2. To receive credit on any problem, you must show work that explains how you obtained your answer or you must explain how you obtained your answer.
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1 Math 50, Fall 2011 Test 3 PRINT your name on the back of the test. Directions 1. Time limit: 1 hour 50 minutes. 2. To receive credit on any problem, you must show work that explains how you obtained your answer or you must explain how you obtained your answer. 3. Write your work in pencil in the provided spaces. Your work must be neat, organized, and legible. Box your answers. 4. You may use a calculator, but you may not use any notes, books, or other resources. 5. You may not share the use of a calculator. You may not use a cell phone, ipod, or similar device. 6. You are expected to do your own work. You are neither to receive nor to give any help on the exam. Additionally, you are expected to report to your instructor anyone that you observe may be receiving or giving any help on the exam. I have read the directions. Initial: Student ID number: 1
2 1. Decide if the line that passes through the points (1, 2) and ( 2, 6) is parallel or perpendicular, or neither so, to graph of the equation y = 0.75x Find an equation of the line that passes through the points (1, 2) and ( 2, 6), and write the equation in point-slope form and in slope-intercept form. (a) point-slope form: (b) slope-intercept form: 3. Graph the line that has slope 0.6 and passes through the point ( 2, 1). (Hint: Express 0.6 as a common fraction.) y x 2
3 4. The following are the graphs of the equations y 1 = f(x) and y 2 = g(x). Find the solutions of the system of equations { y1 = f(x) or state that there are no solutions. y y 2 = g(x) x 5. Solve the following system of equations by the substitution method. { 2x = 5y + 1 3x + y = 7 3
4 6. Solve the following system of equations by the addition method. { 3x = 2y + 7 5x + 4y = 8 7. Consider the system of linear equations { y = Ax + B y = Cx + D (a) Answer true or false: The system may have exactly two solutions. (b) What are the only possible numbers of solutions for the system? or (c) The system has (give the number) or solutions if A = C and B D. (d) The system has (give the number) solutions if A = C and B = D. (e) The system has exactly one solution if (fill in with A, B, C, or D) 4
5 8. Let A = [ 2, + ) and B = (3, + ). Write the following in interval notation. (a) A and B (b) A or B 9. Solve the compound inequalities. Write the solutions using interval notation. (a) 4x + 2 < 1 and 2x 0 (b) 2x 4 or 5x 20 > Solve the following equations with absolute values. (a) x = 7 (b) 2y 3 = 4y 9 5
6 11. Shown below is the graph of the equation y = x 1, where each grid square is 1 unit on a side. y Graph the solution of the inequality y x 1. (Shade the region where the inequality is true. Decide if the graph should be a solid curve or a dashed curve.) x 12. Shown below are the graphs of the equations y = x 1 and y = 5 x 2, where each grid square is 1 unit on a side. y Graph the solution of the system of inequalities { y < x 1, y 5 x 2. x (Shade the region where both inequalities are true. Decide which parts of the graphs should be solid or dashed.) 13. You own a gasoline station. You currently have 14,000 gallons of gasoline in an underground tank that you purchased at $2.00 per gallon. How many gallons of gasoline must you purchase now at $3.50 per gallon to mix with the 14,000 gallons you already have, so that the net cost of the mixed gasolines would be $2.50 per gallon? Solve the problem using two variables. (a) Define the variables. Let x = Let y = 6
7 (b) Write the system of equations. (c) Solve the system of equations. (d) Answer the question. 7
8 14. On a 255-mile trip, G traveled at an average speed of 70 mph, got a speeding ticket, and then traveled at 60 mph for the remainder of the trip. If the entire trip took 4.5 hours and the speeding ticket stop took 30 minutes, how long did G speed before getting stopped? Solve the problem using two variables. Be sure to define the variables; write the equations; solve the system of equations; and answer the question. 8
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