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# Algebra and Geometry

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1. Judy and Pete are building a new house and want to carpet their living room, except
for the entrance way and the semicircle in front of the fireplace that they want to tile
(Alexander & Koeberlein, 2003).

A. How many square yards of carpeting are needed? (Hint: There are 9 square feet in one square yard.) Round to the nearest yard. Show all work to receive full credit.

B. How many square feet are to be tiled? Show all work to receive full credit.

2. Two angles are complimentary of each other. Twice one angle is equal to the other angle plus the product of three and five.

A. Set up a system of linear equations to represent the two angles. (Hint: You will need two equations and two unknowns.)

B. Graph each of the equations on one rectangular coordinate system. (Hint: You must get y by itself before graphing.) Scale the graph accordingly; you will need your x-axis and y-axis to go to at least 100.

C. What do you notice about the intersection of the two lines?

D. Solve the system of equations in part A to determine the degrees of each angle by using Gaussian elimination. SHOW ALL WORK.

3. There are more than 50 ways to prove the Pythagorean theorem. Using the Library, web resources, and other course materials, choose a proof of the theorem that you understand and describe it to the class. Then create a real-world application problem that can be solved by using the Pythagorean theorem. Make sure to include the question, calculations, and the solution.