NAME:Math 103 Exam 1 retake12 December 2008100 pointsInstructions:1. This exam has 6 pages (including this one), which contain 8 problems. Please check that youhave all of the pages.2. Answer all of the following questions clearly and completely. Justify all of your answers.3. You may not use a book or any notes for this exam.4. Give your answer to each problem completely and clearly in the space provided. You may usethe back of the exam pages for scratch work; however, if you want this work to be considered,make note of it in the space provided for the problem.5. Erase or cross out work you do not wish to be graded.6. Credit, partial or full, will be given only if sufficient steps leading to the answers are shown.7. You have 50 minutes to complete this exam.Page 1Problem 1. (8 points) Find the midpoint of the line segment joining the points (2, −5) and (12, 3).Problem 2. (14 points) Solve the following inequalities.(a) (7 points) 4 − 3(1 − x) ≤ 3(b) (7 points) |3t − 2| ≤ 4Page 2Problem 3. (21 points) Solve the following equations.(a) (7 points)x + 13+x + 27= 2(b) (7 points) x2− 4x − 1 = 0(c) (7 points) x4− 10x2+ 25 = 0Page 3Problem 4. (9 points) Find the center (h, k) and the radius r of the circle given by the equationx2+ y2− 10x + 2y − 10 = 0.Problem 5. (10 points) Solve the following system of linear equations. The equations are numbered(1 ) and (2 ) for your convenience.(2x + 4y = −6 (1 )x − 3y = 12 (2 )Page 4Problem 6. (15 points)(a) (7 points) Find all intercepts of the graph of the equation 2y = 8 − 4x.(b) (8 points) Use your answer from part (a) to graph the equation 2y = 8−4x. Be sure to describehow you know what the shape of the graph is.−11−11−22−22−33−33−44−44−55−55xyPage 5Problem 7. (8 points) What is a circle? Be as clear and precise as possible.Problem 8. (15 points) An altitude of a triangle ABC is a line segment which has one endpointat a vertex A of the triangle and the other endpoint on the side BC of the triangle opposite thevertex A, and which is perpendicular to the side BC.Consider the triangle whose vertices are the points (−2, 5), (−1, 0), and (5, 1). Find an equationfor the line containing the altitude from the vertex (−1, 0) to the opposite side.Page