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Math 161 Review for Exam 1 1. Plot at least 5 points and sketch the graph. x (a) y 2 (b) y 3 x 1 (c) y x 2 x 1 (e) y ( x 2) 2 4 (f) y 2 x 3 (g) y 3 (d) y x 3 2 (h) x 1 y 3 25 2 2 2. Find the x-intercept(s) and y-intercept(s) for each equation in problem 1. 3. For each equation in problem 1 tell whether it is symmetric with respect to the x-axis, the yaxis, or the origin. 4. Sketch the graph. (a) 2 x 3 y 12 (b) x 5 (c) y 2 x 4 (d) 3x 7 y 0 5. Solve for x. 2 5 14 2 (a) x 3 x 4 x x 12 (b) 2 x 2 11x 6 (c) 5 2 (d) 23x 7 5x 2x 4 10 (e) (g) 0.2x 0.7x 4 5 (j) 32 x 6 6 x 18 (h) x 2 6 5 x (k) x 2 12 5 x (i) x 2 13 6 x (l) x 2 9 (n) x 2 6 x 0 (o) 2x 8 18 (q) x 2 x 2 54 (r) x 3 3x 2 4 x 12 (t) 2 x 12 11 x (u) x 4 2 x 3 8 x 16 (m) 32x 7 4x 8 22x 6 9 (p) 2x 1 x 4 3 3 x 1 3x 1 5 x 6 (f) xx 6 6 x 4 2 6 2 2 x x (s) 24 11 x 1 x 1 6. Use algebra to solve the following problems. (a) The perimeter of a rectangle is 22 feet. The length is 5 feet more than the width. Find the length and width. (b) A family paid $41.40 including a 15% tip for dinner at a restaurant. What was the original bill before the tip? (c) A chemist wishes to make 300 milliliters of 45% acid solution by mixing a 10% acid solution with a 60% acid solution. How much of each acid solution should be used? (d) A news stand operator pays $360 rent and 28 cents for each newspaper sold. S/he sells the newspapers for 60 cents each. How many newspapers does s/he need to sell in order to break even? Sketch a graph showing income, expense, profit, loss, and break even point. (e) The profit p in dollars of a paint manufacturer selling x gallons of paint is p 0.1x 2 8x 120 . How many gallons of paint does the manufacturer need to sell in order to break even? Sketch a graph of the profit. (f) The height h in feet of a rocket at time t seconds after the fuel runs out is h 16t 2 96t 112 . How long does it take the rocket to reach the ground? Graph. Math 161 Answers to Review 1 1.(a) 1.(b) 1.(c) 1.(d) 1.(e) 1.(f) 1.(g) 1.(h) 4.(a) 4.(b) 4.(c) 4.(d) Math 161 Answers to Review 1 page two 2.(a) (b) (c) (d) (e) (f) (g) (h) y-intercept also (0, 0) y-intercept (0. 2) no y-intercept y-intercept (0, -2) y-intercept (0, 0) y-intercept (0, -3) y-intercept (0, 3) y-intercepts 0,3 6 (0, -2) and (0, 8) x-intercept (0, 0) x-intercepts (-2, 0) and (4, 0) x-intercept (2, 0) x-intercept (2, 0) x-intercepts (-4, 0) and (0, 0) x-intercept (3/2, 0) no x-intercept x-intercepts (-3, 0) and (5, 0) 3.(a) symmetric with respect to the origin (b) none of the given choices but it is symmetric with respect to the line x = 1 (c) none (d) none of the given choices but it is symmetric with respect to the point (0, -2) (e) none of the given choices but it is symmetric with respect to the line x = -2 (f) none of the given choices (g) symmetric with respect to the y-axis (h) none of the given choices 5.(a) no solution (b) 1/2 , - 6 (c) 2 (d) 16/9 (e) 46/15 (f) 1, 6 (g) 26/3 (h) 3, 2 (i) 3 2i (j) all real numbers (k) 5 23 i 2 (l) 3 (m) 4/3 (n) 0, - 6 (o) 8 3 2 (p) 4, 40 (q) 8, 1 29 2 (r) 2, -3 (s) -3/2, - 8/7 (t) 16, 9/4 (u) 2, 1 3 i 6.(a) Solve 2(5 + w + w) = 22 to get width = 3 feet and length = 5 + width = 8 feet. (b) Solve x + 0.15x = 41.40 to get original bill = $36. (c) Solve 0.6x + 0.1(300-x) = 0.45(300) to get x = 210 mL of 60% acid and 300-x = 90 mL of 10% acid. (d) Solve 0.6x = 0.28x + 360 to get x = 1125 newspapers. (e) Solve 0.1x 2 8 x 120 0 to get x = 20 gallons or 60 gallons (f) Solve t > 0 and 16t 2 96t 112 0 to get t = 7 seconds. 6.(d) 6.(e) 6.(f)