Simplify each expression. (Section 1.3, Objective 3) 37. 3x(10 - 2x) - 27x 2 - 2(5x - 6) 38. - 2 3 x - 17 + 1 3 x + 8 39. 4 3 x + 1 - 3 5 x + 3 2 40. 5(2x + 7) - 2(x - 12) Translate each phrase or sentence into an algebraic expression, equation, or inequality. Use the variable x to represent the unknown number. (Section 1.3, Objective 4) 41. One-fourth the difference of a number and 12 42. Six less than three times a number is more than the number plus 9. Solve each problem. (Section 1.3, Objective 5) 43. Jacob has collected 120 dimes and nickels. If x represents the number of nickels he collected, write an expression for the number of dimes he collected. 44. Referring to Exercise 43, if Jacob’s coins total $9.60, write an algebraic expression that represents the total value of his coins. Determine if each equation is a linear equation. If it is a linear equation, determine if x = -2 is a solution of the equation. (Section 2.1, Objective 1) 45. 24x 2 13 5 25 46. 2x 2 + 7 = 14 Use the addition and multiplication properties of equality to solve each linear equation. (Section 2.1, Objectives 2–4) 5x 2 12 47. 17.8 2 d 5 12.1 48. 6 5 3 49. a 2 4 5 5 2 50. 3x 2 13 5 8 Solve each linear equation. If there is no solution, then write for the answer. If there are infinitely many solutions, then write for the answer. (Section 2.1, Objectives 4–6) 51. 29 1 8x 5 412x 2 32 52. 7x 6 2 3x 2 5 2 3 53. 41x 2 22 2 5x 5 2x 2 3x 2 8 54. 71x 1 32 2 4x 5 x 2 5 Translate each statement into a linear equation and solve the problem. (Section 2.2, Objective 1) 55. The product of a number and one-third is 12. Find the number. 56. The quotient of a number and four is 80. Find the number. 57. Four less than three times a number yields 17. Find the number. 58. Twice the sum of two consecutive even numbers is 76. Find the numbers. Find the measure of each angle described or pictured. (Section 2.3, Objective 1) 59. Find the measure of an angle whose complement is 15˚ less than twice the measure of the angle. 60. Find the measure of an angle whose supplement is 42˚ more than twice the measure of the angle. 61. (3a – 10)° (a + 4)° 62. (2x + 26)° (10x – 6)° Use the appropriate formula to solve each problem. (Section 2.3, Objective 2) 63. Find the height of a triangle whose area is 168 ft2 and whose base is 12 ft. 64. The length of a rectangle is 6 ft less than three times its width. If the perimeter is 132 ft, find the length and width of the rectangle. Solve each formula for the specified variable. (Section 2.3, Objective 4) 65. a 5 b 2 3cd for c 66. x 5 1 2 y 1 3zw for y Graph the solution set of each inequality on a number line and express the solution set in interval notation and setbuilder notation. (Section 2.4, Objective 1) 67. 7 , x 68. 212 $ x Solve each inequality. Graph the solution set and write each answer in interval notation and set-builder notation. (Section 2.4, Objective 2) 69. 21a 1 72 2 8 # a 1 10 70. 1 3 (x + 15)<- 4 3 (x - 6) In Professor Long’s algebra class, the course grade is determined by tests (40%), homework (10%), quizzes (20%), and a final exam (30%). (Section 2.4, Objective 3) 71. Ashlee’s test average is 82, homework average is 96, and quiz average is 71. What must she get on the final exam to earn a B in the class, if a B is 80–89? 72. Jennifer’s test average is 68, her homework average is 80, and her quiz average is 63. What must she get on the final exam to earn a C in the class, if a C is 70–79? 208 Chapter 3 Graphs, Relations, and Functions
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