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MATH 095 Intermediate Algebra Spring 2009 Turn in FINAL DRAFTS of these problems. Your finished product should be easy to read and contain how you reached your answers (show work). Use a highlighter to show your final answers. 1. Carpenters stabilize wall frames with a diagonal brace, as shown in the figure. The length of the brace is given by L H 2 W 2 . a. Solve the formula for H . b. If the bottom of the brace is attached 9 feet from the corner and the brace is 12 feet long, how far up the corner post should it be nailed? Give your answer to the nearest tenth of a foot. 2. Find, explain, and correct the errors in this student’s work. Be sure to determine the correct answers. 7x 4 8 x 7 x 4 64 x 2 0 x 2 7 x 60 a. 0 ( x 5)( x 12) x 5 0 or x 12 0 x 5 x 12 or b. 2 9 7i 67i 42i 3. Consider the rectangular electronic billboard on the right. Find the perimeter and the area for the billboard. Leave your answers as simplified radicals. 4. Solve each equation. a. x4 x2 b. 3 x 1 1 0 c. x2 9x 3 x d. 7 x 11 5 0 5. Simplify each expression. x 1 3 x5 6 a. x 3 5 1 x y b. 2 1 2 2 xy c. r 1 2 r r 3 2 d. a 13 4 a2 3 6. Perform the indicated operations. Give answers in standard form. a. (5 4i) (9 3i ) b. (2 3i )(1 i ) c. d. 25 81 3i 2i 7. Explain how to rationalize the denominator. Use an example in your explanation. 8. Find the exact length of side b in the figure. 9. Perform the indicated operations. Assume that all variables represent positive real numbers. a. 13 2 2 b. 8 80 3 45 c. 2 54 x3 5 96 x3 d. 3 5 2 16 Self-Reflection Write a short (one or two paragraphs) self-reflection of this homework assignment. What were your strengths? What were some areas in which you could improve?