1. | The cost of producing an item is $5 per item plus an initial cost of $2000. The selling price is $10 per item. Find the break-even point. | |||||

4000 items | 4500 items | |||||

400 items | 450 items | |||||

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2. | Solve the system of equations y = 0.5x and 4y = x - 2 by graphing. |
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3. | Solve the system of equations by substitution.x = zx - 2y + z = 62 x + y - 2z = 1What is the value of x + y + z? |
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8 | 10 | |||||

9 | 11 | |||||

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4. | Find the value of . | |||||

-17 | 17 | |||||

-3 | 3 | |||||

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5. | Solve the system of inequalities by graphing. | |||||

Hint | ||||||

6. | Find the maximum value of f(x, y) = 2x + y - 2 for the polygonal convex set determined by the system of inequalities. |
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6 | 18 | |||||

12 | 14 | |||||

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7. | Solve the system of three equations by elimination: 5 |
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(2, -5, 3) | infinite solutions | |||||

(3, 4, 2) | no solution | |||||

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8. | ||||||

impossible | ||||||

Hint | ||||||

9. | ||||||

impossible | ||||||

Hint | ||||||

10. | A quadrilateral with vertices A(-2,-3), B(-4,2), C(-2,4) and D(0,2) is translated 5 units to the right and 3 units down. What are the new coordinates? |
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A(-5,2), B(-7, 7), C(-5, 9), D(-3, 7) |
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A(3,0), B(-1,5), C(3,7), D(5,5) |
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A(3,-6), B(1,-1), C(3,1), D(5,-1) |
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A(3,-6), B(1,-1), C(3,7), D(5,5) |
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Hint | ||||||

11. | Use matrices to determine the coordinates of the image of with vertices A(-3,4), B(-5,2) and C(-6,5) once it is rotated 90°. |
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A'(-3,-4), B(-5,-2) and C'(-6,-5) |
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A'(-4,-3), B(-2,-5) and C'(-5,-6) |
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A'(3,4), B(5,2) and C'(6,5) |
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A'(3,-4), B(5,-2) and C'(6,-5) |
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12. | Find the inverse of . | |||||

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13. | Find the maximum value of f(x, y) = 2x + y - 4 for the system of inequalities:y -3x + 1y x - 4x 0y 0 |
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infeasible | 2 | |||||

alternate optimal solutions | unbounded | |||||

Hint | ||||||

14. | Sam has $10,000 to deposit in two different savings accounts. He wants at least $3,000 in the account that earns 3% interest. He wants no less than $5,000 in the account with 7% interest. Write a system of inequalities to represent this situation. | |||||

x 3000y 5000x + y 10,000 |
x 3000y 5000x + y 10,000 |
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x 5000y 3000x + y 10,000 |
x 3000y 5000x + y 10,000 |
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Hint | ||||||