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MATH 101 INTERM. ALGEBRA NAME: ID#: TAKE-HOME EXAM 3 (Chapter 9) Solve the following problems showing all your work for full credit. 1. Evaluate each expression without a calculator. 81 a) (3 pts.) 4 16 1 b) (2 pts.) 32 5 c) (2 pts.) 10000 1 4 2 8 3 d) (4 pts.) 27 e) (4 pts.) 64 2 − 3 2. Express each expression in simple radical form. a) (3 pts.) 48 b) (3 pts.) 3 5 1 2 3 3 c) (4 pts.) 2 d) (3 pts.) 25 1 4 2 − 3 3. Perform the operations and express your answer in simple radical form. a) (4 pts.) 12 + 27 b) (4 pts.) 50 − 45 c) (4 pts.) 6 12 d) (4 pts.) 8 48 4. Solve each quadratic equation. Give roots as exact numbers in simple radical form. a) (4 pts.) x 2 + 1 = 55 b) (4 pts.) x 2 + 4 x − 14 = 0 c) (4 pts.) 3x 2 − 13 = 12 x 5. (4 pts.) Show that the functions y1 = other. 6. Find the variation constant a . a) (3 pts.) y = ax , y = 2 when x = 6 b) (3 pts.) y = ax 2 , y = 45 when x = 3 1 c) (3 pts.) y = ax 3 , y = 0.4 when x = 8 1 d) (3 pts.) y = ax 2 , y = 100 when x = 10 1 x − 4 and y 2 = 3 x + 12 are inverses of each 3 7. (5 pts.) The height of an equilateral triangle varies directly as the length of its sides. The height of an equilateral triangle is 3 cm when the sides are 2 cm each. What is the height, if the sides are 3 cm each? 2 8. Use algebra to solve each equation. Note any extraneous solutions. a) (4 pts.) 2 x 6 = 98 b) (4 pts.) ( x − 2) − 5 = 22 3 c) (2 pts.) x 4 = −30 1 1 d) (4 pts.) x 2 = −2 8 1 3 e) (4 pts.) − 5 x − 4 = 1 9. (5 pts.) Sketch the graph of the inverse function of the function, which graph is given below. Find the coordinates of the point corresponding to the point (1,0 ) . 1 0.5 0 -2 -1 -0.5 0 -1 -1.5 -2 -2.5 1 2 3 4