Precalculus by Richard Wright

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But store up for yourselves treasures in heaven, where moths and vermin do not destroy, and where thieves do not break in and steal. For where your treasure is, there your heart will be also. Matthew‬ ‭6‬:‭20‬-‭21‬ ‭NIV‬‬‬

8-Review

Take this test as you would take a test in class. When you are finished, check your work against the answers. On this assignment round your answers to three decimal places unless otherwise directed.

  1. Solve by substitution: \(\left\{\begin{align} x^2 - y &= 0 \\ 4x + y &= -4 \end{align}\right.\)
  2. Solve by substitution: \(\left\{\begin{align} \frac{1}{2}x + y &= 4 \\ 2x + \frac{1}{2}y &= 9 \end{align}\right.\)
  3. Solve by graphing: \(\left\{\begin{align} y &= -x^2 + 4x \\ y &= -x + 4 \end{align}\right.\)
  4. Solve by graphing: \(\left\{\begin{align} x^2 + y^2 &= 45 \\ x + 2y &= 0 \end{align}\right.\)
  5. Solve by elimination: \(\left\{\begin{align} 3x + 2y &= 19 \\ 5x - 3y &= 0 \end{align}\right.\)
  6. Solve by elimination: \(\left\{\begin{align} 6x + 18y &= 5 \\ 4x - 2y &= 1 \end{align}\right.\)
  7. Solve by elimination: \(\left\{\begin{align} 2x - 2y + z &= -6 \\ 3x + y - z &= -11 \\ y + 2z &= 10 \end{align}\right.\)
  8. Solve by elimination: \(\left\{\begin{align} x - 3y + z &= 7 \\ -x + 4y + z &= -6 \\ 2x - 8y - 2z &= 18 \end{align}\right.\)
  9. Solve by elimination: \(\left\{\begin{align} x + 3y - 4z &= 2 \\ 2x - y + z &= 1 \end{align}\right.\)
  10. Write as partial fractions: \(\frac{x - 8}{x^2 - x - 2}\)
  11. Write as partial fractions: \(\frac{3x + 20}{x^2 + 12x + 36}\)
  12. Write as partial fractions: \(\frac{5x^2 + x + 12}{x^3 + 4x}\)
  13. Sketch the graph of the inequalities: \(\left\{\begin{align} y &< x + 3 \\ y &< -2x + 6 \\ y &> -4 \end{align}\right.\)
  14. Sketch the graph of the inequalities: \(\left\{\begin{align} y &≥ x^2 - 5 \\ y &≤ -\frac{1}{2}x + 3 \end{align}\right.\)
  15. Find the maximum and minimum values of the objective function \(z = x + 3y\) and where they occur, subject to the following constraints.
    \(\left\{\begin{align} x + y &≤ 10 \\ x - y &≥ -4 \\ x &≥ 0 \\ y &≥ 0 \end{align}\right.\)
  16. Bob and Joanna go to a food truck whose prices are not clearly displayed. Bob buys 2 tacos and 3 burritos and pays $5.55. Joanna buys 3 tacos and 1 burrito and pays $4.86. How much does the food truck charge for each taco and burrito?

Answers

  1. (−2, 4)
  2. (4, 2)
  3. (1, 3), (4, 0)
  4. (−6, 3), (6, −3)
  5. (3, 5)
  6. \(\left(\frac{1}{3}, \frac{1}{6}\right)\)
  7. (−3, 2, 4)
  8. No solution
  9. \(\left(\frac{1}{7}a + \frac{5}{7}, \frac{9}{7}a + \frac{3}{7}, a\right)\)
  10. \(\frac{3}{x + 1} + \frac{-2}{x - 2}\)
  11. \(\frac{3}{x + 6} + \frac{2}{\left(x + 6\right)^2}\)
  12. \(\frac{2x + 1}{x^2 + 4} + \frac{3}{x}\)
  15. Min: 0 at (0, 0); Max: 24 at (3, 7)
  16. Taco: $1.29, Burrito: $0.99