190 Chapter 2 Linear Equations and Inequalities in One Variable 17. At a community college, tuition and fees are calculated by the expression 135c + 86.75, where c is the number of credit hours taken per semester. If Bianca takes 10 credit hours next semester, what are her tuition and fees? (Section 1.3, Objective 6 ) 18. Perform the indicated operation and simplify. (Sections 1.4 and 1.5, Objectives 1 and 2 ) a. 5.16 + (-3.97) b. a- 5 4 b + a- 3 2 b c. 5 - 9 + (-10) - (-15) d. 5.4 - (-3.2) + (-2 .1) + 2.8 e. 3 4 - 5 8 - a- 1 2 b f. 28 - E9 - C5 - (1 - 130 - 14)DF g. -62 - (-15) - u2 - 10u For Exercises 19–22, write a mathematical expression needed to solve each problem and then answer the question. (Sections 1.4 and 1.5, Objective 3 ) 19. The highest point on the Australian continent is the peak of Mount Kosciuszko. The peak is 7310 ft above sea level. The lowest point on land in China is the Turpan Pendi, which is 505.2 ft below sea level. What is the difference between these altitudes? 20. If the lowest recorded temperature in New Mexico is -50°F and the highest recorded temperature is 122°F, what is the difference between the highest and lowest temperatures? 21. Dave has $245.75 in his checking account. He deposits his paycheck of $635.25. Dave writes a check for his phone bill for $65.43, for groceries for $125.78, and then for rent for $525. What is Dave’s checking account balance? 22. Find the measure of the unknown angle of the given triangle. b a c a. a = 29°, b = 87° b. b = 103°, c = 43° 23. Find the complement and the supplement of an angle whose measure is 78°. 24. Perform the indicated operation and simplify. (Section 1.6, Objectives 1–3 ) a. (-3.2)(1.5) b. (-18)a-7 24 b c. - (-3)4 d. 0 6 e. 10 ÷ 0 f. 8(-25)(-3) g. a- 5 12 b ÷ a- 10 9 b h. -8 ÷ 20 7 25. Evaluate each expression for the given values of the variables. (Section 1.6, Objective 4 ) a. 1(x1 - x2)2 + (y1 - y2)2 for x1=-2, x2 = 1, y1 = 7, y2 = 3 b. u2x + 3u x - 2 for x=-2, -1, 0, 1, 2 26. Find the additive and multiplicative inverses of each number. Assume all variables are nonzero. (Section 1.7, Objective 1 ) a. - 16x b. 5 8 c. 6a 27. Apply the commutative, associative, and/or distributive properties to rewrite each expression and simplify the result. (Section 1.7, Objectives 2 and 3 ) a. - 18 + c - (-15) b. -2(x - 10y - 7) c. ab - 3 10 b + 2 d. 10a- 2 5 x + 3 2 b 28. Determine if the terms are like or unlike. (Section 1.8, Objective 2 ) a. 8ab2 and -34ab2 b. 1 3 cd2 and - 5 7 c2d c. 4 3 πr3 and πr2h 29. Simplify each algebraic expression. (Section 1.8, Objectives 3 and 4 ) a. - 5(x)(14) b. 15(2x - 1) - 36x c. - (x - 12) - 2(5x + 7) d. 3.7 - 0.8(-0.1x + 2.5) e. - 12a1 3 a - 3 4 b + 14a3 7 a - 1 2 b f. 2x2 - 4(x - 3x2) - x 30. Determine whether the following is an expression or an equation. (Section 2.1, Objective 1 ) a. 6x - 19 = 4x - 11 b. 7x - 15 - 3x + 4 31. Determine if each number is a solution of the equation. (Section 2.1, Objective 2 ) a. x = -2, x = 0, or x = 2; 5x - 2 = -2x - 16 b. x = -2, x = 0, or x = 2; 8x - 12 = -3x + 10 32. For each problem, define the variable, write an equation, and solve the problem. (Section 2.1, Objectives 3 and 4 ) a. Five times the sum of a number and -26 is the same as three times the number. Find the number. b. The sum of a number and 28 is the same as five times the number. Find the number. c. The difference of twice a number and -6 equals 32 less than the number. Find the number. d. One angle is 16° more than another angle. Their sum is 180°. Find the measure of each angle. e. One angle is 12° less than another angle. Their sum is 90°. Find the measure of each angle. f. One angle is 6° more than another angle. Their sum is 90°. Find the measure of each angle. 33. Solve each equation. (Section 2.2, Objectives 2 and 3; Sections 2.3 and 2.4, Objectives 1 and 2 ) a. 7(x - 3) + 18 = 2(x - 6) - 26 b. 2.46x + 12.25 = 5.28x + 8.02
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