In Exercises 11–14, solve the systems of equations by substitution.
11.
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College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)
- For Exercises 73–80, (a) evaluate the discriminant and (b) determine the number and type of solutions to each equation. (See Example 9) 73. Зх? 4х + 6 3D 0 74. 5x - 2x + 4 = 0 75. - 2w? + 8w = 3 76. -6d + 9d = 2 77. Зx(х — 4) 3D х — 4 78. 2x(x – 2) = x + 3 79. –1.4m + 0.1 = -4.9m² 80. 3.6n + 0.4 = -8.1n?arrow_forwardFor Exercises 81–100, make an appropriate substitution and solve the equation. (See Examples 10–11) 81. (2x + 5)? – 7(2x + 5) - 30 = 0 82. (Зх — 7)? - 6(3х — 7)-16 3D 0 83. (x + 2x)? – 18(r + 2x) = -45 84. (x + 3x)? - 86. (у? — 3)? — 9(y? — 3) — 52 %3D 0 14(x + 3x) = -40 85. (x + 2)2 + (x + 2) – 42 = 0 10 2 10 - 61 m - - 27 = 0 x + + 35 = 0 87. 88. - 121 x + т - m m 89. 2 + 2 + = 12 90. + 3 + 6 + 3 = -8 91. 5c2/5 11c/5 + 2 = 0 92. З3 d'/3 – 4 = 0 93. y'/2 – y/4 6 = 0 94. n'/2 + 6n/4 – 16 = 0 95. 9y 10y + 1 = 0 96. 100х-4 29x-2 + 1 = 0 | 97. 4t – 25 Vi = 0 98. 9m – 16Vm = 0 100. 392 + 16q -1 99. 30k-2 – 23k- + 2 = 0 + 5 = 0arrow_forwardExercises 149–151 will help you prepare for the material covered in the next section. 149. Multiply: (Vx + 4 + 1)2. 150. Solve: 4x2 16x + 16 = 4(x + 4). 151. Solve: 26 – 11x 16 – 8x + x?.arrow_forward
- For Exercises 5–10, a. Simplify the expression. b. Substitute 0 for h in the simplified expression. 2(x + h)? + 3(x + h) · 5. (2x + 3x) 3(x + h - 4(x + h) – (3x - 4x) 6. h 1 1 1 1 (x + h) – 2 7. x - 2 2(x + h) + 5 8. 2x + 5 h (x + h) – x 9. (x + h) 10. - X h harrow_forwardIn Exercises 20–21, solve each rational equation. 11 20. x + 4 + 2 x2 – 16 - x + 1 21. x? + 2x – 3 1 1 x + 3 x - 1 ||arrow_forwardExercises 86–88 will help you prepare for the material covered in the next section. If –9 is substituted for x in the equation 4x – 3 = 5x + 6, is the resulting statement true or false? Simplify: 13 – 3(x + 2). Зх + Simplify: 10(**1).arrow_forward
- Exercises 59–66: Use the intersection-of-graphs method to solve the equation. Then solve symbolically. 63. -х + 4 %3D 3хarrow_forwardIn Exercises 105–107, solve each equation using a graphing utility. Graph each side separately in the same viewing rectangle. The solutions are the x-coordinates of the intersection points. 105. |x + 1|| 106. 13(x + 4)| = 12 107. 12x – 3| = 19 – 4x|arrow_forward3 -8 y = x + 6 6.arrow_forward
- For Exercises 7–18, write each expression in terms of i and simplify. (See Example 1) 7. V-121 8. V-100 9. V-98 10. V-63 11. V-4V-9 12. V-IV-36 13. V-10V=5 14. V-6V-15 V-98 15. V-2 V-45 16. V-5 V-63 17. V-80 18. V5 Vīarrow_forwardIn Exercises 65–74, factor by grouping to obtain the difference of two squares. 6x + 9 – y? 12x + 36 – y? 65. x? 66. x2 67. x + 20xr + 100 68. x? + 16x + 64 – x4 69. 9x2 70. 25x? – 20x + 4 – 81y? 30x + 25 – 36y? 71. x* - x? – 2x – 1 72. x4 -х2 — бх — 9 x? + 4xy – 4y2 x²+ 10xy - 25y2 73. z? 74. z? - rarrow_forwardIn Exercises 14–16, divide as indicated. 14. (12x*y³ + 16x?y³ – 10x²y²) ÷ (4x?y) 15. (9x – 3x2 – 3x + 4) ÷ (3x + 2) 16. (3x4 + 2x3 – 8x + 6) ÷ (x² – 1)arrow_forward
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt