Beginning Algebra Test 4

MAT 090 Beginning Algebra NAME: KEY Test #4 State whether the following statements are TRUE or FALSE. No explanation is needed. A) 45% represents the fraction 9/20. TRUE B) The inequality -2 ≥ j corresponds to the interval notation (-∞, -2]. TRUE C) The ordered pair (2, 1) is a solution to the equation x - 2y = 0. TRUE SET UP and SOLVE the following problems. To receive full credit, you need to set up an equation(s). A) Kathleen and Gabe need to rent a power saw from Algebra Rentals. The store charges them a fee of $35 and charges $10 per hour for the saw. If their remodeling budget is $1,500, how many hours can Kathleen and Gabe rent a power saw for their remodeling project?   [10t + 35 = 1500] [t = 146.5 hours] B) The sales tax rate in Jojo's community is 8%. On a recent purchase of a PS4 game, Jojo paid $2.40 in taxes. What was the sticker price for his PS4 game?   [0.08x = 2.40] [x = $30] C) The area of a triangle is 52 ft² and the height is 20 ft. What is the base of this triangle? [52 = (1/2)(20)B] [B = 5.2 ft] D) The perimeter of a rectangle is 62 inches and the length is 9 more than the width. Find the dimensions of this rectangle. [L = W + 9] [62 = 2(W + 9) + 2W] [W = 12 in] [L = 19 in] SET UP ONLY the following word problems. Define and label your unknowns, and set up the equation(s) you would use to solve the word problem. You do not need to solve your equations. SET UP ONLY. A) Double a number minus five is the sum of three and the number.   [2x - 5 = 3 + x] B) Jerry makes a rectangle whose area is 52 in² and the difference between the length and the width is 6. Find the dimensions of this rectangle. [L = W + 6] [52 = LW] C) The Lucero's spent a $400 fixing their kitchen and bathroom of their new home. The amount they spent on the kitchen was $35 more than double the amount spent on the bathroom. How much did they spend on the bathroom project?   [K = bathroom] [3K + 35 = 400] D) A classroom of 125 people is broken up into three groups. The Yankee fans are twice the number of Dodger fans. The number of D-Back fans is 15 less than the sum of the other two. How many fans are there for each team? [Y = Yankees] [D = Dodgers] [B = D-backs] [Y + D + B = 125] [Y = 2D] [B = Y + D - 15] Solve the following three inequalities. Put your answers in INTERVAL NOTATION. A) 4x + 5 < 2x - 9 [2x < -14] [x < -7] [(-\infty, -7)] B) 3x + 2(x - 1) ≥ 6 - 3x [5x - 2 ≥ 6 - 3x] [8x ≥ 8] [x ≥ 1] [[1, ∞)] C) (1/2)x - (2/3) ≤ (1/4)x + (5/6) [(3/4)x ≤ (18/3)] [x ≤ 6] [(-\infty, 6]] For the set of numbers given by the inequality, x ≥ 2, do the following: A) Graph the set on a number line. 2 3 B) Rewrite the set in interval notation. [2, ∞) The graph below measures a distance in feet that an object moved compared to a time in seconds. Use it to answer the following questions:   A) What was the distance at 20 seconds?   45 ft 60 (B) At what time was the distance 30 feet? 100 seconds (C) What was the distance at 40 seconds? 25 ft 25. 10 D) What will be the distance at 80 seconds? 50 ft. 50 ft. 10 60 seconds Five ordered pairs are given. Graph each point on the grid provided. A B C DE (5, 2) (-4, 0) (-3, 1/2) (2, -3) (0, 3) E A (5, 2) (-1 1/2, -2) B D 15 Graph the following equation. You must label at least THREE points. [x - 2y = 6] [-2y = -x + 6] [y = (1/2)x - 3] Points: (0, -3), (2, -2), (6, 0) Graph the following equation. You must label at least THREE points. [3x + 4y = 0] [4y = -3x] [y = (-3/4)x] Points: (0, 0), (4, -3), (-4, 3)