Click on a lesson's answer to return to that lesson's copymaster. Answers to Practice Workbook ■ Lesson 1.1 1. Add 4 to the preceding number; 18, 22, 26 2. Subtract 11 from the preceding number; 55, 44, 33 3. Divide the preceding number by 5; 25, 5, 1 4. Multiply the preceding number by 5; 1250, 6250, 31250 5. Multiply the preceding fraction by 2; 32 64 128 3, 3, 3 6. Add 32 to the preceding number; 9, 21 2 , 12 7. Add 1 to each preceding numerator and 6 7 8 denominator: 5 , 6 , 7 8. Multiply each preceding number by n 1 2 starting with n 5 0; 600, 3600, 25200 9. The pattern is every fourth letter of the alphabet; P, T, X 19. The numbers represent the speed in miles per hour that you are traveling. The larger the number, the faster you are traveling. Therefore, you and your family will arrive at the beach much sooner than your friend and her family, since your family was traveling 320 mph faster than your friendÕs. 20. The numbers represent the points scored for a particular team. Because Dallas scored more than Buffalo, Dallas won the game. ■ Lesson 1.2 1. The quotient of 21 and 3 is 7. 2. The sum of 14 and 5 is 19. 3. The product of 42 and 3 is 126. 4. The difference of 133 and 17 is 116. 5. 178 6. 56 9. 94.4 7. 995 10. 0.245 10. The pattern is every third letter of the alphabet; L, O, R 13. 11. The pattern is every other letter of the alphabet starting with Z and working in reverse; T, R, P 17. 112 18. 56 21. 2.5 22. 14.4 7 8 7 15 14. 6 8 5 3 4 16. 20. 6 23. 14,074 26. 1445 13. 60, 54, 48, 42, 36, 30 30. 10 2 4 5 6 14. 2, 4, 6, 10, 16, 26 32. 5 1 10 1 5 5 20 15. 34. 6,174,100 56 12. 5.71 1 7 19. 352.6 25. 114.375 28. 11. 4.07 15. 12. The pattern is every other letter starting with B; J, L, N 42 7 8. 42.6 24. 80.25 27. 145 29. 3 1 3 1 3 5 9 31. 18 2 12 5 6 33. 239,500 35. $761,800 1. 3 raised to the 4th power is 81. 2. The square root of 1.69 is 1.3. 16. 3. 10.52; 110.25 4. 75; 16,807 5. 1.23; 1.728 7. 17. The larger the number, the warmer the temperature. The smaller the number, the colder the temperature with 328F representing the freezing temperature of water. Therefore it was 708 warmer in Tempe than in Duluth. 18. The larger the number, the better the score with a score of 100 being a perfect score. So, your score is better than your friendÕs by 2 points. 118 Answers to Practice Workbook 64 s 25 d6; 15,625 9. 25 13. 2.74 6. 8.24; 4521.2176 8. 1 s 19 d4; 6561 10. 26 14. 2.06 17. 5.8 18. 3.5 21. 5 22. > 11. 15.6 15. 9 19. 144 23. < 12. 24.41 16. 5 20. 729 24. > 25. The perimeter of the kitchen is 80 ft. The perimeter of the bathroom is 32 ft. The area of the living room is 784 sq ft. The total area is 1248 sq ft. Passport to Algebra and Geometry Copyright © McDougal Littell Inc. All rights reserved. ■ Lesson 1.3 Click on a lesson's answer to return to that lesson's copymaster. 26. a. 512 cubic inches b. 384 square inches c. Yes, if neither the length, width, nor height of the “smaller box” is greater than 8 in. 11. No, the graph only shows the average monthly snowfall is very small, perhaps not measureable. But it does not state that it never snows during those months. ■ Lesson 1.4 ■ Lesson 1.7 1. 7 2. 15 3. 28 4. 0 7. 6 8. 6 9. 120 6. 41 11. 1 12. 30 15. 42.25 13. 57 16. 57 20. 192 10. 16 14. 17 17. 4 21. 34 1. Quadrilateral 5. 8 18. 8 22. 129 19. 42 23. True 3. Hexagon 2. Decagon 4. Octagon 5. It is not a polygon because not all its sides are straight. 6. It is a pentagon. 7. It is not a polygon because it has one more side than number of vertices. 24. False, s18 2 6d 4 2 5 6 25. False, 6 ? s3 2 2d ? 3 5 18 8. It is an octagon. 26. False, s24 2 3d 4 7 1 2 5 5 9. Answers vary. 27. False, s5 1 22d 4 3 5 3 28. True 29. False, 24 4 s4 1 2d 2 22 5 0 30. True 31. 36 4 s9 1 3d 5 3 10. Answers vary. 32. 6 1 s42 4 21d 5 8 33. 42 4 s14 4 2d 5 6 34. 12 2 s4 11. An equilateral octagon ? 2d 5 4 35. Total cost 5 4s5.25d 1 4s1.25d 1 4s1.15d 1 3.75 1 3.00 The total cost is $37.35. The amount of money remaining is $2.65. For Exercises 12–18, see the following table. Copyright © McDougal Littell Inc. All rights reserved. ■ Lesson 1.5 1. 4 2. 21 3. 6 4. 16 5. 14 6. 48 7. 4 8. 0 9. 16 10. 25 Type of Polygon No. of Sides No. of Vertices Total No. Diagonals 11. 4 12. 25 13. 3 14. 20 15. 16 12. Triangle 3 3 0 16. 19 17. 49 18. 64 19. 54 20. 55 13. Octagon 8 8 20 21. 23 22. 5 23. 3 24. 9 14. Nonagon 9 9 27 26. 13 27. 9 28. 49 15. Quadrilateral 4 4 2 16. Hexagon 6 6 9 35. a. 8a 1 6c; b. $112.00 17. Pentagon 5 5 5 36. a. 5 miles; b. 150 minutes 18. Decagon 10 10 35 31. a 32. b 33. 2 29. c 25. 3 30. d 34. 3 37. a. 255 yds; b. 765 ft; c. 114,750 sq ft 19. Yes 20. No, no vertices, no straight edges ■ Lesson 1.6 21. Yes 22. No, curved edges. 1. Pocahontas 2. $75.7 million 3. $333.2 million 4. University of Iowa 5. Yes, five more. 6. Yes, Iowa has dominated. 7. Answers vary. 8. March 9. < 10.8 in. ■ Lesson 1.8 1. n 0 1 2 3 4 5 6 55n 0 55 110 165 220 275 330 10. < 49.8 in. Passport to Algebra and Geometry Answers to Practice Workbook 119 Click on a lesson's answer to return to that lesson's copymaster. 720 n 3. 3x 1 3 1 2 3 4 5 6 720 360 240 180 144 120 n 4. 20x 1 10 x x 1 1 3. 1 n 1 2 3 4 5 6 7 8 9 n 5 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 5. 6 1 10 or 16 7. 3x 1 6 4. x x x 6. 48 1 84 or 132 8. 15y 1 60 10. 16 1 8p 9. 4z 1 12 11. xy 1 3x 12. ac 1 4a n 1 2 3 4 5 6 7 8 9 13. 2x 1 2y 1 2z 14. az 1 4z 1 bz 4 n 4.0 2.0 1.3 1.0 0.8 0.6 0.571428 0.5 0.4 15. fg 1 3f 1 fh 16. 20 1 10y 1 10z 17. 30.8 5. n 1 2 3 4 5 6 7 n 1 1 n 2 1.5 1.3 1.25 1.2 1.16 1.142857 18. 159.12 19. 20,251.5 Total summer earnings 20. a. 1 5 16 6. Weekly earnings job 1 Weekly 1 earnings job 2 n 0 1 2 3 4 nsn 1 1d 2 b. $1256 5 16s56 1 22.50d 0 1 3 6 10 monthly payment 21. a. Total 5 12 for bike 7. 6, 12, 18, 24, 30, 36, 42. Possible explanation: The sequence is the product of the first 7 natural numbers and 6, 6n. 8. 102, 204, 306, 408, 510, 612, 714. Possible explanation: The three digit numbers can be determined by combining the first term as the first digit and twice the first term as the second and third digits. 9. 2 1 9 5 5 5 , 38, 47, 56, 65 1 monthly payment for CD player monthly payment 1 for in-line skates ■ Lesson 2.2 1. 4x 3. 8z 1 10 2. 9y 4. 9a 1 5b 5. 9z 1 9 7. 11s 1 2t 1 4 6. 21z 1 5 8. 12x 1 9y 1 4 11. 6 3 5 5 5 5 , 3750, 18750, 93750, 468750 12. 2x3 1 2x2 13. 9y 1 6 15. 10st 1 12 16. 3x 1 7z 1 8 12. 6144 4 4 5 5 5 , 24, 6, 1.5, 0.375 17. 4x 1 3y 1 26 13. 2500 19. 9x 1 2y, 35 16. 25,010,001 ■ Lesson 2.1 1. 2 units by x 1 3 units, 2sx 1 3d, 2x 1 6 2. 3 units by 2x 1 4 units, 3s2x 1 4d, 6x 1 12 2 b. $783.00 5 12s26.50 1 21.25 1 17.50d 9. 10x 1 11 15. 63,001 2 1 10. 4 3 3 5 5 5 , 324, 972, 2916, 8748 14. 250,000 1 1 1 1 1 1 1 1 10. 2a2 1 10a 11. 6z2 1 7z 14. 10z 1 16 18. 4ab 1 2a 1 4 20. 3y 1 4, 16 21. 7x 1 5y, 41 22. x2 1 xy 1 3y, 33 23. 2x2 1 xy, 30 24. 5x 1 5y, 35 25. Perimeter 5 8x x 1 2 3 4 5 Perimeter 8 16 24 32 40 The perimeter increases by 8 each time x increases by 1. 120 Answers to Practice Workbook Passport to Algebra and Geometry Copyright © McDougal Littell Inc. All rights reserved. 2. Click on a lesson's answer to return to that lesson's copymaster. 26. Perimeter 5 12x 5. 23 6. 54 10. 14.9 x 1 2 3 4 5 9. 77 Perimeter 12 24 36 48 60 13. 4.49 The perimeter increases by 12 each time x increases by 1. d. 3sa 1 1d 1 5sb 1 2d 5 3a 1 5b 1 13 ■ Lesson 2.3 2. c 3. d 20. x 2 7 5 28; 35 3. 5 26. 19,251 11. Yes 12. No, x 5 4 13. Yes, 4 5 4 14. No, 4 Þ 20 15. 5 16. 13 18. 51 20. Identity; true for all values of x. 21. 6.4 million 22. 5.4 million 23. 6.3 million ■ Lesson 2.4 x 1 21 5 65 x 1 21 2 21 5 65 2 21 x 5 44 58 5 y 2 32 58 1 32 5 y 2 32 1 32 90 5 y z 2 28 5 101 z 2 28 1 28 5 101 1 28 z 5 129 312 5 w 1 217 312 2 217 5 w 1 217 2 217 95 5 w Passport to Algebra and Geometry 5. 9 9. 21 9. No, x 5 4 10. Yes 25. 1553 yds 4. 10 8. 20 26. 1411 yds 6. 5 10. 60 14. 33.75 17. 51.2 18. 48 22. 6 23. 5748 15. 15.6 19. 4 20. 3 21. 9 25. 3857 28. 6 Yards per carry Total 12. 2.6 16. 45 24. 4840 27. 4 33. a. yards 5 7. 72 11. 22 31. 5m 5 45, 9 30. 14 29. 17 32. 8c 5 56, 7 ? Number of carries b. x 5 s4.368ds3838d; x 5 16,764.384 yards (NOTE: Actual total yards 16,726.) 19. Conditional equation; true for x 5 12. Copyright © McDougal Littell Inc. All rights reserved. 21. y 1 2.7 5 8.3; 5.6 1. The product of 5 and a number is 10; x 5 2. 13. 45 4. 19. 5418.08 ■ Lesson 2.5 6. 5 subtracted from what number is 3?; 8 x 7. 5 1 x 5 19; 14 8. 5 7; 56 8 3. 16. 10.229 2. The quotient of a number and 2 is 11; z 5 22. 4. a 5. What number can be multiplied by 3 to obtain 36?; 12 2. 15. 522.35 18. 97.02 24. 1538 yds c. 3x 1 5y 1. 12. 8.7 23. a 2 5.01 5 22.7; 27.71 b. 2x 1 3y 17. 24 11. 3.44 14. 62 17. 10.93 8. 618 22. z 1 3.1 5 15.2; 12.1 27. a. x 1 2y 1. b 7. 66 ■ Lesson 2.6 1. a 2. c 3. b 4. d 5. 16 1 n n n 6. 7. 8. 8n 9. n 2 12 12 11 10. 6n 1 14 13. 6sn 1 4d 11. 8 2 5n n 14. m14 16. a 1 5 17. a 1 5 20. a 2 6 21. 12. 3n 1 17 15. 3n 2 6m 18. a 1 or a 3 3 n 4 19. 5c 22. 4a 23. a 1 14 24. a. C 5 38.70 1 5.75m; b. $211.20 ■ Lesson 2.7 1. d 2. b 3. a 5. n 2 5 5 13, 18 7. b 5 9, 63 7 4. c 6. 225.75 5 3x, 75.25 8. 32 5 18 1 y, 14 Answers to Practice Workbook 121 Click on a lesson's answer to return to that lesson's copymaster. 12. 5 days per week 3 2 trips per day 3 16 miles per trip 5 160 miles per week 9. The difference of a and 6 is 13. 10. 45 is the product of 5 and c. 13. 3 miles per day 3 7 days per week 3 21 miles per week 11. The quotient of e and 5 is 40. 12. 15 is 3 more than f. ■ Lesson 2.9 Number 13. Verbal Model: 6 5 21 Missing number 5 x Labels: Algebraic Model: 14. Verbal Model: x 5 21 6 x 5 126 2. Answers vary. 3. Answers vary. 4. Answers vary. 5. Answers vary. 6. Answers vary. 8. y ≥ 12 7. x < 5 5 Number 3 11 165 1. Answers vary. Labels: Missing number 5 x Algebraic Model: 165 5 x ? 11 9. z < 5 10. a > 22 11. b < 10 13. p < 15 14. q > 48.8 17. 110.5 ≥ y 16. 294 > c 22. 69 > 3a, 23 > a 23. The difference of e and 4 is greater than 6. Cost of item for your sister 5 Total cost 24. The sum of 5 and f is less than or equal to 10. Labels: Cost of items for you 5 2.50 1 6.50 1 13.50 25. 28 is less than the product of 7 and r. Cost of item for your sister 5 x 27. No Algebraic Model: 2.50 1 6.50 1 13.50 1 x 5 39.00 31. first five Length 1 Width 25 33. x ≥ 92 Perimeter 4. w 5 22 5. Width is 22 ft and length is 70 feet. 7. 34. Yes, any test score greater than or equal to 92 would guarantee a point total greater than or equal to 540. 1. −3 −1 ? Monthly sales 5 Sales commission 3. < Monthly sales 5 2600 13. 10, 10 Sales commission 5 x 16. 257 122 ? 2600 5 x 10. x 5 104 11. $404 Answers to Practice Workbook 0 4. < 9. 23, 3 1 8. Sales commission rate 5 25 ; 1 25 −2 −1 0 1 2. ? 5 5 $920 Sales commission rate Point total for course to earn an A ≥ 1 sixth exam ■ Lesson 3.1 ? sw 1 48 1 wd 5 184 6. 184 Scores on 30. No 32. 85 1 92 1 88 1 96 1 87 1 x ≥ 540 2. Width 5 w Length 5 w 1 48 Perimeter 5 184 3. 2 29 No 1 5. > 10. 2, 2 2 3 6. > 19. 26, 24, 2, 3, 5 5 7. < 11. 25, 5 14. 100, 100 17. 15 4 8. > 12. 6, 6 15. 700 18. 20 20. 210, 27, 0, 6, 8 Passport to Algebra and Geometry Copyright © McDougal Littell Inc. All rights reserved. ?1 28. Yes exams ■ Lesson 2.8 1. 2 26. The product of 17 and r is less than 102. Scores on x 5 16.50 9. 18. 2.8 < z 19. d 2 5 ≤ 4.25, d ≤ 9.25 21. 40x < 120, x < 3 15. Verbal Model: 1 15. x < 9.7 20. y 1 7 > 10, y > 3 15 5 x Cost of items for you 12. 27 > c Click on a lesson's answer to return to that lesson's copymaster. 21. 23, 22, 1, 2, 4 23. 3 days 22. 23, 21, 0, 1, 2 24. 9 days 25. 7 days 26. 3 days 27. Tampa San Diego −20 −10 0 10 20 30 40 50 60 70 29. 658 2. 26 1 s23d 5 29 1. 3 1 12 5 15 3. 212 1 s212d 5 224 6. 12 1 s218d 5 26 5. 25 1 5 5 0 8. 26 1 s226d 5 0 7. 219 1 12 5 27 9. 4 1 0 5 4 4. 6 1 16 5 22 10. 0 1 s211d 5 211 11. 15 1 s22d 5 13 12. 212 1 0 5 212 25. 5x 1 11, 26 26. > 27. > 28. < 31. > 32. $5yshare 3. 6 2 s28d 5 14 19. x 5 29 20. z 5 2 7. 14 2 s23d 5 17 8. 16 2 s216d 5 32 9. 216 2 16 5 232 23. a, x 5 70, $70 in the account 24. Answers vary. 25. Answers vary. 27. a, c 17. 10x 1 s212d 1 s25d; 10x, 212, 25 18. 26x 2 7 19. 9m 1 2 21. 258x 25. 209 29. Answers vary. 30. Asia North America Africa Europe 30,340 ft 20,602 ft 19,852 ft 18,602 ft 32. 830 ft 2. 8s10d 5 80 4. 215 ? 3 5 245 5. 10 ? s23d 5 230 4. 216 1 15 1 s23d 5 24 7. s23ds27d 5 21 5. 210 1 11 1 s22d 5 21 9. s4ds0d 5 0 6. 210 1 6 1 s28d 5 212 12. 11w 13. 212 8. 6 1 s25d 1 s24d 5 23 16. 212 17. 60 9. 10 1 s22d 1 13 5 21 20. 30 13. 247 24. 3978 6. 7 21. 36 25. 240 ? s24d 5 228 8. s0ds230d 5 0 11. 210a 10. 8y 7. 210 1 s26d 1 s215d 5 231 Passport to Algebra and Geometry 27. 26 26. 6 3. 23 ? s22d 5 6 3. 6 1 s27d 1 s28d 5 29 12. 2342 20. 29y 2 3 23. 6 2 m or 2m 1 6 22. 12z 1. 6 ? 5 5 30 2. 26 1 s22d 1 10 5 2 11. 155 14. 0, 0 ■ Lesson 3.5 1. 6 1 s22d 1 s28d 5 24 10. 265 13. 4, 8 16. 4x 1 s22xd 1 8; 4x, 22x, 8 31. 21030 ft ■ Lesson 3.3 10. 21, 25 12. 0, 24 28. Answers vary. 22. b, x 5 270, 70 feet below sea level 4. 10 2 s22d 5 12 6. 12 2 s28d 5 20 24. 24 21. m 5 13 33. 50th floor 5. 223 2 2 5 225 15. 4, 24 18. Answers vary. 30. < 2. 24 2 s23d 5 21 1. 3 2 7 5 24 14. 0, 21, 22, 23, 24 The numbers decrease by 1. 17. Answers vary. 29. < ■ Lesson 3.4 11. 1, 5 16. Answers vary. 23. 6x 1 8, 26 22. x, 3 24. 19x 1 4, 61 13. 2, 3, 4, 5, 6 The numbers increase by 1. 15. 24, 22, 0, 2, 4 The numbers increase by 2. 18. 2x, 6 20. 5x 1 7, 22 21. 8x 1 6, 30 °F ■ Lesson 3.2 26. b, c 17. 11x 1 4, 37 19. 9x 1 10, 37 St. Paul Copyright © McDougal Littell Inc. All rights reserved. | | | 15. Positive, |115| > |238 1 s242d| 16. 2x, 6 Anchorage 28. 708 | 14. Negative, 2321 > 215 1 43 14. 236 15. 4 18. 230 22. 351 19. 24 23. 24242 26. 299 27. 1806 Answers to Practice Workbook 123 Click on a lesson's answer to return to that lesson's copymaster. 28. 29 29. 25 30. 210 32. 212 33. 5 36. 216 37. 418F, 148F 34. 28 31. 3 35. 24 21. $10,000 23. Answers vary. ■ Lesson 4.1 3. 232 2. 45 5. 218 20. $17,500 22. V 5 25000 2 2500t ■ Lesson 3.6 1. 32 19. 12 2 2 5 10; Answers vary. 6. 0 7. 0 1. 9 4. 26 9. 242 8. 48 6. 225 2. 3 3. 21 7. 36 8. 2 9. 3 10. 10. 218, 217, 216, 215, 214 The numbers increase by 1. 5. 215 4. 8 = 11. 2, 3, 4, 5, 6; The numbers increase by 1. 13. 4 16. 20 17. 218 20. 230 15. 216 14. 6 18. 222 = 19. 230 22. 26 21. 15 = 23. 55.576 seconds 24. Less than result in Exercise 23. If trend of faster times continues, then the average of the next six Olympic games will be faster. 12. 6x 1 11 5 65; 9 11. 2x 1 3 5 13; 5 x x 13. 1 2 5 27; 227 14. 2 6 5 1; 28 3 4 15. 2x 1 17 5 43; 13 16. 4x 1 34 5 94; 15 ■ Lesson 3.7 1. Yes 2. No, y 5 24 3. Yes 4. No, m 5 248 6. 23 5. 3 9. 210 10. 28 13. 33 8. 29 7. 17 11. 23 15. 23 14. 2 12. 16 16. 216 17. x 1 3 5 26, x 5 29 The sum of 29 and 3 is 26. 20. 4080 22. 21334 23. 2528 18. Answers vary. ■ Lesson 4.2 24. 253 26. a 27. b 29. f 30. e 31. 72 5 32t 1. No; x 5 2 28. d 32. t 5 2.25 hours (2 hours 15 minutes) ■ Lesson 3.8 1. S, 3 2. Q, 1 5. U, 2 6. T, 3 10. 2 11. 2 15. 3 units2; 8 units 3. R, 4 4. P, 2 4. Yes 5. 24 8. 11 9. 213 12. 13 13. 26 2. No; y 5 22 6. 12 10. 2 3. Yes 7. 216 11. 29 14. 2x 1 5x 1 s23xd 1 s23d 5 9; 3 8. 1 9. 3 15. 7y 1 2y 2 11 5 238; 23 13. 3 14. 4 16. 10x 2 10 1 4x 1 8 5 180; x 5 13; 1208, 608 7. 4 12. 1 b. Length 5 78 feet Width 5 w d. The width is 36 feet. 21. 36 25. c 17. a. Length 5 2 ? Width 1 Six feet c. 78 5 2w 1 6 w 5 36 18. 23z 5 227, z 5 9 The product of 9 and 23 is 227. 19. 22556 = 16. 36 units2; 26 units 17. 2 1 s212d 5 210; Answers vary. 17. 22x 2 2 1 15x 1 18x 1 2 1 5x 5 360; x 5 6; 1308, 908, 1108, 308 18. 9 2 3 5 6; Answers vary. 124 Answers to Practice Workbook Passport to Algebra and Geometry Copyright © McDougal Littell Inc. All rights reserved. 12. 12 Click on a lesson's answer to return to that lesson's copymaster. 18. a. s8 1 7 1 7 1 4 1 7 1 10 1 10dx 5 323.30 b. x 5 6.10; $6.10 per hour ■ Lesson 4.3 ■ Lesson 4.5 1. c 2. a 5. 1 6. 24 9. 28 4. 26 3. b 10. 7. 26 5 23 13. 3x 1 14 5 x 1 20; x 5 3 2. Divide both sides of the equation by 23 or 1 multiply both sides by 2 3 . 15. 4x 2 2 5 3x 1 2; x 5 4 4. 215 5. 20 4 7. 4 8. 2 3 11. 7 12. 10 9. 2 6. 18 14. 28 16. 4sx 1 3d 5 2x 1 8; x 5 22 18. x 5 6; the length of each side is 20 units. 19. x 1 18 1 10 5 2sx 1 10d; x 5 8 The second culture is 8 days old. The first culture is 26 days old. 15. 4n 1 16 5 100; n 5 21 16. 3n 2 23 5 34; n 5 19 17. 12 n 1 27 5 40; n 5 26 ■ Lesson 4.6 18. 13 5 15 n 2 8; n 5 105 20. a. 14. 5x 1 38 5 2x 1 47; x 5 3 17. x 5 4; the perimeter is 36 units. 10. 10 13. 29 12. 22 11. 2 1. Divide both sides of the equation by 4 or 1 multiply both sides by 4 . 3. 10 8. 231 19. 75 cm 1. StudentsÕ tables and graphs may vary slightly. 2w + 6 Minutes w b. Width 5 11 inches Length 5 28 inches 1 2 3 4 5 Company 1 2.00 2.15 2.30 2.45 2.60 Company 2 2.50 2.60 2.70 2.80 2.90 6 7 8 9 10 Company 1 2.75 2.90 3.05 3.20 3.35 Company 2 3.00 3.10 3.20 3.30 3.40 11 12 13 14 15 Company 1 3.50 3.65 3.80 3.95 4.10 Company 2 3.50 3.60 3.70 3.80 3.90 Minutes 21. ArkansasÕ governor salary 5 $60,000 New YorkÕs governor salary 5 $130,000 ■ Lesson 4.4 Minutes 2. The second line should be 4x 2 8 1 6 5 16; 9 x 5 2 or 4.5 3. 2 4. 4 8. 3 9. 230 6. 22 5. 5 10. 234 7. 2 11. 28 12. a. 220 13. a. 23 b. 220 b. 23 c. Answers vary. Cost (in dollars) Copyright © McDougal Littell Inc. All rights reserved. 1. The second line should be 23x 1 2 5 8; x 5 22 c. Answers vary. 14. 6sx 1 5d 5 42; x 5 2 15. s3x 2 2d 1 s2x 2 1d 1 s7x 1 3d 5 180; x 5 15; 438, 298, 1088 16. 7sxd 1 3s9d 5 5s9 1 xd; x 5 9; 9 pounds of cashews Company 2 3.50 (11, 3.50) 3.00 2.50 Company 1 2.00 2 2. Cost 1 minute Company 1 5 Passport to Algebra and Geometry 4.00 4 6 8 10 12 Number of minutes 1 Cost 1 minute Company 2 Cost per minute after first 1 3 Cost per minute after first 14 t Number of minutes after first 3 Number of minutes after first Answers to Practice Workbook 125 Click on a lesson's answer to return to that lesson's copymaster. 3. Cost first minute Company 1 5 $2.00 Cost per minute after first 5 $0.15 Number of minutes after first 5 t 2 1 Cost first minute Company 2 5 $2.50 Cost per minute after first 5 $0.10 Number of minutes after first 5 t 2 1 4. 2 1 0.15st 2 1d 5 2.50 1 0.10st 2 1d 6. 11 minutes 7. $3.50 8. 2500 1 12x 5 52x; x 5 62.5; so you need to sell at least 63 helmets to break even. ■ Lesson 4.7 2. The second line should be 0.8575x 2 2.037 5 12.64; x < 17.12 7. 1.58 4. 1.08 15. 1.39 6. 1.67 9. 221.58 8. 1.22 11. 25.27 5. 1.12 12. 7.96 16. 0.72 10. 2.62 13. 5.67 14. 12.24 17. $25.65 18. $5.65 19. 29 wings (total bill $4.98) 8. Periodic table of elements introduced. 9. BoyleÕs Law formulated. ■ Lesson 5.2 1. A simple bar graph, one bar could be used for each type of blood. 2. A double bar graph or stacked bar graph 3. 1901Ð10 5. Yes, it appears that during the twentieth century, the number of immigrants was at the highest from 1901Ð1910. Then the number decreased, reaching its lowest from 1931Ð1940. Since then it appears the number of immigrants increased each decade. 6. If the trend continues there should be more than 8000 immigrants from 1991Ð2000. 7. See studentsÕ graphs. Time intervals may vary. One possible graph: 20. < 56.78 miles or 57 miles 1. 8; each side is 6 units. 2. 4; width is 22 units; length is 10 units. 3. x 5 3; each side is 13 units. 4. x 5 25; m/1 5 708, m/2 5 1108 5. x 5 14; m/1 5 458, m/2 5 508, m/3 5 858 7. 52 square inches 8. 12,636 square feet 9. 53,125 square miles; area of rectangle 1 area of triangle ■ Lesson 5.1 10 Number of Students ■ Lesson 4.8 6. 1836 square feet 7. < 1803 6. 25 years 4. 1921 to 1930 and 1931 to 1940 1. The second line should be 5.5x 1 11.25 5 22.5; x < 2.05 3. 23.5 5. There would be half as many TVÕs in each row. 8 6 4 2 0 4.5-4.9 5.0-5.4 5.5-5.9 6.0-6.4 6.5-6.9 7.0-7.4 Time in Seconds ■ Lesson 5.3 1. The units of the horizontal axis are years starting with 1980 increasing in increments of one year. The units of the vertical axis are number of tornadoes starting with 0 increasing in increments of 100. 1. 2. < 1050 Korean Desert Mexican War Civil War French and War Storm Indian War War of 1812 W.W. I 3. 1981, 1983, 1984, 1985, and 1987 1650 1700 1900 1950 2000 W.W. II Vietnam Revolutionary War Spanish American War War 2. 5 seasons 126 1750 1800 1850 3. 33 seasons Answers to Practice Workbook 4. Many possible theories: 1. greenhouse effect causing more severe weather 2. better reporting of data Passport to Algebra and Geometry Copyright © McDougal Littell Inc. All rights reserved. 5. t 5 11 4. 8 seasons (as of 1996) Click on a lesson's answer to return to that lesson's copymaster. Width 2 2 2 2 2 Length 2 3 4 5 6 Perimeter 8 10 12 14 16 18 16 14 12 10 8 6 4 2 0 1. The consumption of poultry appears to be 3 times as much as that of eggs. 2. The consumption of poultry is only about 2 times as much as that of eggs. 3. Yes, because the vertical scale starts at 15 instead of 0. 4. 1 2 3 4 5 Length (in inches) 6 7 1000 800 120 105 90 75 60 45 30 15 0 Red Meat 600 Food 200 5. JulyÕs bill appears to be twice JuneÕs bill. 1970 1980 Year 1990 6. JulyÕs bill is $85 and JuneÕs $65. JulyÕs is only $20 more than JuneÕs. 8. Answers vary. 7. The vertical scale is misleading because the units start at $50. ■ Lesson 5.4 1. A pictograph or bar graph would be best for simple data. Possible graph: Show 8. Number of Performances A Chorus Line Oh Calcutta Cats Les Miserables Phantom of the Opera = 1 thousand shows 2. a. About 1000 thousand or 1,000,000 90 80 70 60 50 40 30 20 10 0 J F M A M J J A S O N D Month ■ Lesson 5.6 1. Yes. Explanations vary. b. In the category of living with their spouses 2. Yes. Explanations vary. c. Answers vary. 3. d. Possibly a stacked bar graph if you want to compare the total of each living arrangement. x x x x x x x x x x x x x x x x 2 3 4 3. A time line is the best way to present the data. Cobb 1910 Eggs Poultry 400 1960 Copyright © McDougal Littell Inc. All rights reserved. Consumption (in pounds) 7. Amount (in $ billions) Perimeter (in inches) 6. ■ Lesson 5.5 Electric bill (in dollars) 5. Klein and Foxx Medwick Hornsby 1920 Zimmerman 1930 1940 Gehrig Robinson Mantle 1950 Williams Passport to Algebra and Geometry x x x x x x x x x x x x x x x x x x x x x x 5 6 x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x 7 8 9 x x x x x x x x x x x x x x x x x x x 10 11 12 1960 Yastrzemski 4. a. 1 hit per game; b. 0.250 batting average Answers to Practice Workbook 127 Click on a lesson's answer to return to that lesson's copymaster. ■ Lesson 5.7 5. Yes: 2, 3, 6, and 9; No: 4, 5, 7, and 10 1. No correlation. Answers vary. 6. Yes: 3, 5, 7, and 9; No: 2, 4, 6, 8, and 10 2. Negative correlation. Answers vary. 7. 8 3. Positive correlation. Answers vary. 9. 1, 4, or 7 8. 1, 3, 5, 7, or 9 10. 0 or 6 4. Positive correlation. As the number of study hours increases, test scores should increase. 11. 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 5. No correlation. The number of pets you own and your age have no pattern. 14. Let a 5 4x and b 5 4y, and let x and y be integers. Then 12. 315 6. Negative correlation. As the number of hours you watch TV increase, test scores should decrease. a. a 1 b 5 4x 1 4y 5 4sx 1 yd b. sa 2 bd 5 4x 2 4y 5 4sx 2 yd c. ab 5 s4xds4yd 1125 1100 1075 1050 1025 1000 975 950 a 4x x 5 5 b 4y y In a, b, and c, x and y can still be integers so that the expressions are always divisible by 4. x In d, may be a fraction or an integer not y divisible by 4. d. 0 5 10 15 20 25 30 35 Altitude (in thousands of feet) 15. 1, 2, 3, 4, 6, 8, 12, 24 8. Negative correlation 16. 1, 2, 3, 6, 9, 18, 27, 54 9. About 1065 ftysec 17. 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 10. About 27,000 feet 18. 1, 3, 5, 7, 15, 21, 35, 105 11. About $44,000 19. 1 mi-by-80 mi, 2 mi-by-40 mi, 4 mi-by-20 mi, 8 mi-by-10 mi, 16 mi-by-5 mi 12. Positive correlation. As the years go by, the average salary increases. 13. Answers will vary slightly. In 1998, the average salary should be about $55,000. ■ Lesson 5.8 1. 6. 1 6 1 3 2. 7. 1 2 1 13 1 3 3. 8. 4. 3 13 2 3 9. 5. 3 26 ■ Lesson 6.2 1. Composite, 39 5 13 ?3 2. Prime, 41 5 41 ? 1 only 1 2 10. 20. 20 yd-by-20 yd 2 13 3. Composite, 57 5 19 ?3 24 33 1. Yes: 2, 3, 4, 6, and 8; No: 5, 7, 9, and 10 5. 6. 2 ? 33 ?3 7. 2 ? 3 ? 7 8. 26 9. 22 ? 3 ? 7 10. 24 ? 32 11. 23 ? 52 12. 22 ? 32 ? 5 13. s21d ? 2 ? 2 ? 3 ? 3; s21d ? 23 ? 32 14. s21d ? 3 ? 3 ? 5; s21d ? 32 ? 5 15. 2 ? 2 ? 2 ? 3 ? x ? x; 23 ? 3 ? x2 16. 2 ? 2 ? 2 ? 2 ? a ? a ? a ? b ? b; 24 ? a3 ? b 2 2. Yes: 3, 5, 7, and 9; No: 2, 4, 6, and 10 17. 90 18. 336 3. Yes: 2, 3, 4, 5, 6, 8, 9, and 10; No: 7 20. 1, 2, 4, 8, 16 4. Yes: 2, 3, 4, 6, 8, and 9; No: 5, 7, and 10 22. 1, 2, 3, 6, 9, 18, 27, 54 11. 5 blue socks, 10 white socks, 4 black socks and 1 argyle sock 379 2528 349 b. 2528 905 2528 < 12. a. 13. < 0.15 < 0.14 0.36 14. 1623 2528 < 0.64 ■ Lesson 6.1 128 Answers to Practice Workbook 4. 19. 2540 21. 1, 2, 3, 4, 6, 8, 12, 24 Passport to Algebra and Geometry Copyright © McDougal Littell Inc. All rights reserved. Speed of Sound (in feet per second) 7. 13. 24 Click on a lesson's answer to return to that lesson's copymaster. 23. 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97 5 5 4 1 1, 13 5 9 1 4, 17 5 16 1 1, 29 5 25 1 4, 37 5 36 1 1, 41 5 25 1 16, 53 5 49 1 4, 61 5 36 1 25, 73 5 64 1 9, 89 5 64 1 25, 97 5 81 1 16 6. 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, . . . 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, . . . 12, 24, 36, 48, 60, 72, . . . LCM 5 60. 24. No other pairs exist because for a pair of numbers to be consecutive one must be even and therefore composite. 7. 36 5 2 ? 2 ? 3 ? 3, 54 5 2 ? 3 ? 3 LCM 5 2 ? 2 ? 3 ? 3 ? 3 5 108 ■ Lesson 6.3 1. 6 6. 165 2. 6 3. 10 7. 2xy 10. 9x 2y 3 4. 18 8. 2xy 2 5. 240 9. 5r 2p 11. 10 and 15, 20 and 25, . . . 12. 3 and 6, 9 and 12, . . . 13. 12 and 24, 36 and 48, . . . 14. Yes 15. No, GCF 5 3 16. Yes 8. 15 5 3 ? 5, 35 5 5 ? 7 LCM 5 3 ? 5 ? 7 5 105 9. 145 5 5 ? 29, 275 5 5 ? 5 ? 11 LCM 5 5 ? 5 ? 11 ? 29 5 7975 10. 81 5 3 ? 3 ? 3 ? 3, 216 5 2 ? 2 ? 2 ? 3 ? 3 LCM 5 2 ? 2 ? 2 ? 3 ? 3 ? 3 ? 3 5 648 12. 3x2 5 3 ? x ? x, 5y 2 5 5 ? y ? y LCM 5 3 ? 5 ? x ? x ? y ? y 5 15x 2 y 2 18. A 5 108, P 5 42 They are not relatively prime, GCF 5 6. 13. 3 and 13 20. GCF 5 2 21. GCF 5 3 22. 7 children; A can of soda costs $0.48 and one candy bar costs $0.35. ■ Lesson 6.4 1. 5, 10, 15, 20, 25, 30, 35, 40, . . . 7, 14, 21, 28, 35, 42, 49, . . . LCM 5 35. 2. 3, 6, 9, 12, 15, 18, 21, 24, 27, . . . 8, 16, 24, 32, . . . LCM 5 24. 3. 9, 18, 27, 36, 45, . . . 12, 24, 36, 48, . . . LCM 5 36. 4. 12, 24, 36, 48, 60, 72, 84, 96, . . . 14, 28, 42, 56, 70, 84, 98, . . . LCM 5 84. 5. 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, . . . 5, 10, 15, 20, 25, 30, 35, . . . 6, 12, 18, 24, 30, 36, . . . LCM 5 30. Passport to Algebra and Geometry ?3 11. 13xy 2 5 13 ? x ? y ? y, 26x 2y 3 5 2 ? 13 ? x ? x ? y ? y ? y LCM 5 2 ? 13 ? x ? x ? y ? y ? y 5 26x 2y 3 17. A 5 28, P 5 22 They are not relatively prime, GCF 5 2. 19. A 5 77, P 5 36 They are relatively prime. Copyright © McDougal Littell Inc. All rights reserved. ?3 14. Possible answers: 4 and 9, 4 and 18, 12 and 18 15. 4 and 25 16. Possible answers: 8 and 18 or 18 and 24 17. 75 bottles, 4 packs 18. 352 miles; AngelÕs car used 11 gallons. MoÕs car used 16 gallons. 19. 84 minutes later at 2:24 A.M. ■ Lesson 6.5 3 1. 4, 7 5. 2, 9. 13. 2 19 1 3z3 9 16 2 2. 4, 9 6. 12, 10. 14. 1 3. 9, 5 7 9 18. Possible answers: 19. Possible answers: 24. > b 4a 2x 12. 2 5y 8. 9 15 64 , 20 16 8 12 10 , 15 , and 20 28 14 21 16 , 24 , and 32 3 1 2 3 , 6 , and 9 15. 17. Possible answers: 20. > 1 3y 3x 2 11. 4 5y 7. 8yz 9 7 4 12 , 49 2 4. 11, 7 21. 5 22. < 25. 5 1 11 26. 16. 25 64 23. 5 27. 2 11 24 28. Mr. MorganÕs class did better because 36 > 21 35 . Answers to Practice Workbook 129 Click on a lesson's answer to return to that lesson's copymaster. ■ Lesson 6.6 4. 20. 1.95 3 106; 1,950,000 11 2. 20 17 5. 2 5 3. 6. 9 25 67 4 21. 3.744 3 1029; 0.000000003744 22. 2.185 3 1023; 0.002185 7. Rational, 0.36, repeating 23. 1 3 106 > 6 3 105 because 1,000,000 > 600,000 8. Rational, 0.625, terminating 24. 1 3 1024 < 4 3 1023 because 0.0001 < 0.004. 9. Rational, 4, terminating 10. Irrational, 5.6568542 . . . , non-repeating 25. Approximately 4.4688 3 1014 mi 11. Rational, 0.5625, terminating 26. 0.006, 6.0 3 1023 gal; 1.994 gal 12. Rational, 0.32, terminating 13. 18. 7 10 38 9 13 25 15. 19. b 20. a 14. 19 20 16. 11 50 21. d 17. 94 99 22. c 23. 0.1, 0.2, 0.3, 0.4, 0.5, 0.6 Each number is a repeating decimal. The digit which is repeating is increasing by one. 24. 25. 2 14 3 in., 43 in., 4.6 in. 4 1 in., 4 in., 4.0 in. ■ Lesson 6.9 1. 2. n 1 2 3 4 5 6 n2 2 n 0 2 6 12 20 30 n 1 2 3 4 5 6 n2 1 2 3 6 11 18 27 38 26. 0.2, 0.16, 0.12, 0.22, 0.1, 0.15, 0.05; Jose, Ken, Vicki, Doug, Cindy, Brenda, JiLynn 3. Possible answer: Add 1 to the denominator of the preceding fraction; 15 , 16 , 17 ■ Lesson 6.7 4. Possible answer: The denominators increase 1 1 1 by consecutive odd integers; 37 , 50 , 65 1. 1 16 1 2. 2 27 5. 3 x2 6. 3. 1 1 16x2 7. s23d22 5 1 8. 1421 5 14 15. 1024 18. 214 19. 7 22. 825 ? 87 23. 27. 55 and 16. 4 20. 9 21. 3 7. 25 and 41; 56 524 sq yd 17. 0 24. > 25. > 28. $4081.47 6. 1.05 3 1025 8. 0.000635 11. 0.00000827 1022 16. Yes 17. No, 7.64 3 1021 18. Yes 19. 1.28 3 130 9. 0.0043 12. 325,000 14. No, 3.5 3 105 108; 1 3 5 7 7 9 7 5 3 1 4. 2.05 3 1022 5. 6.2153 3 107 15. No, 2.65 3 and 1 2. 6.2 3 10 4 3. 3.75 3 1024 13. Yes 1 3 1. 3.5 3 103 10. 97,500 3 5 5 ■ Lesson 6.8 7. 320,000 6. 9 and 11; 13. 14539.336 14. 7396 26. > 5. Each term is the sum of the two previous terms plus one; 41, 67, 109 1 9 10. 37 5 2187 9. x 5 12. x3 11. 8 4. 9 8. Possible answers: 11 and 29, 3 and 37 9. Possible answers: 11 and 19, 7 and 23 10. The midsegment of each side is replaced by 2 new segments. 11. 3 in star 1, 6 in star 2, 18 in star 3 128,000,000 Answers to Practice Workbook Passport to Algebra and Geometry Copyright © McDougal Littell Inc. All rights reserved. 1. 2 31 32 3 Click on a lesson's answer to return to that lesson's copymaster. 12. The factors of 48 except for 1 and 48 are 2, 3, 4, 6, 8, 12, 16, and 24. The factors of 75 except for 1 and 75 are 3, 5, 15, and 25. 75 5 2 1 3 1 4 1 6 1 8 1 12 1 16 1 24 and 48 5 3 1 5 1 15 1 25 ■ Lesson 7.1 1. 5 7 2. 23 6. 3 4 10. 2 x 1 3. 2 3 1 4 3x 7. 4 6 11. z z 8. 2 7 18. 21 9 13. 2 4 5 16. 22 17. 2 3 20. 20.45 19. 0.67 21. 20.88 5 7 2 22. 63 , 6 , 6 ; every fraction after the first is 6 greater than the preceding fraction. The next three 9 11 13 numbers are 6 , 6 , 6 . 23. 24. 11 3, 2 93 , 73 ; the numerators are odd numbers decreasing in order with every other term being negative and the denominators are three. 5 3 1 The next three numbers are 2 3 , 3 , 2 3 . 3 8 1 48 5 78 25. 5 6 2 36 5 26 ■ Lesson 7.2 Copyright © McDougal Littell Inc. All rights reserved. 2. 5. 2 13 18 17 24 4. 7a 15 1 6y 8. 2 9. 12 5y 5b 2 2a 21 1 2n 11. 12. ab 3mn 14. 0.71 15. 0.60 5 1219 24 19. 17. 311 24 5 1223 24 1 5 1 b. 6 ; 20. a. Hank; d. 9 3. 2 16 5x 7. 8 9 14t 13. 20.06 18. 14. < 2 2 s0.702 1 0.842 1 0.24d < 0.22 15. < 5x 2 s0.571x 1 0.545xd < 3.88x 16. < 5.25 1 3.222 2 2.545 < 5.93 18. 20. 90 100 41 100 19. or 0.9 10 100 or 0.1 or 0.41 21. a, to avoid a round-off error, you should begin by rounding the numbers to 3-decimal placesÑ one place more than is required in the final result. ■ Lesson 7.4 1. 5. 1 9 33 7 9. 2 13. 1. 1 14 10. 2 307 24 1 8 13. < 0.806m 1 0.457m < 1.26m 15 4 9 2. 2 25 3. 2 49 68 2 6. 2 15 7. 6x 1 6 10. 2 14. sq in. 27 100 62 3 hr 2 5 11. 153 8 8. 56y 3z 5 sq in. 21. 12. 216x 15. 21 2 sq in. 18. 25.438 17. 3.167 3 20. 20 5 20 23 hr 4. 2 91 5 9 40 23. $30,600 ■ Lesson 7.5 c. $4838 16. 11. Answers vary. 12. < 0.676 2 0.626 < 0.05 22. 1 b. $508 1 6. 30 9. Answers vary. 10. Answers vary. 19. 4 1 27. a. $488 5 $482 3 4 1 59 < 1.06 16. 0.545 26. 506 inches 1. 8 16 17. < 4x 2 s0.556x 2 1.333xd < 4.78x 9. 22c 19 12. 2 5k 15. 21 14. 3 19 5. 2 3 2 5 4. 8. 1 3 5 6 1 8 1 24 24 24 5 1 c. 5 12 4 9 5 6 1 14 5 24 1 24 1 24 1 24 5 5 1 2. y 7 3. 4 3z 1 4 5. 6. 28m 29 16x 7. Did not multiply by the reciprocal. 4. 2 16 1 10 4 3 5 10 4 5 5 5 5 10 ? 16 10 ? 5 5 16 25 5 8 ■ Lesson 7.3 1. 0.96 5. 7.877 2. 0.693 6. 4.247 4. 21.39 3. 9.05 7. 5 16 1 2 6 < 0.65 Passport to Algebra and Geometry Answers to Practice Workbook 131 Click on a lesson's answer to return to that lesson's copymaster. 8. Did not multiply by the reciprocal. 21. 2 1 2 6 4 5 ? 3 6 3 1 2?6 5 3?1 14. 19. 24. 64 189 28. 69 8 25. 11. 16. 21. 19 5z 3 32 9 8 6 5 5 12. 12 17. 32 22. 2 72 7 7p 23 26. 13. 18. 5 18 5 3 23. 2 74 27. 40 loads 7 ounces s 858 d; 23 8 ounces s 28 d 2. 70% 3. 40% 4. 50% 7. 48% 9. 65% 10. 60% Fraction Bored 36% 0.36 9 25 Moving 19% 0.19 19 100 New Furniture 15% 0.15 3 20 Redecorating 16% 0.16 4 25 Other 14% 0.14 7 50 90 70 50 30 Bored Moving 14. Answers vary. 15. $1500 ■ Lesson 7.8 Percent 34% Food 28% Car payment 10% Electricity 4% Water 6% Heat 2% Phone 1% Entertainment 5% Clothing 10% 1. 0.18, 144 2. 0.23, 27.6 4. 1.75, 70 5. 0.006, 3.24 7. c, 4 8. d, 30 11. 5 squares 13. 40.7 9. a, 13.3 10. b, 6.6 17. 21.05 15. 197.88 18. 254.52 20. Perimeter 5 16 cm, area 5 15 sq cm ■ Lesson 7.7 3 cm 2. 0.16 3. 2.50 5. 0.005 6. 0.384 9. 165% 10. 0.8% 12. 38.4% 13. 5 132 6. 0.035, 5.25 19. Perimeter 5 48 cm, area 5 135 sq cm 17. c, because the shaded region is 50% of the entire area. The other three figures all have 75% of the area shaded. 17. 3. 3.6, 28.8 12. 15 squares 14. 7.02 16. 273.6 16. > Other Reason 13. Answers vary. 1. 0.48 New RedecFurniture orating 11. 49% House payment 31. 31.25% Decimal 8. 40% 12. Answers vary. 16. Area 30. 58.3% 28. 225% 10 5. The least is d, 25%. The greatest is a, 75%. 6. 10% 27. 22% Percent Percent 1. 36% 24. 65% Reason 33. ■ Lesson 7.6 23. 87.5% 26. 375% 29. 55.5% 32. 21 20 17 25 18. 4. 0.842 7. 63% 8. 92% 21. Perimeter 5 16 cm. Yes, it is a linear measure. 11. 2.1% 14. < 7 20 19. 15. > 79 100 Answers to Practice Workbook 5 cm 20. 5 4 Passport to Algebra and Geometry Copyright © McDougal Littell Inc. All rights reserved. 9. 1 10. 8 15. 34 20. 10 3 22. 25. 40% 54 3 16 5 24 5 2 69 20 Click on a lesson's answer to return to that lesson's copymaster. 1 22. Area 5 45 cm 2. No, because 333 % of 135 Þ 1 1 s 333 % of 15d 3 s 333 % of 9d. You can see that the percentage rate is multiplied twice on the right and only once on the left. 24. < $657.44 23. $63.96 1. $8.43 2. $62.91 4. 0.2% 5. 11.9% 6. 4.6% 8. 0.3% 9. 7.2% 10. 4.4% 12. 1.4% 13. 6.8% 3. $144.15 14. 2.5% 7. 3.7% 11. 4.8% 15. 0.2% 16. Amount of raise 5 $1206.80 New salary 5 $18,446.80 18. 980 freshmen 19. Increase: $2056.50 Current Price: $22,621.50 19 2. A ratio, 36 or 19 to 36 Copyright © McDougal Littell Inc. All rights reserved. hits 11114game 2 3 miles 1 miles 5 5 0.125 miles per 24 minutes 8 minute minute; a rate because different units of measure 10 students 1 5 or 1 to 6; a ratio because same 5. 60 students 6 units of measure 2 inches 1 inches 5 5 0.05 inch per 40 minutes 20 minutes minute; a rate because different units of measure 2 pictures 2 5 or 2 to 3; a ratio because same 7. 3 pictures 3 units of measure 144 in. 5 9 to 1 16 in. 36 hr 10. 5 3 to 14 168 hr 19. Ratio of the perimeters is 24 5 3 to 2. 72 Ratio of the areas is 24 5 3 to 1. ■ Lesson 8.2 1. Yes, 1 ? 42 5 6 ? 7 2. No, 2 ? 9 Þ 3 ? 4 6. 80 7. 36 4. 3 8. 7 9. 6 x 12 2 y 11. 5 ,x54 5 ,y58 5 15 12 3 4 24 y 7 12. 5 , z 5 54 13. 5 , y 5 63 9 z 11 99 3 w 27 3 6 t 14. 5 , w 5 15. 5 ,t5 4 18 2 10 35 7 16. 30.33 17. 3.2 18. 14.06 10. 1. A rate, 8 feet per second 8. 18. Ratio of the perimeters is 14 24 5 7 to 12. 12 Ratio of the areas is 24 5 1 to 2. 5. 12 ■ Lesson 8.1 6. 17. a, the 36-ounce box for $3.72 is the better bargain because you pay about $0.10 per ounce, whereas, the other is about $0.11 per ounce. 3. No, 5 ? 120 Þ 12 ? 10 21. < 71.7% in December < 28.3% in other months 4. 16. b, one gallon for $4.25 is the better bargain because you pay about $1.06 per quart whereas the other is about $1.08 per quart. 36 20. < 19.6% laid off, < 80.4% retained Yes, 80.4% of 153 < 123 people, which is the number of employees retained. 3. A rate, < 1.27 hits per game 15. a. 24.25 miles per gallon b. < 59.7 miles per hour ■ Lesson 7.9 17. 78,540 seats 32 oz 36 in. 13. 5 9 to 7 5 4 to 3 28 in. 24 oz 14. 50 cubic feet per hour 12. 32000 m 5 8 to 1 4000 m 7 pt 11. 5 7 to 16 16 pt 9. Passport to Algebra and Geometry 19. d 5 24, e 5 18 21. 5 bags 20. q 5 13, r 5 5 22. 300 cement blocks 23. 2000 defective parts ■ Lesson 8.3 1. 105 teachers 2. a. 56 kph b. Yes, you are traveling 68.75 mph. 3. 1834 cups of flour 5. 110 employees 7. 9334 pounds 4. 85 inches of snow 6. 22 days 8. 4623 minutes 9. < 21,691 people Answers to Practice Workbook 133 Click on a lesson's answer to return to that lesson's copymaster. ■ Lesson 8.4 12. 1. 3.2% 2. 86.4 3. 39.56 5. 21.6 6. 1368 7. 1569.5 9. 106.98% 13. 10% 10. 45 4. 650 11. 100 Country Percent Population China 21% 1.151 3 109 8. 14 India 16% 8.768 3 108 12. 300 former Soviet Union 5% 2.74 3 108 United States 5% 2.74 3 108 Indonesia 4% 2.192 3 108 Brazil 3% 1.644 3 108 14. 150 p 25 5 , p 5 3.70% 15. 675 100 a 52 16. 5 , a 5 84.24 162 100 17. p 5 25% 18. a 5 20 Possible model: Possible model: 13. $21,116.67 14. They played 40 games and won 38. 15. $17.31 ■ Lesson 8.6 Each =5 Each =1 19. b 5 80 Possible model: 1 1. A 25% increase 2. A 333 % decrease 3. A 20% decrease 4. A 163 % increase 5. A 25% decrease 6. A 5% increase 2 7. < a 1.7% increase 8. < a 7.7% decrease 9. < a 12.7% increase 10. < a 2.2% decrease 11. Each number is a 300% increase of the preceding number. 512, 2048, 8192 12. Each number is a 50% decrease of the preceding number. 40, 20, 10 13. Each number is a 900% increase of the preceding number. 10,000, 100,000, 1,000,000 = 0.8 20. $975.48 21. Sales tax 5 $87, total bill 5 $1537 22. $3.05 is the tip. < 18.0% tip rate s17.99%d 23. < $35,714.29 4. $1500 2. $3375 3. $1125 5. 5.727 3 107 sq mi 6. 1.168 3 107 sq mi 7. 5.097 3 106 sq mi 8. 1.718 3 107 sq mi 9. 2.978 3 106 sq mi 10. 9.335 3 106 sq mi 11. 5.097 3 106 sq mi 134 15. False, four times a number is a 300% increase of the number 16. True ■ Lesson 8.5 1. $12,500 14. Each number is a 60% decrease of the preceding number. 400, 160, 64 Answers to Practice Workbook 17. False, a 90% decrease of 60 is 60 2 54 5 6. 18. True 19. Answers vary. 20. Answers vary. 21. Original Number New Number Percent Change 55 66 20% increase 55 44 20% decrease 200 350 75% increase 1400 350 75% decrease 60 75 25% increase 60 45 25% decrease Passport to Algebra and Geometry Copyright © McDougal Littell Inc. All rights reserved. Each Click on a lesson's answer to return to that lesson's copymaster. 22. 42.9% ■ Lesson 8.8 23. 34.5% ■ Lesson 8.7 1. 36 outcomes possible 1. 720 ways 2. 2. 15 gifts white shirt-dark blue tie white shirt-stripe blue tie white shirt-paisley tie white w/blue stripe shirt-dark blue tie white w/blue stripe shirt-stripe blue tie white w/blue stripe shirt-paisley tie off white shirt-dark blue tie off white shirt-stripe blue tie off white shirt-paisley tie light blue shirt-dark blue tie light blue shirt-stripe blue tie light blue shirt-paisley tie light blue w/stripe shirt-dark blue tie light blue w/stripe shirt-stripe blue tie light blue w/stripe shirt-paisley tie 3. C D D B C D D B B C C B B A C D 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 B D D A B D D A A B B A A C B D 1 1 1 2 2 2 3 3 1 3 2 3 4 4 4 5 5 5 6 6 6 1 1 1 2 2 2 3 3 3 5 4 6 4 4 4 5 5 5 6 6 6 3. Two is the smallest and 12 is the largest. 1 36 12 b. 36 6 c. 36 1 18 36 5 2 35 e. 36 7 f. 21 36 5 12 4. a. d. 5 13 5 16 5. Answers vary. Experimental probabilities should approach theoretical probabilities as the number of trials increase. 6. 64 ways 7. 9. 720 ways 1 64 10. 1 16 8. 1 720 11. 1 120 ■ Lesson 9.1 C D D A C D D A A C C A Copyright © McDougal Littell Inc. All rights reserved. A B C D B C C A B C C A A B B A A D B C 1. 6, 26 4. 0.8, 20.8 1 125,000 5. 20, 220 7. 3. 1.4, 21.4 6. 56 , 2 56 8. 24 ways; the probability that Angel and Bo will 1 12 be standing next to each other is 24 5 2 . 4. 125,000 combinations; 2. !12, 2 !12 6 and 7 8 and 9 9. 5. 35,152 combinations of call letters The probability that the second letter is a Q is 1352 35152 1 5 26 . 6. 180 times Passport to Algebra and Geometry 5 and 6 10. 5, 25 11. 25, 225 12. 5.477, 25.477 Answers to Practice Workbook 135 Click on a lesson's answer to return to that lesson's copymaster. 13. 5.196, 25.196 14. 8, 28 15. 4, 24 ■ Lesson 9.3 In Exercises 16–18, estimates may vary slightly. 1. c 5 10 2. b 5 36 16. 5.5, !30 < 5.477 4. b 5 40 5. a 5 7 7. c 5 35 8. b 5 30 17. 6.8, !45 < 6.708 18. 3.1, !10 < 3.162 19. x 5 !121, x 5 11 10. 20. q2 2 10 5 39, q 5 7, 27 A 37 12. A 20 12 2. Rational, a quotient of integers 3. Irrational, cannot be written as a quotient of integers (or decimal is non-terminating, non-repeating) B 4. Rational, 2 !16 5 24, an integer is always a rational number 13. 25 15. 8. Sometimes, for example !4 is rational but !2 is irrational. B 10. Always, real numbers are rational and irrational. 12. 23, rational, result is an integer , irrational, not a quotient of integers −5 24. > 29. < 136 −4 −3 −2 25. < 30. !32 −1 0 1 26. > 31. !50 2 27. < 4 5 27 45 36 C 19. a 5 48 20. b 5 60 22. About 130.3 feet s127.3 1 3d 28. > 23. About 17 miles 32. !4.5 or ! Answers to Practice Workbook C 21. The maximum height the ladder will reach is about 38.7 feet, and the minimum height is about 35.7 feet. 9 2 3 4 A 18. b 5 52 18. d 12 17. B 19–23. − 16 5 16. Not a right triangle 11. !18, irrational, cannot be written as quotient of integers (or non-terminating, non-repeating decimal) 5 2 A 3 9. Never, integers are always rational. − 16 3 C 9 2 24. About 179 feet s178.9d Passport to Algebra and Geometry Copyright © McDougal Littell Inc. All rights reserved. 7. Sometimes, for example is rational but not an integer. 17. e 20 14. Not a right triangle 3 2 16. a C B A 6. Rational, !94 5 32 , a quotient of integers 15. b 16 15 5. Irrational, cannot be written as a quotient of integers (or decimal is non-terminating, non-repeating) 14. c C 11. Not a right triangle 25. < 20.4 ft 1. Rational, a quotient of integers 6 35 B ■ Lesson 9.2 !2 9. a 5 18 23. 26 sq ft 24. < 5.1 ft by 5.1 ft 13. 6. c 5 53 12 21. 25y 2 5 49, y 5 75 , 2 75 22. 12 ft by 12 ft 3. a 5 40 Click on a lesson's answer to return to that lesson's copymaster. ■ Lesson 9.4 18. x < 2 1. P 5 82 units, A 5 420 sq units −1 2. P 5 20 units, A 5 25 sq units 3. P 5 108 units, A 5 306 sq units 0 1 2 3 −5 −4 −3 −2 12 13 14 15 19. y < 23 4. 6 feet from the base 5. < 180.3 miles −6 6. < 43.0 yards 7. < 204.9 feet (60 1 60 1 84.9d 20. r ≤ 14 ■ Lesson 9.5 1. 11 0 1 2 3 4 21. 28 < t 2. −3 −2 −1 0 −9 1 3. −7 −6 −5 7 8 9 10 22. 7 < x −11 −10 −9 −8 −7 6 4. −6 −5 −4 −3 −2 23. 5 ≤ x, 5 is less than or equal to x. 24. 210 ≥ t, 210 is greater than or equal to t. 5. 8 9 10 11 12 25. 24 < w, 24 is less than w. 26. q 1 12 < 24, q < 216 6. 3 4 5 6 8. x ≤ 15 7. x > 22 10. x ≥ 0 11. x ≤ 3 7 9. x < 0 12. x > 25 13. x < !10 Copyright © McDougal Littell Inc. All rights reserved. −8 27. z 2 10 ≤ 5, z ≤ 15 28. p 2 16 > 212, p > 4 29. 42 ≥ t 1 22, 20 ≥ t 2 3 4 5 2 3 4 5 6 1 5 ? 5x ≤ 1 5 ? s232d x ≤ 2 32 5. −3 −2 −1 0 16. x ≤ 2 !15 −5 −4 −3 −2 17. w ≥ 21 −2 35. Answers vary. ■ Lesson 9.6 15. x ≥ 2 !5 −6 33. h > 2 1. The direction of the inequality symbol is not reversed when you multiply both sides by a positive number. Line 2 should be 14. x > !11 −4 32. t ≤ 25 31. h > 18 34. Answers vary. 1 30. a ≥ 13 2. The direction of the inequality symbol is reversed when you multiply both sides by a negative number. Line 2 should be 1 22 ? s 2 2 dz < 22 ? s25d z < 10. 3. c −1 0 1 4. b 5. a 6. d 2 Passport to Algebra and Geometry Answers to Practice Workbook 137 Click on a lesson's answer to return to that lesson's copymaster. 7. n < 19. At least 345 pounds 12 5 20. At least 56.6 mph −1 0 1 2 3 21. $15.00 per square yard 22. 20 singles 11 8. m > 2 3 ■ Lesson 9.7 −5 −4 −3 −2 −1 24 25 26 27 −1 0 1 2 −2 −1 0 1 9. x ≥ 24 23 5 3 ≥ k −2 3 11. 2 32 > c 7 23x ≥ 23 23 7 x ≥ 2 . 3 2. The direction of the inequality symbol is not reversed when you add a negative number to both sides. Line 3 should be 15y 1 10 2 10 > 23 2 10 −3 15y > 213 13 y > 2 15 . 12. 2 35 ≤ w 3. Never −2 −1 0 1 2 5. b 4. Always 6. a 12. x ≤ 40 −26 14. −25 −24 −23 −22 −5 13. x ≥ 5 11. a < 3 19 14. x > 2 2 15. 2n 1 2n 1 2 1 2n 1 4 ≤ 18; n ≤ 2 16. 2n 1 2n 1 2 1 2n 1 4 > 66; n > 10 ≤ m 2 19 6 8. d 10. z ≥ 2180 9. x < 23 13. p ≥ 225 7. c −4 −3 −2 −1 17. 2n 1 2n 1 2 1 2n 1 4 < 212; n < 23 18. x ≤ 12 19. x > 5 20. You must earn at least a 92 on the sixth exam. 15. 37.5 < p ■ Lesson 9.8 36 37 38 39 40 1. No, 2 1 5 >/ 8 3. No, 8 1 10 >/ 18 16. a < 272 5. −75 −74 −73 −72 −71 17. d < 2 32 −4 −3 −2 −1 0 18. w > 20.4 −1 138 0 1 2 2. Yes 4. Yes Measure of Side 3 is greater than Measure of Side 3 is less than 6 in. 14 in. 8 cm 26 cm 8 ft 32 ft 30 m 120 m 45 yd 295 yd 3 Answers to Practice Workbook Passport to Algebra and Geometry Copyright © McDougal Littell Inc. All rights reserved. 10. 1. The direction of the inequality symbol is reversed when you divide both sides by a negative number. Line 3 should be Click on a lesson's answer to return to that lesson's copymaster. 6. Yes 7. Yes 8. Yes 10. No 11. No 12. e 1 d 13. b 14. a 9. Yes 5. c 6. a 7. d 8. b 9. 10. 15. d 16. 2 in., 6 in., 6 in.; 3 in., 5 in., 6 in.: 4 in., 4 in., 6 in.; 4 in., 5in., 5 in. 17. a. Yes, a triangle can be formed by side lengths of three consecutive integers except for the case of lengths 1, 2, 3. b. Yes, a triangle can be formed by side lengths of three consecutive even integers except for the case of lengths 2, 4, 6. c. Yes, a triangle can be formed by side lengths of three consecutive odd integers except for the case of lengths 1, 3, 5. 18. 35 ft < 3rd side < 585 ft; at least 1170 feet; less than 550 feet ■ Lesson 10.1 1. OP, PU, OU → → → → → 2. PO, PQ, PR, PN, PU ↔ ↔ ↔ ↔ 3. NR and OU, MS and OU ↔ ↔ → → → 4. NR and MS 5. OP, PU, or OU 6. RP 7. a ray 8. a line 9. The length of a line segment 10. a line segment 11. 7 12. A, B, C, D, E or F, G, H, I, J ↔ ↔ ↔ →→ → 13. DE, GH, FJ 14. IC, IH, IJ Copyright © McDougal Littell Inc. All rights reserved. 15. 17. Yes 11. 808 12. 1308 13. 808 acute angle 15. c 16. a 14. 142.58 obtuse angle 17. b ■ Lesson 10.3 1. m i n 2. No, l and p are not parallel, so their corresponding angles are not congruent. 3. /12, /10 4. /2, /4, /8, /6 5. /1 and /5, /4 and /8, /2 and /6, /3 and /7 6. /1 > /2 Corresponding angles of i lines > or /1 > /6 corresponding angles of i lines > /2 > /3 Vertical angles > or /2 > /5 Corresponding angles of i lines > /3 > /4 Corresponding angles of i lines > /4 > /5 Vertical angles > /5 > /6 Corresponding angles of i lines > 7. Danver 105° FH BS Ryan 75° MB Morgan 16. 18. Yes 19. planes ■ Lesson 10.2 1. /ZVW or /YVW, /ZYW, /ZYX, /WYX, /YWX, /VWZ, /YWZ 2. /VWY, /XWZ 3. /WZV, /WZY, /YXW 4. /VWZ, /YWZ, /XWY, /VWY, /XWZ, /XWV Passport to Algebra and Geometry 8. Accept all reasonable answers. Consider Morgan Road at the intersection with Danver Drive to be a straight angle. Therefore, the angle at which the fire hydrant is placed has a measure of 758, 1808 2 1058 5 758. Since this angle and the angle given at Ryan Street and Morgan Road are congruent, it can be shown that Danver Drive and Ryan Street are parallel. (Actually, we will prove formally later in the text.) 9. The fire hydrant, bus stop, and mailbox are all placed at 758 angles. Answers to Practice Workbook 139 Click on a lesson's answer to return to that lesson's copymaster. ■ Lesson 10.5 10. In Exercises 1–3, sketches may vary slightly. 1. ■ Lesson 10.4 2. 3. 4. Acute isoceles 1. A vertical line of symmetry 2. A rotational symmetry of 1808, and 2 lines of symmetry 3. A horizontal line, a vertical line of symmetry, a rotational symmetry of 1808 6. Right isoceles In Exercises 7 and 8, sketches may vary slightly. 4. 908 or 1808 in either direction 7. Right isoceles 5. 608, 1208, or 1808 in either direction 8. Acute scalene B A 6. 458, 908, 1358 or 1808 in either direction 7. Answers may vary. 5. Right scalene 8. Answers may vary. A B C C 9. Perimeter 5 8 1 4!2 units < 13.66 units Area 5 8 square units y B (−3, 4) A (2, 4) y B (−2, 4) 2 4 C (−3, −4) x 10. a. Answers vary. −4 −2 −2 4 x D (2, −1) 1. Parallelogram 18. Sometimes C (−2, 0) 2 −4 −4 A (0, −5) 2. Rhombus 3. Trapezoid y 4 x 17. Never 15. Sometimes ■ Lesson 10.6 y 4 13. Right scalene 14. Equilateral, equiangular 16. Never −4 b. Answers vary. B (2, 0) 11. Perimeter 5 6 1 3!2 units < 10.24 units 9 Area 5 2 square units 12. Acute isoceles −4 C (−2, −1) D (2, −4) 2 A (2, 4) 2 −4 −2 −2 C (0, 5) 4 10. Perimeter 5 4 1 4!2 units < 9.66 units Area 5 4 square units b. Answers vary. 4. Sometimes, A rectangle with 4 equal sides is a square. B (2, 0) 4 A (0, −5) x 5. Never, A parallelogram has opposite sides parallel, a trapezopid only has one pair of opposite sides parallel 6. x 5 8 cm, y 5 14 cm 7. x 5 y 5 16 yd 8. Not possible 9. Check studentÕs sketches. Accept all parallelograms. 140 Answers to Practice Workbook Passport to Algebra and Geometry Copyright © McDougal Littell Inc. All rights reserved. 9. a. Answers vary. Click on a lesson's answer to return to that lesson's copymaster. 10. 15. 688, 888, 1088, 1288, 1488 16. 82.58, 97.58, 112.58, 127.58, 142.58, 157.58 18 in. 18 in. 12 in. ■ Lesson 10.9 12 in. 36 in. 1. MK shortest, LK longest 2. AB shortest, AC longest 12 in. 18 in. 3. XZ shortest, ZY longest 12 in. 36 in. 4. /C smallest, m/A 5 m/B largest 12 in. 5. /G smallest, /F largest 12 in. 6. /H smallest, /I largest 36 in. 7. AC, AB, BC, DC, BD 11. 2 trapezoids, 3 rectangles 8. KM, KL, LM, LN, NM 12. The two trapezoids that are the sides of the box are congruent. The two rectangles that are the face and base of the box are congruent. 9. x 5 15, /B smallest, /A largest, AC smallest, BC longest ■ Lesson 10.7 1. b 2. a 3. c 11. b.; An equilateral triangle is also equiangular. 4. equilateral: a, c; equiangular: a, b; regular: a 5. equilateral 10. x 5 10, /F smallest, /FED largest, DE smallest, DF largest 12. c.; An isoceles triangle has two angles of equal measure. 6. equiangular 7. equilateral, equiangular, regular 8. x 5 3 13. a.; Length of the sides satisfies the Pythagorean theorem. 9. x 5 4 14. 5 BS N 10 12 10 m/AF 5 608 N W 12 E S 15 m/BS 5 408 10° 60 15 m/SJ 5 808 30° 10 10 60° 15 Copyright © McDougal Littell Inc. All rights reserved. 80° 40 AF 5 SJ E S 10. x 5 4 Therefore, Angel Falls and Buck Springs are furthest apart. Angel Falls and San JosŽ are closest. The distance between Buck Springs and San JosŽ 40 < d < 60. 13 13 13 13 13 13 ■ Lesson 11.1 1. 108 units2, 3s108d 5 324 units2 or 1 2 2 s12 1 24d ? 18 5 324 units 13 13 11. 1358 12. 4 13. 32 units 14. 10808 ■ Lesson 10.8 1. 408 2. 908 6. 12 7. 9 11. 1208, 608 3. 1108 8. 6 9. 3 12. 1608, 208 4. 5 5. 9 10. 1448, 368 13. 8 Passport to Algebra and Geometry 2. 25!3 units2, 2s 25!3 d 5 50!3 units2 or s10ds 5!3 d 5 50!3 units2 3. 4 3 Area of triangle 5 Area of hexagon, 4s 36!3 d 5 144!3 units2; P 5 36 units; P 5 72 units 14. 10 Answers to Practice Workbook 141 Click on a lesson's answer to return to that lesson's copymaster. 4. 6 3 Area of triangle 5 Area of hexagon, 6s 4!3 d 5 24!3 units2; P 5 12 units; P 5 24 units 5. X9 5 s23, 4d, Y9 5 s21, 2d, Z9 5 s24, 1d 6. 7. In Exercises 5 and 6, one possible answer is given. 5. 8. 12 units2 16 units 9. Yes 10. No 12. 6. 11. No 13. y 4 y 2 −2 −2 6 units2 12 1 2!2 units 7. 1800 ft2 −4 −2 −2 x 4 −4 8. 8712 ft2 9. 106 units2 ■ Lesson 11.2 1. /X 2. YZ 3. /Z 5. /B 6. AC 7. DF 8. /N 9. m/X 11. a and d; b and c 2 14. x −4 y 4 2 4. BC −4 2 4x 10. NO 12. c and d 13–15. Answers vary. One possible answer given. 15. A, H, I M, O, T, U, V, W, X, Y 13. 16. ÒOH MOM MY MOUTH TOO HOT Ó 14. 17. Answers vary. ■ Lesson 11.4 16. 1. 908 2. 1808 4. 808 clockwise 3. 908 5. 1208 counterclockwise 6. 358 counterclockwise 17. 18. 7. DE 8. KF 11. nHAB 10. OQ 13. 19. 16 1. X9 5 s23, 24d, Y9 5 s21, 22d, Z9 5 s24, 21d 2. X9 5 s3, 4d, Y9 5 s1, 2d, Z9 5 s4, 1d 3. X9 5 s3, 24d, Y9 5 s1, 22d, Z9 5 s4, 21d 4. X9 5 s3, 24d, Y9 5 s1, 22d, Z9 5 s4, 21d 142 Answers to Practice Workbook Y X′ X A′ 15. Z O B′ ■ Lesson 11.3 12. QLMO 14. B A 20. 9 9. PK O Y′ Z′ L K M N K′ N′ L′ O M′ Passport to Algebra and Geometry Copyright © McDougal Littell Inc. All rights reserved. 15. Click on a lesson's answer to return to that lesson's copymaster. ■ Lesson 11.5 7. m/J 5 53.38; JL 5 !101 1. b.; 5 units left and 6 units up. 2. c.; 3 units left and 5 units down. 3. a.; 5 units left and 4 units down. 4. c 5. a 7. 8. C′ B′ A′ C A tan J 5 C′ 1. a and c 5 4. Yes, 4 2. a and c 3. a and b 5. No 6. AB BC CD DA (or reciprocals) 5 5 5 JK KL LM MJ 7. 2 1 8. a. 16, b. 17, 9. L 3 20 10. 1 , 3 4 3 11. 1 , 2 3 12. 2 , 2 1. 5.8 ft high, 5.5 ft wide, 12.8 ft long 3. < 616 m 5. < 4.8 acres Copyright © McDougal Littell Inc. All rights reserved. 4. < 19,360 m 2 6. < 278 miles yd wide by 3 yd long 2 2 8. 346 3 yd, 83 yd 1 10. 13 in. by 3 in. 9. 40 times longer 11. Yes 12. 7 ft 6 in. ■ Lesson 11.8 22 < 0.940 1. !548 8 < 0.342 3. !548 5. 11 4 5 2.75 6. 8 < 0.342 2. !548 22 < 0.940 4. !548 4 11 sin A 5 15 17 8 sin B 5 17 8 cos A 5 17 cos B 5 15 17 tan A 5 15 8 8 tan B 5 15 9. N 5 0.36 10. N 25 43 4 c. 13 ■ Lesson 11.7 2. < 80 ft < 1.34 8. m/B 5 28.18; BC 5 15 11. Answers vary. ■ Lesson 11.6 7. 6 6 < 0.597 !101 !65 < 0.802 cos L 5 !101 6 tan L 5 < 0.744 !65 C C′ 10. ANGEL 1 13 !65 < 0.597 sin L 5 C B B′ A′ !101 A B A 9. 6 cos J 5 B < 0.802 !101 6. b B′ A′ !65 sin J 5 M 7 O 24 M 27 O 11. x 808 408 208 108 58 18 sin x 0.985 0.643 0.342 0.174 0.087 0.017 tan x 5.671 0.839 0.364 0.176 0.087 0.017 12. As x gets smaller the values of sin x and tan x get closer. 13. As x gets smaller, the hypotenuse and the adjacent side become closer to the same length. Therefore, the ratios become closer. 14. and 15. Length of guy wire (ft) 50 100 150 200 Vertical distance to guy wire (ft) 25 50 75 10 sine ratio 25 50 50 100 75 100 100 200 16. The sine ratio of opposite side to the hypotenuse remains constant. Passport to Algebra and Geometry Answers to Practice Workbook 143 Click on a lesson's answer to return to that lesson's copymaster. ■ Lesson 11.9 4. 15.49 1. 401.9 cm 2 2. 88.0 in.2 6. 5.71 4. 251.2 cm 2 5. 156 m 2 8. m/R 5 618 p 5 6.65 q 5 13.72 7. 263.8 m 2 2. 0.5446 3. 0.9998 5. 9.54 7. m/N 5 488 o 5 20.07 n 5 22.29 9. m/V 5 288 t 5 15.05 s 5 17.04 11. < 184 ft 10. < 2145 ft ■ Lesson 12.4 1. 216 cm3 4. 4676 cm 3 2 1. 38.3 in., 116.8 in. 2 2. 6.9 in., 3.8 in. 2 3. 8.8 ft, 6.2 ft 4. 89.2 in., 633.1 in. 5. 15.3 in., 30.6 in. 3 in. 1 ft 4 in. 3 in. 3 in. 5 in. 16 in. 11. Each pillar requires 48 in.3. All four require 192 in.3. ■ Lesson 12.2 2. Cylinder 3. Cone 5. ■ Lesson 12.5 1. 50.24 m3 4. < 3679.69 cm3 5. 56.52 mm3 6. 628 ft3 7. 1017.36 in.3 7. b. 12 vertices, 11. a. 5 faces, b. 6 vertices, b. 16 vertices, 8. 226.08 in.3 11. 19 mm 9. 22 in. 12. 2.5 ft 13. r 5 3.5 in., h 5 2 in., V 5 76.93 in.3, The radius of the cylinder is half of the width of the base of the prism. The height of the cylinder and prism are the same. Extra space 5 119.07 in.3 9. 10. a. 8 faces, 2. 49,062.5 in.3 3. 803.84 in.3 10. 7 cm c. 18 edges c. 9 edges c. 24 edges 14. Volume 5 4421.12 in.3 Time < 36.8 minutes ■ Lesson 12.6 1. 128 cm3 3. 201.0 m3 144 9. V 5 108 in.3 10. V 5 96 in.3 12. Yellow area < 12.6 in.2, red area < 100.5 in.2, blue area < 201 in.2 12. a. 10 faces, 6. 18 cm 8. V 5 128 in.3 8 in. 11. Middle radius 5 6 in., Outer radius 5 10 in. 8. 5. 16 in. 4 in. 10. 85,486.5 ft 6. 3. 360 m3 6. 9.2 cm, 18.4 cm 2 4. 2. 90 in.3 7. 10 m 8. 28.5 in.2 9. 518.1 ft 9. 126 in.2 12. Answers may vary slightly. < 753.6 mm 2 2 1. Prism 8. 54 in.2 11. 126 in.2 ■ Lesson 12.1 7. 29.4 6. 178 ft2 10. No, where the faces meet, the surface area has been eliminated. 12. < 499 ft cm 2 3. 33.5 in.2 Answers to Practice Workbook 2. 160 in.3 4. 5887.5 cm 3 Passport to Algebra and Geometry Copyright © McDougal Littell Inc. All rights reserved. 1. 1.8807 ■ Lesson 12.3 Click on a lesson's answer to return to that lesson's copymaster. 5. 6. 3 cm 5. Answers vary. 4 in. 3 in. 5 cm 5 cm V 5 25 cm V < 37.68 in. 3 3 7. 682.7 cm3 8. 962.9 cm3 x 28 24 0 4 8 y 9 6 3 0 23 6. Answers vary. 9. 24 in.3 10. Yes, volume of cone < 150.72 yd3. x 26 24 22 0 2 4 6 y 8 7 6 5 4 3 2 11. 6,250,000 tons 12. No, each cone requires < 5.02 grams. For twelve the jeweler would need < 60.24 grams. 7. Yes, for each 1 unit increase in x, there is a corresponding 4 unit increase in y. ■ Lesson 12.7 8. Yes, for each 1 unit decrease in x, there is a corresponding 3 unit decrease in y. 1. 4.5p < 14.1 in.3 2. 166.6p < 523.3 cm 1 9. 3x 1 2 y 5 10, Answers vary: s0, 20d, s1, 14d, s2, 8d 3 3. 221.83p < 696.6 in.3 10. x 2 4y 5 212, Answers vary: s24, 2d, s0, 3d, s4, 4d 4. 3.6586p < 11.5 m3 5. 2.61 3 1011, 1.46 3 1010, 2.23 3 1011, 3.93 3 1010, 3.65 3 1014, 2.21 3 1014, 1.75 3 1013, 1.53 3 1013, 1.51 3 109 11. b, Answers vary: s80, 75d, s100, 55d, s90, 65d 12. c, Answers vary: s110, 70d, s100, 80d, s90, 90d 13. a, Answers vary: s70, 20d, s10, 80d, s30, 60d 6. 38.1 minutes 7. < 385,173.3 ft3 14. 1920 8. < 41,809.2 cm3 9. 20 mm, 20p mm, 1.333.3p mm3 or 4000 3 p mm3 17. 2700 2. a 3. c 4. Yes 5. Yes 11. 5 yd, 10 yd, 10p yd 6. No possible solution: s24, 24d ■ Lesson 12.8 8. 1. Yes, 2:1 2. Yes, 2:3 3. Not similar 6. 324 cm3, 1:3 −4 −2 9. 108 10. 288 cm2, 72 in.3, 240 −4 −2 −2 4x 2 675 cm3, in.2, 18 10. 11. y 1125 in. cm2, −4 −2 2 4x y x 2 −2 −4 3 79.39 ft 12. ■ Lesson 13.1 1. Yes 4 2 2 3.75 cm3 12. 113.04 in.3, 7234.56 in.3 13. 267.95 4x 3 11. 50 cm3, 1350 cm2 ft3, 2 7. 243 ft2, 182.25 ft3 8. 533.8 in.2, 942.0 in.3, 4804.2 in.2, 25,434 in.3 in.2, y 2 2 5. 2432p in.2, 15360p in.3 7. Yes 9. y 4 4. 256 in.2, 224 in.3 Copyright © McDougal Littell Inc. All rights reserved. 16. 60 ■ Lesson 13.2 1. b 10. 18 in., 36 in., 17,496p in.3 15. 2340 2. No 13. y y 6 3. Yes 4 (2, 4) 4 4. Answers vary. 2 x 23 22 21 0 1 2 3 y 27 26 25 24 23 22 21 Passport to Algebra and Geometry x −2 2 4 −8 −6 −4 (−2, −2) 2x 6 Answers to Practice Workbook 145 Click on a lesson's answer to return to that lesson's copymaster. 14. c 5 3 15. c 5 26 16. ■ Lesson 13.4 1. Falls to the right 5. m 5 26 is steeper. 2 6. m 5 5 10 15 20 25 30 40 Altitude (in thousands of feet) 6 4 6. 2 y −2 4x x 8. d 4x 9. c 5 12. m 5 2 2 y −4 (−2, −1) −2 4x 2 (−1, −2) −6 1 13. m 5 3 14 14. m 5 17 2 x (0, −6) 8 15. m 5 15 5 16. m 5 2 12 17. m 5 15 18. m 5 43 8 ↔ ↔ ↔ ↔ 19. MN i XY, m MN 5 3 5 m XY ↔ ↔ ↔ ↔ 20. MN yi XY, m MN 5 12 , m XY 5 2 12 ↔ ↔ ↔ ↔ 21. MN yi XY, m MN 5 5, m XY 5 15 ↔ ↔ ↔ ↔ 22. MN i XY, m MN 5 23 5 m XY 4 2 4x 2 (−3, −2) 2 2x −2 2 y −4 −2 −2 −2 y −4 −2 −6 11. m 5 0 −4 −2 −2 2 (−3, 0) 2 −4 (0, 4) 2 4 3. x-intercept: 2, y-intercept: 4 5. 4 (2, 6) (−3, 4) 2. x-intercept: 2, y-intercept: 24 y y y 6 1. x-intercept: 23, y-intercept: 3 4. 3 8. m 5 2 5 4 10. m 5 3 h ■ Lesson 13.3 10. a 11. x-intercept: 1.98, y-intercept: 4.25 12. x-intercept: 2.81, y-intercept: 210.25 ■ Lesson 13.5 14. s0, 16,500d, After 0 years of ownership the car has value $16,500. s11, 0d, The car has $0 value after 11 years. Answers to Practice Workbook 2. m 5 2 12 , y-intercept: 2 1. m 5 2, y-intercept: 4 6 13. s0, 32d, 08C is equivalent to 328F. s217.7, 0d, 08F is equivalent to 217.78C. 146 5 7. m 5 2 6 2 9. m 5 5 The points are close to being linear, but not exactly. The change in altitude is 5000 feet while the speed of sound drops 19 feet per second, then 20 feet per second, then 20, then 21, then 21, then 20 and lastly 22. The change is not exactly uniform, but very close. 7. b 4. m 5 4 is steeper. 3. Horizontal 5 −4 2. Rises to the right Copyright © McDougal Littell Inc. All rights reserved. Speed of sound (in feet per second) v 1125 1100 1075 1050 1025 1000 975 y y 4 4 −4 −2 2 x −2 −2 2 4 x Passport to Algebra and Geometry Click on a lesson's answer to return to that lesson's copymaster. 3. m 5 3, y-intercept: 22 4. m 5 24, y-intercept: 7 ■ Lesson 13.6 1. 90 s y y 86 Scores 8 2 6 −4 −2 −2 2 4x 82 78 74 70 −6 −4 −2 1 5. m 5 2 10 , y-intercept: 0 1 2 3 4 5 6 7 8 9 Hours 6. m 5 22, y-intercept: 9 y 12 6 2 x 2 2. 8 −6 4 −4 −4 Wind chill 20 10 x −10 4 h For 9 hours of practice the estimated score is approximately 70. y 10 −6 66 4x 8 12 −20 −10 Actual temp. 10 20 30 −20 7. c 8. a 9. d 1 3; 11. False, m 5 10. b y-intercept: 2 43 13. False, m 5 2 32 , falls to right 14. True, m 5 origin. 1 3, rises to right and passes through 15. m 5 1.79; y-intercept: 42.76 17. 57.08 pounds At a temperature of 208F the wind chill factor is approximately 38F. At a temperature of 108F the wind chill factor is approximately 288F. 3. a. Verbal Model: C 0.25 3 3 60 Number of quarters Number of dimes 1 0.10 5 50 50 0.25q 1 0.10d 5 50 or 25q 1 10d 5 5000 Algebraic Model: 40 30 20 10 1 2 3 4 5 6 7 8 9 t Year 1 19. y 5 2 x 1 2 b. q 200 190 160 140 100 d 0 25 100 150 250 q 80 60 40 20 0 d 300 350 400 450 500 20. y 5 3x 2 1 21. y 5 23x 2 3 q 200 Quarters Copyright © McDougal Littell Inc. All rights reserved. 18. Consumption (in pounds) 16. 1.79 pounds −50 12. True 150 100 50 50 150 250 350 450 d Dimes Passport to Algebra and Geometry Answers to Practice Workbook 147 Click on a lesson's answer to return to that lesson's copymaster. 3. c. s0, 200d 0 dimes and 200 quarters totals $50. s500, 0d 500 dimes and 0 quarters totals $50. 10. y 10 6 2 −6 Sales of sale 4. a. 0.03 3 priced goods 1 0.04 3 Sales of regular priced goods 6 −6 5 $250 commission Possible solutions: s0, 4d, s0, 5d, s3, 6d 11. 0.03s 1 0.04r 5 250 b. s x 2 0 1000 2000 3000 4000 r 6250 5500 4750 4000 3250 s 5000 6000 7000 8000 8333.33 r 2500 1750 1000 250 0 y Sales of regular priced 1 6500 −4 −2 −2 2 4x Possible solutions: s21, 21d, s22, 0d, s23, 26d r 12. y 2 5500 4500 −2 3500 2 2500 −2 1500 −4 4x 500 s c. s0, 6250d $0 sales of sale priced goods 1 $6250 of sales of regular priced goods totals $250 commission. s8333.33, 0d $8333.33 sales of sale priced goods 1 $0 of sales of regular priced goods totals $250 commission. 5. a. The times are decreasing almost linearly. b. The pattern is close to linear. If the pattern continues in 2000, the winning time could be approximately 48 seconds. Possible solutions: s0, 23d, s1, 24d, s2, 25d 13. b 1 2g < 45 14. P ≤ 400 or 2l 1 2w ≤ 400 15. d 2 c ≥ 42 16. j 1 p > 70 17. a. 625a 1 500r ≥ 25,000 b. 50 40 30 20 10 r 5 10 15 20 25 30 35 40 a All terrain bikes c. Answers vary. ■ Lesson 13.7 1. Yes 2. No 3. No 5. Yes 6. Yes 7. b 4. Yes 8. c 9. a c. Possible solutions: s0, 50d, s10, 40d, s20, 28d, s30, 15d, s40, 0d 18. y < 2x 1 1 19. y ≥ 2x 20. y < 2x 2 2 148 Answers to Practice Workbook Passport to Algebra and Geometry Copyright © McDougal Littell Inc. All rights reserved. 3000 5000 7000 Sales of sale priced Racer bikes 1000 Click on a lesson's answer to return to that lesson's copymaster. ■ Lesson 13.8 3. y Frequency 1. Estimates vary, !72 < 8.49 2. Estimates vary, !80 < 8.94 3. Estimates vary, !73 < 8.54 4. Estimates vary, s 2 , 2 d 4 3 2 1 7 1 5. Estimates vary, s 2 2 , 0d 5 1.0-1.9 2.0-2.9 3.0-3.9 Number 6. Estimates vary, s 2 2 , 2 2 d 1 1 7. Center at s0, 0d, radius < 4.1 8. WY 5 XZ 5 !40 < 6.32 9. b. ■ Lesson 14.1 1. 31, 30.5, 30 3. 9, 9, 8 2. 17.6, 17.45, no mode 4. 47, 48, 48 6. 12.8, 14, 14 5. 20 7. Answers vary. 8.–10. Measures and explanations vary. 12. < 2.8, 3, 3 11. 5 13. Possible answer: The mode would be the best measure because the comparison was one of quantity. 14. 71,000; 65,500; 96,000 | 5. 0.39 0.38 0.37 0.36 0.35 0.34 0.33 0.32 0.31 6. 0 8 133468 067899 133 233679 99 8 y 6 Frequency ■ Lesson 14.2 1. 30, 42, 43, 52, 53, 53, 54, 61, 67, 67, 68, 70, 71, 72, 72, 73 5 4 3 2 1 y .310 .330 5 Frequency x 4. 6 002 5 011133 4 123779 3 0233345667999 2 0033445567889 1 236677899 6 0 represents 60. 15. Possible answer: The median because the very high priced homes distort the mean. Copyright © McDougal Littell Inc. All rights reserved. Group #1 Group #2 5 .350 .370 Batting Average .390 x ■ Lesson 14.3 4 3 1. 1 and 40 2 3. 75% 1 6. 1 30 35 40 45 50 55 60 65 70 75 x Number 2. Group #1: 2.6, 2.7, 2.8, 2.9, 3.3, 3.5, 3.5 Group #2: 1.9, 2.0, 2.1, 3.8, 3.8, 3.9 Passport to Algebra and Geometry 2. 7, 18 and 29 4. 25% 16 5. 50% 34 99 82 7. Answers vary. 8. 80 88 81 84.5 87 Answers to Practice Workbook 149 Click on a lesson's answer to return to that lesson's copymaster. 9. 23y3 2 2y 1 10, 23y3, 22y, 10 9. Winning Scores 55 14 30 38 10 14 12. 215x2 1 11 13. 14. t Losing Scores 3 11. z 4 2 7z 2 1 z 19 11. Data can vary. Possible real-life situations: exam scores with extra credit, golf scores, or basketball scores. ■ Lesson 14.4 3 5 6 , 23 21 15 3 2 1 2 3 4 5 h 1438 1390 1310 1198 1054 t 6 7 8 9 10 h 878 670 430 158 2146 43 26 23 8 , 29 25 8 10 0 29 15. 878 ft 16. Between 9 and 10 seconds 17. 54 ft, 2262 ft; It takes between 10 and 11 seconds for the penny to strike the ground. ■ Lesson 14.6 29 3 43 4 3 5 9 15 5 , 2. 3 6 14 3 212 34 1 2 0 5 ,3 3. 3 4 17 23 11 23 4. 2 17 31 10. Answers vary. 0 1. 9 19 2 5m 1. 24x3 1 2x2 24 1 2x 1 8 123x3 27x 1 3 2 210 3 7 4 4 2. 1 2x 1 4 2x2 3x3 1 2x2 2 6x 1 7 2 s2x3 2 6x2 2 4x 2 8d x3 1 8x2 2 2x 1 15 3. 5x2 1 x 2 10 3 5. a 5 2 , b 5 6, c 5 3, d 5 4 4. 2k3 2 3k2 1 2k 1 12 5. 4w3 2 w2 2 2w 2 18 6. Many correct answers. 6. 22d 4 2 d 3 2 9d 2 2 6d 2 18 7. Many correct answers. 7. 6x3 2 13x2 1 12x 2 5 3 43 635 758 215 295 8. 785 823 , 293 320 814 730 345 292 8. 3y 4 2 17y 3 2 13y 2 1 12y 2 21 4 9. 216x 1 23 11. w 2 1 11w 2 8 3 12. x3 1 x2 1 4x 2 9 13. 3x2 1 9x 2 34, 230 9. Stand 1 - August Stand 2 - July 420 463 10. 492 503 470 438 10. 29k2 2 14k 1 18 16. 23x2 1 36x 1 80, 161 15. 7x2 1 11x, 96 4 14. x2 1 7x 1 4, 124 ■ Lesson 14.7 1. 12x3 2 6x 2. 23t 5 2 2t 3 1 3t 2 3. 6w5 2 18w3 2 6w 4. 212c 4 1 24c 2 11. Stand 2 - $1404 profit 5. 26x 4 1 6x3 2 12x 2 1 15x ■ Lesson 14.5 6. 2n7 1 3n6 2 2n5 1 6n3 1. Yes, a trinomial 2. Yes, a binomial 3. Not a polynomial 4. b 5. c 8. 6x 1 150 1 2 2x 6. a 2 2x, 8. 218k 4 1 12k 2 1 42k 9. 3p4 2 2p3 1 6p2 10. I: 4x2 1 3x, II: 10x2 2 20x, III: 4x2 1 3x 7. 22z3 1 14z2 1 3z, 22z3, 14z2, 3z 4 7. 7z3 2 3z2 1 2z 6x 4, 1 x2, 2 22x Answers to Practice Workbook 11. 18x2 2 14x 12. 12 s2xdfs5x 2 10d 1 s13x 2 4dg 5 18x2 2 14x Passport to Algebra and Geometry Copyright © McDougal Littell Inc. All rights reserved. 24 10. 22x2 1 10x Click on a lesson's answer to return to that lesson's copymaster. 13. They are equivalent. 14. nsn 2 3d 5 n2 2 3n 15. x2s2x 1 5d 5 2x3 1 5x2 16. 12 s5xds6x 1 2d 5 15x2 1 5x 17. 150x3 1 50x2 18. 220x2 1 40x 19. V 5 4500 cm2; SA 5 2100 cm2 ■ Lesson 14.8 1. s3x 1 5ds2x 1 4d 5 s3x 1 5ds2xd 1 s3x 1 5ds4d 5 6x2 1 10x 1 12x 1 20 5 6x2 1 22x 1 20 2. 5x2 1 11x 1 2 3. 3x2 1 19x 1 20 4. 2x2 1 15x 1 28 5. 12x2 1 30x 1 12 6. 2x2 1 17x 1 36 7. 15x2 1 19x 1 6 8. 12x2 1 60x 1 72 9. 20x2 1 91x 1 99 10. 42x2 1 142x 1 120 11. x2 1 15 2x 1 9 12. 5x2 1 35 2 x 1 15 13. 6x2 1 11x 1 4 14. x2 1 14x 1 30 15. 8x 1 18 16. s4x 1 2d by s3x 1 2d Area 5 12x2 1 14x 1 4 Copyright © McDougal Littell Inc. All rights reserved. 17. s4x 1 5d by s3x 1 4d Area 5 12x2 1 31x 1 20 Passport to Algebra and Geometry Answers to Practice Workbook 151