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# 5.8: Quiz II

Difficulty Level: At Grade Created by: CK-12

Multiple Choice – Please circle the letter of the correct answer and write that letter in the space provided to the left of each question.

1. ________ Let There Be Light is a local business that installs outdoor lights for the Christmas season. They offer customers three options for payment. One option charges $200. A second option charges$100 and $.25 per light. The third option charges$150 and .10 per light. Which of the following system of equations best represents this problem if x\begin{align*}x\end{align*} is the number of lights and y\begin{align*}y\end{align*} is the total cost? (a) y=200xy=25x+100y=10x+150\begin{align*}\begin{Bmatrix} y=200x \\ y=25x+100\\ y=10x+150 \end{Bmatrix}\end{align*} (b) y=x+200y=.25x+100y=.10x\begin{align*}\begin{Bmatrix} y=x+200 \\ y=.25x+100\\ y=.10x \end{Bmatrix}\end{align*} (c) y=200y=.25xy=.10x+150\begin{align*}\begin{Bmatrix} y=200 \\ y=.25x\\ y=.10x+150 \end{Bmatrix}\end{align*} (d) y=200y=.25x+100y=.10x+150\begin{align*}\begin{Bmatrix} y=200 \\ y=.25x+100\\ y=.10x+150 \end{Bmatrix}\end{align*} 1. ________ Which statement is true for the following system of equations? {y=23x5y=14x+6}\begin{align*}\begin{Bmatrix} y=\frac{2}{3}x-5 \\ y=-\frac{1}{4}x+6 \end{Bmatrix}\end{align*} (a) L1L2@(12,9)\begin{align*}L_1 \cap L_2 @ (-12,9)\end{align*} (b) L1L2@(12,32)\begin{align*}L_1 \cap L_2 @ \left(12, -\frac{3}{2}\right)\end{align*} (c) L1L2@(12,3)\begin{align*}L_1 \cap L_2 @ (12,3)\end{align*} (d) L1L2@(12,13)\begin{align*}L_1 \cap L_2 @ (-12,-13)\end{align*} 1. ________ My piggy bank contains 595 coins made up of nickels and quarters. I have a total of109.75. What system of linear equations represents this problem?

(a) {n+q=595.05n+.25q=109.75}\begin{align*}\begin{Bmatrix} n+q=595 \\ .05n+.25q=109.75 \end{Bmatrix}\end{align*}

(b) {n+q=595.5n+.25q=109.75}\begin{align*}\begin{Bmatrix} n+q=595 \\ .5n+.25q=109.75 \end{Bmatrix}\end{align*}

(c) {n+q=5955n+25q=109.75}\begin{align*}\begin{Bmatrix} n+q=595 \\ 5n+25q=109.75 \end{Bmatrix}\end{align*}

(d) {n+q=109.75n+q=595}\begin{align*}\begin{Bmatrix} n+q=109.75 \\ n+q=595 \end{Bmatrix}\end{align*}

1. ________ Which of the following systems of linear equations best represents the solution?

(a) x=6y=xy=6x+4\begin{align*}\begin{Bmatrix} x=6 \\ y=x\\ y=6x+4 \end{Bmatrix}\end{align*}

(b) y=6y=xx4y+16=0\begin{align*}\begin{Bmatrix} y=6 \\ y=x\\ x-4y+16=0 \end{Bmatrix}\end{align*}

(c) x=6y=x4xy+4=0\begin{align*}\begin{Bmatrix} x=6 \\ y=x\\ 4x-y+4=0 \end{Bmatrix}\end{align*}

(d) y=6xy=0x+4y4=0\begin{align*}\begin{Bmatrix} y=6 \\ x-y=0\\ x+4y-4=0 \end{Bmatrix}\end{align*}

1. ________ “Bay Bye Babysitting” is planning to advertise its services by giving its customers three options. If two of the options must cost \$70.00 for 6 hours of service, then which of the following could be one of those options where ‘x\begin{align*}x\end{align*}’ is the time in hours and ‘y\begin{align*}y\end{align*}’ is the cost in dollars?
1. y=8x\begin{align*}y=8x\end{align*}
2. y=18x\begin{align*}y=\frac{1}{8}x\end{align*}
3. y=5x+40\begin{align*}y=5x+40\end{align*}
4. y=3x+20\begin{align*}y=3x+20\end{align*}
1. ________ Which of the following inequalities is represented below?
1. 5x+3y15\begin{align*}5x+3y \le 15\end{align*}
2. 5x+3y<15\begin{align*}5x+3y<15\end{align*}
3. 3x+5y<15\begin{align*}3x+5y<15\end{align*}
4. 5x+3y15\begin{align*}5x+3y \ge 15\end{align*}
1. ________ For which of the following systems of equations is (3, -4) the solution?

(a) {2x5y=143x+2y=6}\begin{align*}\begin{Bmatrix} 2x-5y=-14 \\ 3x+2y=-6 \end{Bmatrix}\end{align*}

(b) {y=2x103xy=5}\begin{align*}\begin{Bmatrix} y=2x-10 \\ 3x-y=5 \end{Bmatrix}\end{align*}

(c) \begin{align*}\begin{Bmatrix} 2x+3y=12 \\ 3x-2y=1 \end{Bmatrix}\end{align*}

(d) \begin{align*}\begin{Bmatrix} 3x-2y=17 \\ 2x+3y=-6 \end{Bmatrix}\end{align*}

1. ________ Which system of linear inequalities describes the graph below?

(a) \begin{align*}\begin{Bmatrix} y \ge - \frac{2}{3}x+2 \\ x \ge 1 \end{Bmatrix}\end{align*}

(b) \begin{align*}\begin{Bmatrix} y \le -\frac{2}{3}x+2 \\ x \le 1 \end{Bmatrix}\end{align*}

(c) \begin{align*}\begin{Bmatrix} y \ge - \frac{2}{3}x+2 \\ x \le 1 \end{Bmatrix}\end{align*}

(d) \begin{align*}\begin{Bmatrix} y \le - \frac{2}{3}x+2 \\ x \ge 1 \end{Bmatrix}\end{align*}

1. ________ A toy company makes two types of play hammers as an accessory for the Tots Tool Bench. They make regular hammers and sledge hammers. The company has 480 units of wood and 300 units of iron in stock. The regular hammers \begin{align*}(x)\end{align*} require 4 units of wood and 2 units of iron. Sledge hammers \begin{align*}(y)\end{align*} require 3 units of wood and 3 units of iron. Which list of constraints represents this problem?

(a) \begin{align*}\begin{Bmatrix} 4x+3y \ge 480 \\ 2x+3y \ge 300\\ x \ge 0\\ y \ge 0 \end{Bmatrix}\end{align*}

(b) \begin{align*}\begin{Bmatrix} 4x+3y \le 480 \\ 2x+3y \le 300\\ x \le 0\\ y \le 0 \end{Bmatrix}\end{align*}

(c) \begin{align*}\begin{Bmatrix} 4x+3y \le 480 \\ 2x+3y \le 300\\ x \ge 0\\ y \ge 0 \end{Bmatrix}\end{align*}

(d) \begin{align*}\begin{Bmatrix} 4x+3y<480\\ 2x+3y<300\\ x<0\\ y<0 \end{Bmatrix}\end{align*}

1. ________ For the following region and the equation \begin{align*}z=5x-3y+4\end{align*}, at which point does ‘\begin{align*}z\end{align*}’ have a maximum value?
1. (1,-3)
2. (-2,4)
3. (3,3)
4. (-5,-1)

1. D
2. C
3. A
4. B
5. C
6. A
7. D
8. B
9. C
10. A

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