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Math 141 WIR2_Dr. Rosanna Pearlstein 1. For the following quadratic equations, do the following: a) Determine whether the graph opens up or down. b) Find the vertex of the parabola. c) Find the maximum and minimum values. d) Find the x-intercepts. I. 1.Q, 2.1, 2.2 II. 2. If the demand of an item is given by (where x is the number of items) find the revenue function. a) What number of items produced yields maximum revenue? b) If the cost is , find the equilibrium point. 3. For each linear system below, use the Gauss-Jordan elimination method to determine the solution(s) or lack thereof. A. B. C. { { { 4. (From our textbook, Finite Mathematics by Tan, 2.1 #28). Box Office Receipts. A theater has a seating capacity of 900 and charges $4 for children, $6 for students, and $8 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled $5600. How many children attended the show? 5. Which of the following matrices is in row-reduced form? A. B. [ | ] C. [ | ] [ | ] 6. Pivot each of the two matrices below about the boxed element. A. B. [ | ] [ | ] 7. Solve the linear systems below, using the Gauss-Jordan elimination method. { { 8. Solve the linear systems below. Express the solutions using parameters. I. II. { { 9. Determine the value of k for which systems A and B below have infinitely many solutions and no solution respectively. A. B. { { 10. Comment on the following statements: are they true or false? Why? (a) A linear system with the same number of equations as unknowns always has a solution. (b) A linear system with more equations than the number of unknowns never has a solution. (c) A (2×2) linear system of two lines in the plane will have a solution if the two lines are not parallel. (d) A (3×3) linear system of three planes in space will have a solution if the three planes are not parallel. (e) A linear system with more variables than equations always has a solution. (f) A linear system with more variables than equations either has no solution or it has infinitely many solutions.