217, 223, 227, 299, 311, 340, 163, 205, 208, 226, 246, 267, Medicine, 630 344, 351, 354, 451, 457, 471, 279, 309, 360, 399, 405, 429, Model Building, 308, 321 495, 537 481, 503, 543, 547, 573, 621 Music, 630 Art and Design, 148 Design, 161, 185, 457, 491, 564 Navigation, 121, 443, 612, 615, 616, Astronomy, 40, 227, 232, 527, 560, Drafting, 129 620, 621 563, 575, 577, 582, 585, 591 Earnings, 582 News Media, 50, 69, 79, 84, 88 Baked Goods, 582 Earthquakes, 603 Newspaper, 53, 55 Biology, 59, 582 Education, 84, 387 Number Sense, 37, 130, 205 Boating, 509, 621 Electronics, 249 Number Theory, 279 Bridge Building, 153, 163, 184 Encryption, 363, 365 Nutrition, 596 Budgeting, 279 Energy, 568 Oceanography, 576 Business, 41, 69, 93, 275, 298, 350, Engineering, 58, 115, 157, 202, 307, Office Work, 404 372, 394, 527, 596 353 Packaging, 224, 233, 266, 469, 483, Card Games, 386, 387, 395 Entertainment, 89, 269 508 Carpentry, 107, 135 Farming, 270, 596 Park Admissions, 365 Carpeting, 216 Finance, 8, 21, 22, 69, 75, 247, 261, Payroll, 474 Cartography, 250 267, 270, 275 Photography, 65, 294, 301, 303, Catering, 582 Fitness, 257, 408 308, 313, 319, 327, 395 Chemistry, 39, 501, 603 Flight, 601, 607 Photo Processing, 297 City Planning, 125, 616 Food Concessions, 373 Physics, 166, 522, 523, 527, 532, 533, Communication, 9, 29 Food Distribution, 373 537, 543, 551, 582, 586, 635 Communications, 577, 592, 621, Food Prices, 581 Plumbing, 439 625, 628 Food Service, 29 Population, 361, 595, 596, 598, 599, Community Service, 270 Forest Management, 611 626 Computer Design, 592 Framing, 303 Postage, 582 Computer Graphics, 344 Game Development, 371 Product Design, 255 Computer Science, 388 Games, 213, 214, 386, 393, 394, 395 Product Development, 485, 499 Consumer topics Geography, 13, 102, 107, 130, 634, Real Estate, 257, 298, 323, 596, 598 banking, 21, 22, 24, 25, 55, 60, 635 Recreation, 22, 74, 181, 209, 217, 69 Geology, 521 247, 266, 297, 339, 384 best buy, 33, 233 Geometric Construction, 131, 166 Reporting, 88 budgets, 447 Geometry, 473, 480 Retail, 9, 64, 298 costs, 9, 22, 24, 29, 32, 33, 37, 59, Graphic Art, 369 Ride Design, 370 65, 70, 74, 85, 211, 267, Graphic Design, 349, 354 Ride Management, 343 269, 272, 273, 275, 285, Graphing, 64, 65 Road Planning, 438 297, 373, 469, 480, 484, Gravity, 518 Safety, 620 491, 501, 581, 582, 583, 586 Health, 86, 279 Sales, 37, 79, 373, 407, 491, 582 credit, 75 Hiring, 404 Satellite Communications, 567 depreciation, 53–55, 596, 598 History, 205, 399 Satellite Photography, 307 discounts, 33, 37, 79 Home Repair, 432 Scale Models, 317 home ownership, 596, 598 Income, 470, 598 Scheduling, 126, 398 incomes, 8, 29, 32, 41, 64, 81, 89, Income Tax, 260, 261 Science, 29, 37, 535, 550, 564, 635 91, 247, 279, 282–283, 285, Inventions, 438 Sculpture, 480 299, 373, 470, 474, 507, Inventory, 364 Sewing, 31, 485 582, 598 Investing, 298 Shipping, 265, 471, 491 interest, 55, 60, 596, 598 Investments, 596, 598 Skydiving, 543 investments, 55, 60, 270, 298, Journalism, 85 Small Business, 285, 429, 484, 501, 596, 598 Landscape Architecture, 440 507, 522 profits, 37 Landscaping, 475, 480, 490, 495 Sound, 603 retail, 9 Language, 13, 19, 40 Souvenirs, 373 savings, 55, 60 Language and Communication, 4 Souvenir Sales, 359

Index taxes, 33, 260, 261, 582 Magnetism, 587 Space Exploration, 545, 581 vehicle ownership, 37, 299, 596, Manufacturing, 224, 231, 245, 250, Spatial Sense, 111 598 261, 270, 277, 282, 285, 360, Sports, 82, 85, 92, 130, 181, 208, Construction, 23, 156, 173, 175, 406, 409, 479, 489, 493 226, 227, 382, 385, 386, 387, 190, 308, 429, 432, 439, 456, Manufacturing Industry, 242 389, 392, 394, 395, 397, 403, 475, 485, 501, 509, 616 Map Making, 117 404, 405, 407, 408, 409, 412, Consumerism, 466 Marketing, 84, 388, 474 533, 537, 546, 547, 565 Cost Analysis, 204, 233 Math History, 429 Spreadsheets, 87 Cryptography, 359

784 Index Stage Design, 189, 208 Base Angles Theorem, 161 Cartographer, 133 Statistics, see Statistics Base of exponential form, 34 Cashier, 33 Surveying, 121, 135, 179, 312, 327, Bases Commercial Fisher, 633 443, 451, 619, 634 of isosceles triangles, 160 Construction Supervisor, 347 Surveys, 398 of prisms, 220 Cross-Country Bus Driver, 113 Technical Art, 151 of trapezoids, 188 Cryptographer, 15 Technology, 596 Bearing, 121 Engineering Technician, 273 Television, 55, 59 Bell curves, 415 Environmental Journalist, 61 Temperature, 13, 23, 28, 63, 256 Bernoulli, Jacques, 404 Heavy Equipment Operator, 211 Test Taking, 83, 388, 414 Best fit, lines of, 406 Jeweler, 159 Ticket Sales, 362 Biconditionals, 129 Landscape Architect, 453 Tiling, 110 Biconditional statements, 129 Photographic Process Worker, 325 Time, 41 Binary system, 45 Physical Therapist, 411 Transportation, 387, 471, 475, 484 Binomial factors in polynomials, Pilot, 529 Travel, 138, 402, 509, 586 finding, 488–491 Police Photographer, 305 Urban Planning, 446 Binomials, 468 Precision Assembler, 253 Vehicle Ownership, 596, 598 expanding, 482 Team Dietician, 391 Weather, 85, 215, 387 two, multiplication of, 482–485 Transcriptionist or Prompter Wildlife Management, 631 Bisectors Operator, 81 Arc Addition Postulate, 440 of angles, 115 Cayley, Arthur, 359 Arcs perpendicular, see Perpendicular Cells in spreadsheets, 30 circles and angles and, 440–443 bisectors Center major, 440 of segments, 114 of dilation, 348 minor, 440 Boundary, 77, 276 of gravity, 166 Areas, 206–209 Box-and-whisker plots, 406–409 of rotation, 342 of circles, 200 Brainstorming, 243, 471 of sphere, 221 circumferences and, 424 defined, 206 Centi, prefix, 39 probability and, 212–215 ■ C ■ Central angles, 440 of rectangles, 200 Central tendency, measures of, see surface, see Surface areas Calculators, 29, 30–31, 39, 40, 84, 226, Measures of central tendency of triangles, 200 247, 289, 298, 311, 405, 428, 615, Chapter Assessment, 45, 97, 143, 195, Arithmetic average, 83 616, 625 237, 289, 331, 377, 419, 461, 513, ASA (Angle-Side-Angle) Postulate, charting and data analysis 555, 607, 639 148–149, 155 software, 531 Chapter Investigation, 3, 13, 23, 31, Assessment computer language, 45, 97 44, 49, 65, 75, 89, 96, 101, 110, Chapter, 45, 97, 143, 195, 237, 289, computer program, 413 121, 137, 142, 147, 157, 167, 175, 331, 377, 419, 461, 513, 555, drafting program, 461 189, 199, 209, 223, 227, 233, 236, 607, 638 geometry software, 106, 109, 115, 241, 251, 261, 285, 288, 293, 299, Standardized Test Practice, 46–47, 119, 121, 153, 155, 157, 165, 309, 323, 330, 335, 345, 360, 371, 98–99, 144–145, 196–197, 166, 174, 179, 189, 316, 320, 376, 381, 386, 395, 399, 409, 414, 238–239, 290–291, 332–333, 351, 371, 431, 433, 441, 443, 418, 423, 429, 439, 451, 460, 465, 378–379, 420–421, 462–463, 451 471, 481, 495, 501, 512, 517, 523, 514–515, 556–557, 608–609, graphing, 64–65, 245, 246, 248, 255, 533, 537, 551, 556, 559, 568, 583, 640–641 258, 261, 278, 283, 358, 360, 603, 608, 611, 617, 621, 627, 638 Associative property 363, 364, 370, 409, 426, 520, Chapter Review, 42–44, 94–96, of addition, 21 521, 522, 523, 524, 525, 526, 140–142, 192–194, 234–236, of multiplication, 27 530, 532, 563, 566, 567, 575, 286–288, 328–330, 374–376, Asymptotes, 576 590, 626, 628, 629, 639 416–418, 458–460, 510–512,

Auxiliary lines, 151 spreadsheet program, 87 552–554, 594–596, 626–628 Index Average Calipers, 202 Check Understanding, 7, 11, 27, 38, arithmetic, 83 Careers 57, 67, 76, 114, 116, 120, 125, Axis Actuary, 497 151, 154, 161, 179, 189, 212, 216, of cone, 221 Aerospace Engineer, 367 225, 245, 255, 256, 264, 301, 306, of cylinder, 220 Air Traffic Controller, 549 311, 338, 342, 348, 352, 359, 368, of symmetry, 338, 521 Animator, 177 393, 397, 403, 407, 427, 449, 469, Archaeologist, 229 493, 498, 520, 524, 525, 574, 575, ■ ■ Astronaut, 571 581, 591, 615, 629 B Astronomer, 589 Choosing strategies, 634–635 Base angles, 160 Brokerage Clerk, 477 Chords, 441 of trapezoid, 188 Building Inspector, 435 Circle graphs, 446–447

Index 785 Circles, 440, 560 defined, 154 Data Activity angles and arcs and, 440–443 proofs and, 160–163 American Spending Habits, 465 areas of, 198 Conics, 572 Camera Settings and Image Sizes, circumferences of, see Conic sections, 572 293 Circumferences of circles Conjectures, 124 Classic Wooden Roller Coasters, constructions with, 454–457 Consecutive sides, 178 335 right angles and, 424–463 Consecutive vertices, 178 Cryptology—The Science of Secret secants of, 441 Constant functions, 62 Communication, 3 segments and, 448–451 Constants, 274, 468 Home Run Greats, 381 standard equations of, see of proportionality, 581 How Does Gravity Affect Weight, Standard equations of circles of variation, 580 517 tangents of, 441 Constraints, 282 Latitude and Longitude of World Circumferences of circles, 200, Constructions, 118–121 Cities, 101 206–209, 560 angle bisector, 118–119 Seven Wonders of the Ancient areas and, 424 with circles, 454–457 World, 199 defined, 206 segment bisector, 118 Solar System, 559 Circumscribed polygons, 455 Consumer topics, see Applications Suspension Bridges of New York, Clockwise rotations, 342 Convenience sampling, 82 147 Closed circle, 77 Converse Tall Buildings, 423 Closed dot, 48 of conditional, 129 U.S. Airport Traffic, 611 Closed half-plane, 77 of Pythagorean Theorem, 431 U.S. Goods—Imports and Exports, Closure property Convex polygons, 178 241 of addition, 21 Coordinate planes, 56–59 Where Can You Find the News?, 49 of multiplication, 27 defined, 56 Data File, 13, 29, 31, 37, 59, 68, 75, 89, Clusters, 87 dilations in, 348–351 163, 205, 208, 226, 246, 267, 279, Cluster sampling, 82 points on, 50 309, 360, 399, 405, 429, 481, 503, Coefficients, 468 rotations in, 342–345 543, 547, 573, 621 Collinear points, 104 Coordinates, 105 Decagons, 178 Column matrix, 275 of points, 11 Decimal points, moving, 39, 203 Columns in spreadsheets, 30 Coplanar points, 104 Decimals Combinations Corollaries, 161 converted to percents, 385 defined, 404 Correlation fractions and percents and, 380, permutations and, 402–405 negative, 406 Decimal system, 39 Combined variation, 587 positive, 406 Declining-balance method, 53–54 Commutative property Corresponding angles, 120 Deductive reasoning of addition, 21 Corresponding Angles Postulate, 129 of multiplication, 27 defined, 134 Corresponding sides, 154, 300 Complementary angles, 109 inductive reasoning versus, 135 Cosine functions, 614 Complements of events, 393 proofs and, 134–137 Counterclockwise rotations, 342 Completing squares, 534–537 Definitions, 104 Counterexamples, 128 defined, 534 Degree measure of angle, 108 Critical Thinking, 13, 23, 37, 41, 351 Composite of transformations, 352 Degrees, geographic, 102 Cross products Compound events, 392–395 Denominators, rationalizing, 428 of binomials, 483 defined, 392 Dependent events in proportion, 296 Compound inequalities, 17 defined, 397 Cross section, 223 solving, 243 independent events and, 396–399 Cubes, 221 Concave polygons, 178 Dependent systems, 259 two, difference of, 503 Conclusion, 128 Dependent variables, 57 Customary units, 202–205 Concurrence, 165 Depreciation, 53–54 Cylinders, 220 Concurrent lines, 165 Depression, angle of, 609 axis of, 220 Conditionals, 128 Description notation, 6 converse of, 129 Determinants Index Conditional statements, 128–131 ■ D ■ defined, 274 defined, 128 of matrices, 336 Cones, 221 Dashed line, 277 matrices and, 274–275 Congruence symbol (≅), 154 Data, 82 of systems of equations, 274 Congruent angles, 154 displaying, 86–89 Diagonals of polygons, 178 Congruent figures, 154 extremes of set of, 407 Difference Congruent segments, 154 measures of central tendency and, of two cubes, 503 Congruent triangles, 148–149, 82–85 of two squares, 483 154–157, 294–295 using, see Data File Different signs, numbers with, 20, 26

786 Index Dilations Equilateral polygons, 179–180 Factoring patterns, special, 492–495 centers of, 348 Equilateral triangles, 150 Factors, 473 in coordinate planes, 348–351 Equivalent ratios, 296 extracting, 478 defined, 348 Error Alert, 22, 54, 175, 184, 299, 405, Feasible region, 282 Dimensions of matrix, 358 475, 491, 582 Femto, prefix, 39 Direct proofs, 170 Talk About It, 130, 166, 208, 257, Figures Directrix, 566 370, 389, 433, 456 congruent, 154 Direct square variation, 581 Estimation with addition and defined, 104 Direct variation, 580–583 subtraction, 20–23 intersection of, 105 defined, 580 Euclid, 250 similar, 300 Disjoint sets, 16 Euler, Leonhard, 17 three-dimensional, see Three- Dispersion, measures of, 412 Events dimensional figures Displaying data, 86–89 complements of, 393 Finding binomial factors in Distance, 105 compound, see Compound events polynomials, 488–491 Distance formula, 545 dependent, see Dependent events Finite sets, 6 Distributive property, 34–37 independent, see Independent First product, 483 defined, 34 events Flip, 338 Division, 4 mutually exclusive, 392 Foci of ellipses, 574 multiplication and, 26–29 Expanding binomials, 482 Focus, 566 properties of exponents for, 35 Experimental probability, 384 f of x notation, 57 Domains, 56 Experiments, 384 FOIL process, 483, 502 Drawing angles, 103 with sine functions, 628–631 Fractals, 307, 308 Drawings, scale, see Scale drawings Exponential decay, 595 Fractions Exponential form, 34 percents and decimals and, 380 Exponential functions, 594–597, 600 ■ ■ Frequency distribution, 414 E Exponential growth, 595 Frequency table, 82 Exponents, 34 Function notation, 57 Edge of polyhedron, 220 properties of, 34–37 Functions, 520 Edges, lateral, 220 for division, 35 constant, 62 Efficiency rating, 273 for multiplication, 35 defined, 56 Elements, prime, 473 quotient property of, 38 exponential, 594–597 Elements of matrices, 275, 358 scientific notation and, 38–41 graphs of, 518–519 Elevation, angle of, 619 simplifying, 466 linear, see Linear functions Elimination, process of, 138 Extended Response, 47, 99, 145, 197, logorithmic, 600–603 Ellipses 239, 291, 333, 379, 421, 463, 515, periodic, 628 foci of, 574 557, 609, 641 range of, 57 graphing, 575 Exterior, of angles, 109 relations and, 56–59 hyperbolas and, 574–577 Exterior angles, 120 Fundamental counting principle, 402 Empty set, 6, 16 of polygons, 179 Endpoints of rays, 105 of triangles, 151 Enlargement, 348 Exterior Angle Theorem, 151 ■ ■ Equality Exterior sides, 109–110 G addition property of, 66 Extracting factors, 478 Galileo Galilei, 543 multiplication property of, 67 Extremes Gaps, 87 Equal matrices, 358 in proportions, 296 GCF (greatest common factor), 479 Equations of set of data, 407 Gears, 342 defined, 7 General case, 502–503 graphing, 242 ■ ■ General quadratic function, 524–527 linear, 62 F “General to particular” reasoning, 135

for lines, writing, 254–257 5–step problem solving plan, 5, 31, Geometric constructions, see Index quadratic, see Quadratic equations 93, 139, 171, 389, 447, 479, 503, Constructions solving, 242 551, 573, 635 Geometry software, 349, 353, 448, 562 solving multi-step, 72–75 45–45–90 Triangle Theorem, 437, 613 Geometric iteration, 53 solving one-step, 66–69 Face of polyhedron, 220 Geometric mean, 299 standard, of circles, see Standard Faces, lateral, 220 Geometry, 104–233, 296–357, equations of circles Factorial notation, 403 426–457, 614–635 systems of, see Systems of Factoring 30-60-90 Triangle Theorem, 436, 611 equations graphing and, 530–533 45-45-90 Triangle Theorem, 437 writing, see Writing equations polynomials, 478–481 AA Similarity Postulate, 310 Equiangular polygons, 179–180 prime, 467 acute angles, 109 Equiangular triangles, 150 trinomials, 498–501, 506–509 acute triangles, 150

Index 787 alternate exterior angles, 120 golden rectangles, 195, 205 platonic solids, 221 alternate interior angles, 120 half planes, 77, 276 points, 11, 48, 104 altitudes, 164–167, 317 heptagons, 178 point symmetry, 345 Angle Addition Postulate, 109 Heron’s formula, 429 Polygon Exterior Angle Theorem, angle bisectors,115, 118–119 hexagonal prisms, 220 179 angles, 100–101, 108–111, 114–117, hexagonal pyramids, 220 polygons, 148–197, 455 120, 147, 154–155, 160, hexagons, 178, 180 Polygon Sum Theorem, 179 178–182, 342, 423, 440–443 hypotenuse, 175 polyhedra, 181, 220–221 Angle-Side-Angle (ASA) Postulate, images, 338 preimages, 338 146–147, 155 included angles, 155 prisms, 220–221 Arc Addition Postulate, 440 included sides, 155 proportional segments, 316–323 arcs, 440–443 indirect measurements, 326–327 Protractor Postulate, 108 areas, 198, 206–209, 212–215, 422 inscribed angles, 441 pyramids, 220 auxiliary lines, 151 inscribed polygons, 455 Pythagorean Theorem, 430–433, axes, 220–221, 338, 521 interior angles, 120, 147, 150, 178 517, 544–547 base angles, 160–161, 188 isosceles trapezoids, 189 quadrilaterals, 178, 182–185, Base Angles Theorem, 161 Isosceles Trapezoid Theorem, 189 188–191 bases, 160, 188, 220 isosceles triangles, 150, 160–161 rays, 105, 115 bisectors, 114–115, 118, 164–167 Isosceles Triangle Theorem, 161 rectangles, 183, 195, 198 centers, 166, 221, 342, 348 kites, 189 rectangular prisms, 220, 224, 230 central angles, 440 legs, 160, 188, 430 reflections, 338–341, 369 chords, 441 lines, 62, 104–107, 119, 151, 165, regular polygons, 179–180 circles, 198, 440–457 334–335, 338, 406 regular polyhedra, 181, 221 circumferences, 198, 206–209, 422 line segments, 105 rhombus, 183 circumscribed polygons, 455 loci, 220–223 Rhombus-Diagonal Theorem, 183 collinear points, 104 major arcs, 440 right angles, 100, 109 complementary angles, 109 measurements, 39, 101, 108, right cones, 221 concave polygons, 178 200–239, 326–327 right cylinders, 220 concurrent lines, 165 medians, 164–167, 188, 317, 321 right prisms, 220 cones, 221 midpoints, 14, 335, 545 right triangles, 150, 436–439, congruence, 146–147, 154–157, minor arcs, 440 618–621 160–163, 292–293 n-gons, 178 rotations, 342–345 consecutive sides, 178 nonagons, 178 Ruler Postulate, 105 constructions, 118–121, 454–457 noncollinear points, 104 scale drawings, 306–309 convex polygons, 178 noncoplanar points, 104 scalene triangles, 150 coplanar points, 104 oblique cones, 221 secants, 441 corresponding angles, 120, 129 oblique cylinders, 220 secant segments, 448 Corresponding Angles Postulate, oblique pyramids, 220 Segment Addition Postulate, 106 129 obtuse angles, 109 segments, 105, 114, 154, 448–451 corresponding sides, 154, 300 obtuse triangles, 150 Side-Angle-Side (SAS) Postulate, cubes, 221 octagons, 178 146–147, 155 cylinders, 220 opposite angles, 182 sides, 108, 150, 155, 178, 182 decagons, 178 opposite rays, 115 Side-Side-Side (SSS) Postulate, degrees, 108 parallel lines, 118–121, 320–323 146–147, 155 diagonals, 178 Parallel Lines Postulate, 120 similar figures, 294–333 dilations, 348–351 Parallelogram-Angle Theorem, 182 skew lines, 119 edges, 220 Parallelogram-Diagonal Theorem, slides, 338 endpoints, 105 182 spheres, 221, 226, 232 equiangular polygons, 150, parallelograms, 182–185 SSS Similarity Postulate, 331 179–180 Parallelogram-Side Theorem, 182 straight angles, 109 equilateral polygons, 150, 179–180 pentagonal prisms, 221 supplementary angles, 109

Index exterior angles, 120, 151, 179 pentagons, 178 surface areas, 224–227 Exterior Angle Theorem, 151 perimeters, 198, 206–209 symmetry, 335, 338, 345 exterior sides, 109–110 perpendicular bisectors, 164–167 tangents, 441 faces, 220 Perpendicular Bisector Theorem, tangent segments 449 geometry software, 106, 109, 115, 165 terminal sides, 624 121, 153, 155, 157, 165–166, perpendicular lines, 100, 118–121, three-dimensional figures, 174, 179, 316, 320, 351, 371, 248 220–227, 230–233 431, 433, 441, 443, 451 pi (π), 226 transformations, 336–379 glide reflections, 353 planes, 104 translations, 338–341

788 Index transversals, 120 ■ ■ Inner product, 483 Trapezoid-Median Theorem, 188 H Input values, 57 trapezoids, 188–191, 321 Half-plane, 77, 276 Inscribed angles, 441 Triangle Inequality Theorem, 173 closed, 77 Inscribed polygons, 455 triangles, 147, 150–153, 157, open, 77 Inside calipers, 202 172–175, 198, 316–319, 610 Harriot, Thomas, 11 Integers, 10 Triangle-Sum Theorem, 150 Hectare, 309 negative, 10 triangular pyramids, 220 Hecto, prefix, 39 positive, 10 trigonometry, 612–641 Heptagons, 178 Intercept, 440 Unequal Angles Theorem, 173 Heron’s formula, 429 Interior, of angles, 109 Unequal Sides Theorem, 173 Hexagonal prisms, 220 Interior angles, 120 Unique Line Postulate, 105 Hexagonal pyramids, 220 of polygons, 178 Unique Plane Postulate, 105 Hexagons, 178, 180 of triangles, 147, 150 vertex angles, 160 Hipparchus, 629 Internet, 419, 513 vertical angles, 100, 115 Histograms, 87, 381, 414 Interquartile range, 408 Vertical Angles Theorem, 115, 134 Horizontal line, 245 Intersection vertical lines, 245 Hyperbolas of figures, 104 vertices, 108, 150, 178, 220 ellipses and, 574–577 of sets, 16–19 volumes, 230–233 standard equation of, 576 defined, 16 Geometry software, see Calculators, Hypotenuse, 175 Inverse operations, 66 geometry software Hypothesis, 128 Inverse property Glide reflection, 353 of addition, 21 Golden Rectangle, 205 ■ I ■ of multiplication, 27 GPE (greatest possible error), 202 Inverses Grand products, 502 Identifying angles, 102 additive, 21 Graphing Identity property multiplicative, 27 of addition, 21 ellipses, 575 Inverse square variation, 585 of multiplication, 27 equations, 240 Inverse variation, 584–587 if-then statements, 128 factoring and, 530–533 defined, 584 Image, 338 hyperbolas, 576 Irrational numbers, 10, 426–429 Included angles, 155 inequalities, 50 defined, 426 Included sides, 155 Isosceles trapezoids, 189 linear functions, 62–65 Inconsistent systems, 258 Isosceles Trapezoid Theorem, 189 parabolas, 520–523 Independent events Isosceles triangles, 150 quadratic inequalities, 590–593 defined, 396 legs of, 160 real numbers, 11 dependent events and, 396–399 Isosceles Triangle Theorem, 161 sine functions, 614–617 Independent systems, 258 Iteration, numeric, 53 solving systems of equations by, Independent variables, 57 Iterations 258–261, 561 Indirect measurement, 326–327 defined, 53 Graphing calculators, see Calculators, Indirect proofs patterns and, 52–55 graphing defined, 170 Graphs, 86 writing, 170–171 ■ ■ circle, 446–447 Inductive reasoning J of functions, 518–519 deductive reasoning versus, 135 Joint variation, 587 misleading, 92–93 defined, 124 of numbers, 11 in mathematics, 124–127 ■ ■ using, in writing equations, Inequality(ies), 11 K 550–551 addition property of, 76 Kilo, prefix, 39 Gravity, center of, 166 compound, see Compound Kites, 189 ≥ Greater than or equal to symbol ( ), 11 inequalities Index Greater than symbol (), 11 defined, 76 ■ L ■ Greatest common factor (GCF), 479 graphing, 50 Greatest possible error (GPE), 202 multiplication property of, 76 Last product, 483 Grid In, 47, 199, 145, 197, 239, 291, solving, 76–79 Lateral edges, 220 333, 379, 421, 463, 515, 557, systems of, see Systems of Lateral faces, 220 609, 641 inequalities Latitude, 102 Group work, 3, 10, 49, 86, 101, 104, transitive property of, 77 Leaf, 86 147, 172, 212, 230, 241, 293, 306, in triangles, 172–175 Legs 335, 381, 406, 412, 423, 465, 471, Infinite number of solutions, 259 of isosceles triangle, 160 488, 495, 501, 517, 540, 559, 611, Infinite sets, 6 of right triangle, 430 617, 627 Initial sides, 624 of trapezoid, 188 Index 789 Less than or equal to symbol (), 11 die, 386, 396 Measure, units of, 202–205 Less than symbol ( ), 11 flat objects, 104 Measurement, 200–239 Like terms, 73, 468 geoboards, 244 defined, 202 Lin, Maya Ying, 183 graph paper, 282, 338, 430 indirect, 326–327 Linear equations, 62, 242 metric ruler, 154 precision of, 202 Linear functions, 62 mirrors, 326 Measure of angle, 108, 423 defined, 62 modeling, 64, 72, 74, 149, 419, 478, Measures of central tendency, 51, 380 graphing, 62–65 492, 500, 534, 536 data and, 82–85 Linear inequalities, 76–79 number cubes, 419 defined, 83 Linear programming, 282–285 paper folding, 114, 160, 220, 455 Measures of dispersion, 412 defined, 282 pencil, 282 Measuring angles, 103 Linear systems of equations, 242–291 protractor, 101, 108, 110, 111, 114, Medians, 51, 83, 164–167 Lines 154, 163, 195, 202, 300, 447, defined, 164 auxiliary, 151 448 of similar triangles, 317 of best fit, 406 ruler, 114, 338, 448 of trapezoids, 188, 321 concurrent, 165 scissors, 224, 338, 436, 440, 574 Mega, prefix, 39 defined, 104 spinners, 388, 395, 419 Mental Mathematics, 7, 8, 9, 33, 37, 231 parallel, see Parallel lines steel scales, 202 Mental Math Tip, 35, 39, 183, 203, perpendicular, see Perpendicular straightedge, 118, 119, 121, 131, 231, 531, 614 lines 150, 164, 165, 182, 195, 224, Metric system, 39 points and planes and, 104–107 310, 316, 436, 440, 454 Metric units, 202–205 of reflection, 338 string, 574 Micro, prefix, 39 skew, 119 tangram, 188, 195, 331 Micrometers, 202 slopes of, see Slopes of lines tape, 224 Mid Chapter Quiz, 25, 71, 123, 169, straight, 62 thumbtacks, 574 219, 263, 315, 357, 401, 445, 487, of symmetry, 337, 338 tiles, 52 539, 579, 623 trend, 406 Map, 103, 110, 113, 133, 306, 307, 308, Midpoint formula, 337, 545 writing equations for, 254–257 583 Midpoints of segments, 114 Line segments, 105 Mapping, 56 Midpoint Theorem, 114 Loci Math: Who, Where, When, 11, 17, 183, Minor arcs, 440 defined, 222 207, 250, 308, 359, 404, 470, 543, Minutes in degrees, 102 three-dimensional figures and, 619 Misleading graphs, 92–93 220–223 Mathematical notation, 66–67 Mixed Review Exercises, 9, 13, 19, 23, Logarithm, 600 Mathematics 29, 31, 37, 41, 55, 59, 65, 69, 75, Logarithmic equation, 601 essential, 4–47 79, 85, 89, 93, 107, 111, 117, 121, Logarithmic function, 600–603 inductive reasoning in, 124–127 Logic language of, 6–9, 49 127, 131, 137, 139, 153, 157, 163, literature and, 143 MathWorks, 15, 33, 61, 81, 113, 133, 167, 171, 175, 181, 185, 191, 205, writing and, 143 159, 177, 211, 229, 253, 273, 305, 209, 215, 217, 223, 227, 233, 247, Logical reasoning, 103 325, 347, 367, 391, 411, 435, 453, 251, 257, 261, 267, 271, 275, 279, using, 138–139 477, 497, 529, 549, 571, 589, 633 285, 299, 303, 309, 313, 319, 323, Longitude, 102 Matrices 327, 341, 345, 351, 355, 361, 365, Lower quartile, 407 addition with, 358–361 371, 373, 387, 389, 395, 399, 405, defined, 275, 358 409, 415, 429, 433, 439, 443, 447, ■ ■ determinants and, 274–275 451, 457, 471, 475, 481, 485, 491, M determinants of, 336 495, 501, 503, 509, 523, 527, 533, Major arcs, 440 more operations on, 362–365 537, 543, 547, 551, 565, 569, 573, Mandelbrot, Benoit B., 308 multiplication with, 358–361 577, 583, 587, 593, 617, 621, 627, Manipulatives, 45, 97, 419 polygons and, 368 631, 635 Algeblocks, 62, 64, 66, 72, 268, 478, for reflections, 369 Mode, 51, 83 492, 500, 534, 536 transformations and, 368–371 Modeling, 64, 72, 74, 147, 478, 492, blocks, 52, 237 transformations with, 369 500, 534, 536

Index cardboard, 574 using, 372–373 Monomials, 468 cards, 10, 419 Matrix addition, 359 multiplication by, 472–475 centimeter ruler, 172, 300, 326 Matrix multiplication, 362 Multiple Choice, 46, 98, 144, 196, 238, coins, 389, 396 Matrix subtraction, 361 290, 332, 378, 420, 462, 514, 556, compass, 118, 119, 121, 131, 164, Maximum value, 283 608, 640 165, 182, 195, 202, 224, 310, Mean, 51, 83 Multiple transformations, 352–355 316, 436, 440, 448, 454, 562 geometric, 299 Multiplication, 4 construction paper, 224 Mean proportional, 299 associative property of, 27 dice, 392 Means in proportions, 296 closure property of, 27

790 Index commutative property of, 27 ■ ■ Patterns, division and, 26–29 O defined, 52 identity property of, 27 Objective function, 282 iterations and, 52–55 inverse property of, 27 Oblique cones, 221 special factoring, 492–495 with matrices, 358–361 Oblique cylinders, 220 Pentagonal prisms, 221 matrix, 362 Oblique square pyramids, 220 Pentagons, 178 by monomials, 472–475 Obtuse angles, 109 Percents properties of exponents for, 35 Obtuse triangles, 150 decimals and fractions and, 380 row-by-column, 362 Octagons, 178 decimals converted to, 385 scalar, 359 Odds, 386 defined, 385 solving systems of equations by, One-step equations, solving, 66–69 of numbers, 424 268–271 Open circle, 77 probability and, 384–387 of two binomials, 482–485 Open dot, 48 Perfect square trinomials, 492 Multiplication and addition method, Open half-plane, 77 Perihelion, 561 269 Open sentences, 7 Perimeters, 206–209 Multiplication property Operations, inverse, 66 defined, 206 of equality, 67 Opposite angles, 182 of rectangles, 200 of inequality, 76 Opposite rays, 115 of triangles, 200 of minus one, 771 Opposite sides, 182 Periodic functions, 618 of zero, 27 Opposites of numbers, 10 Periods, 628 Multiplicative inverses, 27 addition property of, 21 Permutations Multi-step equations, solving, 72–75 of opposites, 12 combinations and, 402–405 Mutually exclusive events, 392 Ordered pairs, 56, 368 defined, 403 Order of operations, 466 Perpendicular bisectors, 164–167 Ordinate, 56 defined, 165 ■ N ■ Origin, 56 Perpendicular Bisector Theorem, 165 Outcomes, 384 Perpendicular lines, 102, 118–121 Naming sides of triangles, 610 Outer product, 483 defined, 119, 248 Nano, prefix, 39 Outliers, 87 parallel lines and, 248–251 Natural numbers, 10 Output values, 57 Personal polygons, 461 Negative correlation, 406 Outside calipers, 202 Pi (), 226 Negative integers, 10 Overlapping triangles, 157 Pico, prefix, 39 Negative reciprocals, 248 Planes Negative slope, 244 coordinate, see Coordinate planes n factorial, 403 ■ P ■ defined, 104 n-gons, 178 points and lines and, 104–107 Nonagons, 178 Parabolas, 566–569 Plans for proofs, 156 Noncollinear points, 104 defined, 520 Plato, 221 Noncoplanar points, 104 graphing, 520–523 Platonic solids, 221 Normal curves, 415 Parallel lines, 118–121, 295 Playfair, John, 250 Not equal to symbol (), 10 defined, 119, 248 Plots, 86 Not greater than symbol (), 172 perpendicular lines and, 248–251 Points Not less than symbol (), 172 proportional segments and, collinear, 104 Null set, 6 320–323 on coordinate planes, 50 Number lines, 10, 20 Parallel Lines Postulate, 120 coordinates of, 11 Numbers Parallelogram-Angle Theorem, 182 coplanar, 104 book of, 45 Parallelogram-Diagonal Theorem, 182 defined, 104 with different signs, 20, 26 Parallelograms, 182–185 lines and planes and, 104–107 game of, 45 defined, 182 noncollinear, 104

graphs of, 11 Parallelogram-Side Theorem, 182 noncoplanar, 104 Index irrational, see Irrational numbers “Particular to general” reasoning, 135 Point-slope form, 254–256 natural, 10 Partner work, 6, 93, 104, 114, 118, Point symmetry, 345 opposites of, see Opposites of 130, 150, 164, 172, 178, 188, 206, Polygon Exterior Angle Theorem, 179 numbers 224, 244, 264, 268, 276, 282, 296, Polygons, 148 percents of, 422 300, 306, 310, 326, 338, 348, 352, angles and, 178–181 random, 388 358, 368, 384, 388, 392, 396, 402, circumscribed, 455 rational, 10, 243, 428 426, 436, 448, 468, 472, 482, 488, concave, 178 real, see Real numbers 492, 498, 506, 524, 534, 540, 544, convex, 178 with same sign, 20, 26 562, 566, 574, 580, 584, 600, 614, defined, 178 whole, 10 618, 624, 628 diagonals of, 178 Numeric iteration, 53 Pascal, Blaise, 470 equiangular, 179–180

Index 791 equilateral, 179–180 mutually exclusive events, 392 Proportional segments exterior angles of, 179 odds, 386 parallel lines and, 320–323 inscribed, 455 permutations, 403–405 triangles and, 316–319 interior angles of, 178 random numbers, 388 Proportions matrices and, 368 sample spaces, 385 defined, 296 personal, 461 simulations, 388–389 ratios and, 296–299 regular, 179–180 theoretical 385–386 solving, 561 similar, see Similar polygons tree diagrams, 385 writing, 297 triangles and quadrilaterals and, Problem Solving Skills Protractor Postulate, 108 148–197 choosing strategies, 634–635 Pyramids, 220 vertex of, 178 circle graphs, 446–447 hexagonal, 220 Polygon-Sum Theorem, 179 determinants and matrices, oblique square, 220 Polyhedra, 181, 220 274–275 triangular, 220 edges of, 220 general case, 502–503 Pythagorean Theorem, 430–433, 519 faces of, 220 indirect measurement, 326–327 converse of, 431 regular, 181, 221 misleading graphs, 92–93 defined, 430 vertices of, 220 simulations, 388–389 using, 544–547 Polynomials, 466–515 solving simpler problems, 216–217 Pythagorean triples, 433 addition of, 468–471 using graphs in writing equations, defined, 468 550–551 ■ ■ factoring, 478–481 using logical reasoning, 138–139 Q finding binomial factors in, 488–491 using matrices, 372–373 Quadrant (instrument), 603 quadratic, 498 using technology, 30–31 Quadrants, 56 simplifying, 469 visual thinking, 572–573 Quadratic equations, 493–494 in standard form, 469 writing indirect proofs, 170–171 defined, 520 subtraction of, 468–471 Problem Solving Strategies standard, 524–527 Population, 82 Act it out, 388 Quadratic formula, 540–543, 672 Positive correlation, 406 Eliminate possibilities, 138 defined, 540 Positive integers, 10 Guess and check, 170 Quadratic function, general, 524–527 Positive slope, 244 Look for a pattern, 502 Quadratic functions, 518–557 Postulates, 105 Make a table, chart or list, 92, 372, Quadratic inequalities, graphing, Power of a product rule, 35 446 590–593 Power of a quotient rule, 35 Solve a simpler problem, 216 Quadratic polynomials, 498 Power rule, 35 Use a formula, 274 Quadratic relations, 560–609 Precision of measurement, 202 Use a model or a picture, 326 Quadratic terms, 498 Predictions, 52 Quadrilaterals, 178 Prefixes Use an equation or formula, 30 other polygons and triangles and, in metric system, 39 Use a picture, diagram or model, 148–197 of polygons, 178 572 special, 182–185, 188–191 Preimage, 338 Using many, 624 Quartiles Price, unit, 204 Work backward, 550 lower, 407 Prime elements, 473 Problem Solving Tip, 12, 73, 129, 137, upper, 407 Prime factoring, 467 156, 166, 213, 259, 265, 266, 268, Quotient property of exponents, 38 Prisms, 220 269, 277, 297, 364, 385, 437, 455, Quotient rule, 36 bases of, 220 469, 472, 489, 499, 534, 535, 541, Quotients, square roots of, 427 hexagonal, 220 544, 592 pentagonal, 221 Process of elimination, 138 rectangular, see Rectangular Product property of square roots, 541 ■ R ■ prisms Product rule, 35 right rectangular, 220 Products Radicals, rationalizing, 613 Probability, 201, 384–405 grand, 502 Radicands, 427 area and, 212–215 square roots of, 427 Random numbers, 388

Index combinations, 404–405 Programming, 389 Random sampling, 82 complements of events, 393 Proofs Range compound events, 392–395 congruent triangles and, 160–163 of functions, 57 dependent events, 396–399 deductive reasoning and, 134–137 interquartile, 408 events, 392–399 direct, 170 of relations, 56 experimental, 384 indirect, see Indirect proofs of values, 51 fundamental counting principle, plans for, 156 Rate, 204 402 of theorems, 134 unit, 204 independent events, 396–399 Proportionality, constant of, 581 Rating scale, 406

792 Index Rationalizing denominators, 428 122–123, 132–133, 158–159, Secant segments, 448 Rationalizing radicals, 613 168–169, 176–177, 186–187, Secants of circles, 441 Rational numbers, 10, 243, 428 210–211, 218–219, 228–229, Seconds in degrees, 102 Ratios, 202–205, 294 252–253, 262–263, 272–273, Segment Addition Postulate, 106 defined, 202 280–281, 304–305, 314–315, Segment bisector construction, 118 equivalent, 296 324–325, 346–347, 356–357, Segments, 105 proportions and, 296–299 366–367, 390–391, 400–401, angles and, 114–117 trigonometric, 614–617 410–411, 434–435, 444–445, bisectors of, 114 writing, 203, 294 452–453, 476–477, 486–487, circles and, 448–451 Rays, 105 496–497, 504–505, 528–529, congruent, 154 opposite, 115 538–539, 548–549, 570–571, line, 105 Readiness, 4–5, 50–51, 102–103, 578–579, 588–589, 598–599, midpoints of, 114 148–149, 200–201, 242–243, 622–623, 632–633 proportional, see Proportional 294–295, 336–337, 382–383, Rhombus, 183 segments 424–425, 466–467, 518–519, Rhombus-Diagonal Theorem, 183 secant, 448 560–561, 612–613 Right angles, 102, 109 tangent, 449 Reading Math, 10, 21, 56, 66, 67, 105, circles and, 424–463 Sentences, 7 110, 118, 129, 134, 135, 155, 160, Right cones, 221 open, 7 172, 178, 206, 221, 274, 275, 276, Right cylinders, 220 Sequences, 52 386, 408, 428, 455, 483, 492, 498, Right rectangular prisms, 220 Set-builder notation, 6 524, 580, 584 Right triangles, 150, 613 Sets, 6 Real numbers, 10–13 solving, 618–621 disjoint, 16 defined, 10 special, 436–439, 613 empty, 6, 16 graphing, 11 Roster notation, 6 finite, 6 Reasoning Rotations infinite, 6 deductive, see Deductive reasoning angles of, 342 intersection of, see Intersection of sets “general to particular,” 135 centers of, 342 null, 6 geometry and, 102–145 in coordinate planes, 342–345 replacement, 7 inductive, see Inductive reasoning defined, 342 union of, see Union of sets logical, see Logical reasoning Row-by-column multiplication, 362 universal, 16 “particular to general,” 135 Row matrix, 275, well-defined, 6 Reciprocals, 27 Rows in spreadsheets, 30 Shortest Path Postulate, 172 negative, 248 Ruler Postulate, 105 Short Response, 47, 99, 145, 197, 239, Rectangle-Diagonal Theorem, 183 Rules, 57 291, 333, 379, 421, 463, 515, 557, Rectangles, 183 ■ ■ 609, 641 areas of, 198 S Side Golden, 195, 205 Same sign, numbers with, 20, 26 of angle, 108 perimeters of, 198 Sample, 82 of polygon, 178 Rectangular prisms, 220 Sample space, 385 of triangle, 150 surface area of, 224 Sampling naming, 612 volumes of, 230 cluster, 82 Side-Angle-Side (SAS) Postulate, Reduction, 348 convenience, 82 148–149, 155 Reference angle, 614 methods of, 82 Sides Reflections random, 82 consecutive, 178 defined, 338 systematic, 82 corresponding, 154 glide, 353 SAS (Side-Angle-Side) Postulate, exterior, 109–110 lines of, 338 148–149, 155 included, 155 matrices for, 369 SAS Similarity Postulate, 311 initial, 624 translations and, 338–341 Scalar, 359 opposite, 182 Reflexive property, 34 Scalar multiplication, 359 terminal, 624 Index Regular polygons, 179–180 Scale, 306 Side-Side-Side (SSS) Postulate, Regular polyhedra, 181, 221 Scale drawings, 306–309 148–149, 155 Relations defined, 306 Similar figures, 300 defined, 56 Scale factor, 348 Similarity symbol (), 300 functions and, 56–59 Scalene triangles, 150 Similar polygons, 300–303 range of, 56 Scatter plots defined, 300 Repeating decimals, 10 boxplots and, 406–409 Similar terms, 73 Replacement sets, 7 defined, 406 Similar triangles, 294–333 Review and Practice Your Skills, Scientific notation altitudes of, 317 14–15, 24–25, 32–33, 60–61, defined, 39 medians of, 317 70–71, 80–81, 90–91, 112–113, exponents and, 38–41 postulates for, 310–313

Index 793 Simpler problems, solving, 216–217 Squares, 183 modes, 49, 83 Simplifying completing, see Completing squares normal curves, 415 exponents, 464 difference of two, 483 outliers, 87 polynomials, 469 Squares of numbers, 425 populations, 82 Simulations, 388–389 SSS (Side-Side-Side) Postulate, quartiles, 407 defined, 388 148–149, 155 random samplings, 82 Sine curve, 625–626 SSS Similarity Postulate, 311 ranges, 49 Sine functions, 614 Standard deviation, 412–415 rating scales, 406 experiments with, 628–631 defined, 412 samplings, 82 graphing, 624–627 Standard equations scatter plots, 406–409 SI system, 39 of circles, 562–565 spreadsheets, 30, 395, 399, 500, 531 Skew lines, 119 defined, 562 standard deviations, 412–415 Slide, 338 of hyperbolas, 576 stem-and-leaf plots, 86 Slope-intercept form, 254–256 Standard form surveys, 384, 467 defined, 245 for equation of ellipse, 574 systematic sampling, 82 slopes of lines and, 244–247 polynomials in, 469 tally systems, 82 Slopes of lines Standardized Test Practice, 46–47, trend lines, 406 defined, 244 98–99, 144–145, 196–197, variances, 412 slope-intercept form and, 244–247 238–239, 290–291, 332–333, Steel scale, 202 SOH CAH TOA memory device, 614 378–379, 420–421, 462–463, Stem, 86 Solid line, 277 514–515, 556–557, 608–609, Stem-and-leaf plots, 86 Solids, Platonic, 221 640–641 Straight angles, 109 Solution, 7 Extended Response, 47, 99, 145, Straight lines, 62 methods of, 289 197, 239, 291, 333, 379, 421, Strategies, choosing, 634–635 Solutions 463, 515, 557, 609, 641 Subsets, 6 of equations, 7 Grid In, 47, 99, 145, 197, 239, 291, Substitution infinite number of, 259 333, 379, 421, 463, 515, 557, defined, 264 of systems of equations, 258 609, 641 solving systems of equations by, Solving Multiple Choice, 46, 98, 144, 196, 264–267 compound inequalities, 243 238, 290, 332, 378, 420, 462, Substitution property, 34 equations, 242 514, 556, 608, 640 Subtraction, 4 inequalities, 76–79 Short Response, 47, 99, 145, 197, addition and, 518 multi-step equations, 72–75 239, 291, 333, 379, 421, 463, estimation with, 20–23 one-step equations, 66–69 515, 557, 609, 641 matrix, 361 proportions, 561 Standard quadratic equations, of polynomials, 468–471 right triangles, 618–621 524–527 solving systems of equations by, simpler problems, 216–217 Statements 268–271 systems of equations biconditional, 129 Supplementary angles, 109 by addition, subtraction, and conditional, see Conditional Surface areas multiplication, 268–271 statements defined, 224 by graphing, 258–261, 561 Statistics, 82–93, 406–415 of three-dimensional figures, by substitution, 264–267 bell curves, 415 224–227 word problems, 5 box-and-whisker plots, 407–409 Survey, 384, 467 Space, 104 boxplots, 406–409 Symmetric property, 34 sample, 385 circle graphs, 446–447 Symmetry, 337 Special factoring patterns, 492–495 clusters, 87 axis of, 338, 521 Special right triangles, 436–439, 613 cluster samplings, 82 lines of, 337, 338 Spheres, 221 convenience samplings, 82 point, 345 surface area, 226 correlations, 406 Systematic sampling, 82 volumes of, 232 data, 82–89, 407 Systems Spreadsheets, 30, 395, 399, 500, 531 frequency distributions, 414 dependent, 259 cells in, 30 frequency tables, 82 of equations, 258–261, 561

Index columns in, 30 gaps, 87 defined, 258

rows in, 30 histograms, 87, 381, 414 determinants of, 274 Square bracket symbol ( ), 110 interquartile ranges, 408 linear, 242–291 Square matrix, 275 lines of best fit, 406 solutions of, 258 Square roots, 425 means, 49, 83 solving, see Solving systems of defined, 426 measures of central tendency, 49, equations product property of, 541 83–85, 380 three, 267 of products, 427 medians, 49, 83 inconsistent, 258 of quotients, 427 misleading graphs, 92–93 independent, 258

794 Index of inequalities, 276–279 Transitive property, 34 Unequal Sides Theorem, 173 defined, 276 of equality, 34 Union of sets, 16–19 of inequality, 77 defined, 16 ■ ■ Translations Unique Line Postulate, 105 T defined, 338 Unique Plane Postulate, 105 30-60-90 Triangle Theorem, 436, 613 reflections and, 338–341 Unit price, 204 Tally system, 82 Transversals, 120 Unit rate, 204 Tangent functions, 614 Trapezoid-Median Theorem, 188 Units of measure, 202–205 Tangent segments, 449 Trapezoids, 188–191 Universal set, 16 Tangents of circles, 441 base angles of, 188 Universe, 16 Technology, 45, 289, 461 defined, 188 Upper quartile, 407 calculators, 29, 30–31, 39, 40, 84, isosceles, 189 Using 226, 247, 289, 298, 311, 405, legs of, 188 graphs in writing equations, 428, 546, 615, 616, 625 medians of, 321 550–551 charting and data analysis Tree diagrams, 385 logical reasoning, 138–139 software, 531 Trend lines, 406 matrices, 372–373 computer program, 413 Triangle Inequality Theorem, 173 Pythagorean Theorem, 544–547 geometric drawing software, 119, Triangles, 178 technology, 30–31 189 acute, 150 geometric software, 106, 115, 179, angles of, 149 ■ ■ 316 areas of, 198 V geometry software, 109, 121, 153, congruent, see Congruent triangles Values 155, 157, 165, 166, 174, 320, defined, 150 absolute, 12 351, 371, 431, 433, 441, 443, equiangular, 150 input, 57 451 equilateral, 150 output, 57 graphing, 64–65, 245, 246, 248, 255, exterior angles of, 151 range of, 49 258, 261, 278, 283, 358, 360, inequalities in, 172–175 Variables, 7 363, 364, 370, 408, 426, 520, interior angles of, 147, 150 dependent, 57 521, 522, 523, 524, 525, 526, isosceles, see Isosceles triangles independent, 57 530, 532, 563, 566, 567, 575, medians of, 317 600, 626, 628, 629, 639 Variance, 412 naming sides of, 612 Variation spreadsheet program, 87 obtuse, 150 spreadsheets, see Spreadsheets combined, 587 overlapping, 157 constant of, 580 using, 30–31 perimeters of, 198 Technology Note, 106, 115, 119, 179, direct, see Direct variation proportional segments and, direct square, 581 189, 226, 245, 258, 278, 283, 311, 316–319 316, 349, 353, 358, 360, 363, 405, inverse, see Inverse variation quadrilaterals and other polygons inverse square, 585 408, 413, 426, 500, 525, 531, 575, and, 148–197 625 joint, 587 right, see Right triangles Terminal sides, 624 Venn, John, 17 scalene, 150 Terminating decimals, 10 Venn diagrams, 16–19 similar, see Similar triangles Terms, 52 Vertex triangle theorems and, 150–153 like, 73, 468 of angle, 108 vertex of, 150 in proportion, 296 of parabola, 521 Triangle-Sum Theorem, 150 quadratic, 498 of polygon, 178 Triangle theorems, triangles and, undefined, 104 of polyhedron, 220 150–153 Theorems, 114, 134 of triangle, 150 Triangular pyramids, 220 proofs of, 134 Vertex angles, 160 Trigonometric ratios, 614–617 Theoretical probability, 385–386 Vertical angles, 102, 115

Think Back, 82 Trigonometry, 612–641 Vertical Angles Theorem, 115, 134 Index Thinking, visual, 572–573 Trinomials, 468 Vertical line, 245 Three-dimensional figures factoring, 498–501, 506–509 Vertical line test, 57, 518–519 defined, 220 perfect square, 492 Vertices, consecutive, 178 loci and, 220–223 Triples, Pythagorean, 433 Visual thinking, 572–573 surface areas of, 224–227 Turn, 342 Vocabulary, 42, 94, 140, 192, 234, 286, volumes of, 230–233 328, 374, 416, 458, 510, 552, 604, Transformations, 336–379 ■ U ■ 636 composite of, 352 Volumes with matrices, 369 Undefined slope, 245 defined, 230 matrices and, 368–371 Undefined terms, 104 of three-dimensional figures, multiple, 352–355 Unequal Angles Theorem, 173 230–233 Index 795 ■ ■ 167, 171, 175, 181, 185, 190, 204, ■ ■ W 208, 215, 217, 223, 227, 232, 247, Y Well-defined sets, 6 251, 257, 261, 266, 270, 275, 278, y-axis, 56 Whole numbers, 10 284, 299, 303, 309, 313, 319, 323, y-coordinates, 56 Word problems, solving, 5 340, 341, 344, 345, 353, 361, 365, y-intercept, 245 Writing 371, 386, 387, 388, 395, 399, 405, You Make the Call, 69, 74, 107, 121, equations, using graphs in, 409, 413, 429, 433, 439, 443, 451, 136, 162, 215, 247, 340, 361, 547, 550–551 456, 470, 475, 480, 484, 490, 494, 630 equations for lines, 254–257 501, 503, 509, 522, 527, 533, 536, indirect proofs, 170–171 543, 547, 551, 564, 568, 569, 573, ■ ■ proportions, 297 577, 582, 586, 593, 617, 626, 631 Z ratios, 203, 292 Zero, 10 Writing Math, 8, 13, 19, 22, 28, 31, 37, ■ X ■ multiplication property of, 27 41, 55, 59, 64, 68, 74, 75, 79, 85, no reciprocal for, 27 88, 89, 93, 106, 110, 111, 117, x-axis, 56 Zero pairs, 62 121, 127, 131, 136, 152, 157, 163, x-coordinates, 56 Zero slope, 245 x-intercept, 245 z-score, 413 Index

796 Index