A-4 Answers to Selected Exercises 85. 17m4 + 3n217m4 - 3n2 87. 319r - 10212r + 12 89. 1x - 121y + 22 91. 13x - 4219x - 342 93. 1 2k21k - 12 95. x + 1 x + 4 97. p + 6q p + q 99. 2m m - 4 , or -2m 4 - m 101. q + p pq - 1 103. 10 22 105. 524 2 107. - 23 50p 5p 109. 212 m 111. 66 113. -9m22m+ 5m2m, or m A -9 2m+ 52m B 115. 6 A 3 + 22 B 7 In Exercises 117–125, we give only the corrected right sides of the equations. 117. x3 + 5x 119. m6 121. a 2b 123. 1-22-3 125. 7b 8b + 7a Chapter RTest [R.1] 1. 0.6; 66 2 3 % 2. 5 4 , or 1 1 4 ; 125% [R.1, R.3] 3. - 17 63 4. -1 [R.2] 5. false 6. true 7. false 8. true 9. (a) -13, - 12 4 (or -3), 0, 249 (or 7) (b) -13, - 12 4 (or -3), 0, 3 5 , 5.9, 249 (or 7) (c) All are real numbers. [R.3] 10. 4 11. 103.9 12. (a) associative property (b) commutative property (c) distributive property (d) inverse property [R.5] 13. 5x2 - 4x + 2 14. 36r2 - 60r + 25 15. 3t3 + 5t2 + 2t + 8 16. 2x2 - x - 5 + 3 x - 5 17. $11,224 18. $12,480 [R.6] 19. 13x - 7212x - 12 20. 1x2 + 421x + 221x - 22 21. 2m14m+ 3213m- 42 22. 1x - 221x2 + 2x + 421y + 321y - 32 23. 1a - b21a - b + 22 24. 11 - 3x2211 + 3x2 + 9x42 [R.7] 25. x41x + 12 31x2 + 12 26. x 4x + 12 1x + 221x + 1212x - 32 27. 2a 2a - 3 , or -2a 3 - 2a 28. y y + 2 [R.4, R.8] 29. 3x2y422x 30. 222x 31. x - y 32. 7 A 211 + 27 B 2 33. y x 34. 9 16 35. 2.1 sec Answers in Exercises 49–57 exist in equivalent forms. 49. x = -3a + b 51. x = 3a + b 3 - a 53. x = 3 - 3a a2 - a - 1 55. x = 2a2 a2 + 3 57. x = m + 4 2m + 5 59. (a) $63 (b) $3213 61. 68°F 63. 10°C 65. 37.8°C 67. 463.9°C 69. 45°C 1.2 Exercises 1. 8 hr 3. $40 5. 90 L 7. A 9. D 11. 90 cm 13. 6 cm 15. 600 ft, 800 ft, 1000 ft 17. 4 ft 19. 50 mi 21. 2.7 mi 23. 45 min 25. 1 hr, 7 min, 34 sec; It is about 1 2 the world record time. 27. 35 km per hr 29. 7 1 2 gal 31. 2 L 33. 4 mL 35. short-term note: $100,000; long-term note: $140,000 37. $10,000 at 2.5%; $20,000 at 3% 39. $50,000 at 1.5%; $90,000 at 4% 41. (a) $52 (b) $2500 (c) $5000 43. (a) F = 14,000x (b) 1.9 hr 45. (a) 17.2 million (b) 2026 (c) They are quite close. (d) 16.3 million (e) When using the model for predictions, it is best to stay within the scope of the sample data. 1.3 Exercises 1. 1-1; -1 3. complex conjugates 5. denominator 7. true 9. false; -12 + 13i 11. real, complex 13. pure imaginary, nonreal complex, complex 15. nonreal complex, complex 17. real, complex 19. pure imaginary, nonreal complex, complex 21. 5i 23. i110 25. 12i12 27. -3i12 29. -13 31. -216 33. 13 35. i13 37. 1 2 39. -2 41. -3 - i16 43. 2 + 2i12 45. - 1 8 + 12 8 i 47. 12 - i 49. 2 51. 1 - 10i 53. -13 + 4i12 55. 8 - i 57. -14 + 2i 59. 5 - 12i 61. 10 63. 13 65. 7 67. 25i 69. 12 + 9i 71. 20 + 15i 73. 2 - 2i 75. 3 5 - 4 5 i 77. -1 - 2i 79. 5i 81. 8i 83. - 2 3 i 85. E = 2 + 62i 87. Z = 12 + 8i 89. i 91. -1 93. -i 95. 1 97. -i 99. -i 1.4 Exercises 1. G 3. C 5. H 7. D 9. D; E1 3 , 7F 11. C; 5-4, 36 13. 52, 36 15. E - 2 5 , 1F 17. E - 3 4 , 1F 19. 5{106 21. E1 2F 23. E - 3 5F 25. 5{46 27. E {3 13F 29. 5{9i6 31. U 1 {213 3 V 33. E -5{i 13F 35. U 3 5 { 13 5 i V 37. 51, 36 39. E - 7 2 , 4F 41. E1{ 13F 43. E - 5 2 , 2F 45. U 2 { 110 2 V 47. U1{ 13 2 i V 49. He is incorrect because c = 0. 51. U 1 { 15 2 V 53. E3{12F 55. 51{2i6 57. U 3 2 { 12 2 i V Chapter 1 Equations and Inequalities 1.1 Exercises 1. equation 3. first-degree equation 5. contradiction 7. true 9. false 11. 5-46 13. 516 15. E - 2 7F 17. E - 7 8F 19. 5-16 21. 5106 23. 5756 25. 506 27. 5126 29. 5506 31. identity; 5all real numbers6 33. conditional equation; 506 35. contradiction; ∅ 37. identity; 5all real numbers6 39. l = V wh 41. c = P - a - b 43. B = 2 - hb h , or B = 2 h - b 45. h = S - 2pr 2 2pr , or h = S 2pr - r 47. h = S - 2lw 2w + 2l
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