A-5 Answers to Selected Exercises 59. U -1 { 197 4 V 61. U -2 { 110 2 V 63. U -3 { 141 8 V 65. 556 67. E2, -1{i13F 69. U -3, 3 2 { 313 2 i V 71. t = { 12sg g 73. v = {1FrkM kM 75. t = {22a1r - r02 a 77. t = v0 { 2v0 2 - 64h + 64s 0 32 79. (a) x = y { 28 - 11y2 4 (b) y = x { 26 - 11x2 3 81. (a) x = -2y { 210y2 + 4 2 (b) y = 2x { 210x2 - 6 3 83. 0; one rational solution (a double solution) 85. 1; two distinct rational solutions 87. 84; two distinct irrational solutions 89. -23; two distinct nonreal complex solutions 91. 2304; two distinct rational solutions 93. no In Exercises 95 and 97, there are other possible answers. 95. a = 1, b = -9, c = 20 97. a = 1, b = -2, c = -1 Chapter 1 Quiz [1.1] 1. 526 2. (a) contradiction; ∅ (b) identity; {all real numbers} (c) conditional equation; E11 4 F 3. y = 3x a - 1 [1.2] 4. $10,000 at 2.5%; $20,000 at 3% 5. $7.61; The model predicts a wage that is $0.04 less than the actual wage. [1.3] 6. - 1 2 + 16 4 i 7. 3 10 - 8 5 i [1.4] 8. U1 6 { 111 6 i V 9. E { 129F 10. r = { 12 u u 1.5 Exercises 1. A 3. D 5. A 7. B 9. 7, 8 or -8, -7 11. 12, 14 or -14, -12 13. 7, 9 or -9, -7 15. 9, 11 or -11, -9 17. 20, 22 19. 6, 8, 10 21. 7 in., 10 in. 23. 100 yd by 400 yd 25. 9 ft by 12 ft 27. 20 in. by 30 in. 29. 1 ft 31. 4 33. 3.75 cm 35. 5 ft 37. 1012 ft 39. 16.4 ft 41. 3000 yd 43. (a) 1 sec, 5 sec (b) 6 sec 45. (a) It will not reach 80 ft. (b) 2 sec 47. (a) 0.19 sec, 10.92 sec (b) 11.32 sec 49. (a) $178.7 million (b) 2014 51. (a) 19.2 hr (b) 84.3 ppm (109.8 is not in the interval 350, 1004.) 53. (a) 5082.9 million metric tons (b) 2020 55. $611 billion 57. 80 - x 58. 300 + 20x 59. R = 180 - x21300 + 20x2 = 24,000 + 1300x - 20x2 60. 10, 55; Because of the restriction, only x = 10 is valid. The number of apartments rented is 70. 61. 80 63. 4 1.6 Exercises 1. rational equation 3. 1 4 5. rational exponent 7. D 9. E 11. - 3 2 , 6 13. 2, -1 15. 0 17. 5-106 19. ∅ 21. ∅ 23. 5-96 25. 5-26 27. ∅ 29. E - 5 2 , 1 9F 31. E 3 4 , 1F 33. 53, 56 35. E -2, 5 4F 37. 1 7 8 hr 39. 78 hr 41. 13 1 3 hr 43. 10 min 45. 536 47. 5-16 49. 556 51. 596 53. 596 55. ∅ 57. 5{26 59. 50, 36 61. 5-26 63. E - 2 9 , 2F 65. 546 67. 5-26 69. E2 5 , 1F 71. 5316 73. 5-3, 16 75. 5256 77. 5-27, 36 79. 5-29, 356 81. E3 2F 83. E 1 4 , 1F 85. 50, 86 87. U {1, { 110 2 V 89. E {13, {i15F 91. 5-63, 286 93. 50, 316 95. E - 5 2 , -2, 0, 1 2F 97. U -6 {213 3 , -4 { 12 2 V 99. E - 2 7 , 5F 101. E - 1 27 , 1 8F 103. E { 1 2 , {4F 105. h = d2 k2 107. m= 1 - n3/424/3 109. e = Er R + r 111. 5166 112. 5166 113. Answers may vary. 114. 546 Summary Exercises on Solving Equations 1. 536 2. 5-16 3. E -3{312F 4. 52, 66 5. ∅ 6. 5-316 7. 5-66 8. 566 9. E1 5 { 2 5 i F 10. 5-2, 16 11. E - 1 243 , 1 3125F 12. 5-16 13. 5{i, {26 14. 5-2.46 15. 546 16. U1 3 { 12 3 i V 17. E 15 7 F 18. 546 19. 53, 116 20. 516 21. ∅ 22. a = {2c2 - b2 1.7 Exercises 1. F 3. A 5. I 7. B 9. E 11. A square bracket is used to show that a number is part of the solution set, and a parenthesis is used to indicate that a number is not part of the solution set. 13. 3-4, ∞2 15. 3-1, ∞2 17. 1-∞, ∞2 19. 1-∞, 42 21. C - 11 5 , ∞B 23. A -∞, 48 7 D 25. 3500, ∞2 27. The product will never break even. 29. 1-5, 32 31. 33, 64 33. 14, 62 35. 3-9, 94 37. A - 16 3 , 19 3 D 39. 1-4, 12 41. 1-∞, -22 ´13, ∞2 43. C - 3 2 , 6D 45. 1-∞, -34 ´3-1, ∞2 47. 3-2, 34 49. 3-3, 34 51. ∅ 53. C 1 - 12, 1 + 12 D 55. A 57. 1-5, 34 59. 1-∞, -72 ´3-2, ∞2 61. 1-∞, -22 63. 1-∞, 62 ´C 15 2 , ∞B 65. 1-∞, 12 ´A 9 5 , ∞B 67. 1-3, 74 69. A -∞, - 3 2B ´C - 1 2 , ∞B 71. 1-2, ∞2 73. 11, ∞2 75. A0, 4 11B ´A 1 2 , ∞B 77. 1-∞, -24 ´11, 22 79. A -∞, 5 2B ´38, ∞2 81. C 3 2 , ∞B 83. A 5 2 , ∞B 85. C - 8 3 , 3 2D ´16, ∞2 87. (a) 2001 (b) 2012 89. between (and inclusive of) 4 sec and 9.75 sec 91. between (and inclusive of) 1 sec and 1.75 sec 93. between -1.5 sec and 4 sec 95. E4 3 , -2, -6F
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