5. The height of a baseball hit upward with an initial velocity of 112 ft/sec from an initial height of 8 ft is represented by the expression -16t2 + 112t + 8, where t is the number of seconds after the ball has been hit. What is the height of the ball after 4 sec? (Section 1.3, Objective 6 ) 6. Perform the indicated operation and simplify. (Sections 1.4 and 1.5, Objectives 1 and 2) a. 5.4 - 9.2 + (-8.4) - (-11.5) b. 5 6 - 3 4 - a- 1 4 b c. 30 - { 7 - 4 - (2 - 120 + 5 )} Write the mathematical expression needed to solve each problem and then answer any questions. (Sections 1.4 and 1.5, Objective 3) 7. Sherry has $235.65 in her checking account. She deposits her paycheck of $567.45. Sherry writes a check for phone bill for $47.82, for groceries for $135.93, and then for rent for $475. What is Sherry’s checking account balance? 8. Selena wants to mix a 4% salt solution with a 30% solution to get a 25% solution. Let x oz represent the volume of the 4% salt solution. If Selena wants 50 oz of 25% salt solution, write an expression that represents the volume of the 30% salt solution. 9. In a rectangle, the length is two more than four times the width. If w represents the width, write an expression that represents the length of the rectangle. 10. Find the complement and the supplement of an angle whose measure is 63°. 11. Perform the indicated operation and simplify. (Section 1.6, Objectives 1–3 ) a. (-5.4)(3.6) b. (-36)a 5 16 ba- 8 15 b (-5)3 d. -7 c. - 0 e. 6(-15)(-4) f. a15 14 b ÷ a- 10 21 b 12. Evaluate each expression for the given values of the variables. (Section 1.6, Objective 4 ) a. b2 - 4ac for a = -2, b = 1, c = 5 b. u3 + xu x - 1 for x = -1, 0, 1 13. Apply the commutative, associative, and/or distributive properties to simplify each expression. (Section 1.7, Objectives 2 and 3 ) a. 13 + c - (-25) b. -4(x + 3y - 8) c. ax - 11 6 b + 2 d. 8a3 4 x - 1 2 b 14. Simplify each algebraic expression. (Section 1.8, Objectives 3 and 4 ) a. 3(4x - 5) - 16x b. -(2x - 7) - 3(-2x + 5) c. 4.8 - 0.3(-0.5x + 1.4) d. 15a2 5 x - 1 3 b - 10a1 2 x + 4 5 b e. 5x2 - 7(x + x2) - 8x 15. Determine whether each of the following is an expression or an equation. (Section 2.1, Objective 1) a. 5x - 28 = 2x - 12 b. x - 10 + 3x + 5 16. Determine if the given numbers are solutions of the equation. (Section 2.1, Objective 2) a. Is x = -2, x = 0, or x = 1 a solution of 7x - 3 = -x - 19? b. Is x = -2, x = 0, or x = 3 a solution of x - 2 = -4x + 13? 17. For each exercise, define the variable, write an equation, and solve the problem. (Section 2.1, Objectives 3 and 4 ) a. The sum of a number and 32 is the same as three times the number. Find the number. b. The difference of three times a number and -5 equals 7 less than the number. Find the number. c. One angle is 14° more than another angle. Their sum is 90°. Find the measures of each angle. 18. Solve each equation. (Section 2.2, Objectives 2 and 3; Sections 2.3 and 2.4, Objectives 1 and 2) a. 3(x - 2) - 28 = 5(x - 1) + 9 b. 5(1 - x) - 7x = 13 - (2 - 4x) c. - 2 5 (5x + 10) + 3 = x - 5 d. - 0.2y + 14.1 = 2.3y + 4.1 For each exercise: (1) assign a variable to the unknown, (2) write an equation that represents the situation, (3) solve the equation, and (4) answer the question using complete sentences. (Section 2.2, Objective 4; Section 2.3, Objectives 3 and 4 ) 19. The cost to rent a midsize car for one day is $68 plus $0.36 per mile. This daily cost is represented by the equation 68 + 0.36x, where x is the number of miles driven. How many miles has the car been driven if the cost of the rental car is $199.40? 20. The sum of three consecutive odd integers is 75. Find the integers. 21. The sum of the two smaller of three consecutive integers is the same as 30 less than three times the largest integer. Find the integers. 22. Solve each equation. If the equation is a contradiction, write the solution as ∅. If the equation is an identity, write the solution as . (Section 2.4, Objectives 1– 4 ) a. 7(2y - 1) - ( y - 5) = 3( y + 2) + 8 b. 0.7x + 1.1x = 7.2 c. 0.015x + 0.024 (480 - x) = 8.82 d. - 1 2 (x - 3) = 1 3 (2 x + 9) + 1 6 288 Chapter 3 Linear Equations in Two Variables
hendricks_beginning_algebra_1e_ch1_3
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