Question

1. a system of three linear inequalities is graphed below: which points are possible solutions in the solution set? a. (5,0) b. (3,2) c. (0,0) d. (3, - 2) e. (4,2) f. (1,2) 9. ellie earns $12.50 per hour as a server working x hours per week. she also earns $9.50 per hour editing poetry for y hours per week. ellie needs to make at least $145 to pay her cell phone bill, but she has at most 23 total hours per week with her busy college schedule. the system of linear inequalities modeling this situation is shown. 12.50x + 9.50y ≥ 145 x + y ≤ 23 which statement(s) represents a solution to the system of linear inequalities? a. ellie can work as a server for 4 hours and edit poetry for 10 hours. b. ellie can work as a server for 13 hours and edit poetry for 10 hours. c. ellie can work as a server for 4 hours and edit poetry for 19 hours. d. ellie can work as a server for 10 hours and edit poetry for 19 hours. 10. which statement describes the effects on the graph of f(x), when f(x) is replaced by f(-\frac{1}{4}x - 1)+3?

Explanation:

8.

Step1: Check point (5,0)

Substitute into the inequalities by observing the graph. Visually, it's outside the shaded region.

Step2: Check point (3,2)

Locate on the graph. It lies within the shaded solution - set region.

Step3: Check point (0,0)

Observe its position on the graph. It's outside the shaded region.

Step4: Check point (3, - 2)

See its location on the graph. It's outside the shaded region.

Step5: Check point (4,2)

Locate on the graph. It lies within the shaded solution - set region.

Step6: Check point (1,2)

Observe on the graph. It lies within the shaded solution - set region.

Step1: For option A

Substitute \(x = 4\) and \(y=10\) into \(12.50x + 9.50y\): \(12.5\times4+9.5\times10=50 + 95=145\), and \(x + y=4 + 10=14\leq23\). So it's a solution.

Step2: For option B

Substitute \(x = 13\) and \(y = 10\) into \(12.50x+9.50y\): \(12.5\times13+9.5\times10=162.5+95 = 257.5\geq145\), and \(x + y=13 + 10=23\leq23\). So it's a solution.

Step3: For option C

Substitute \(x = 4\) and \(y = 19\) into \(x + y\): \(x + y=4+19 = 23\leq23\), but \(12.5\times4+9.5\times19=50+180.5 = 230.5\geq145\). So it's a solution.

Step4: For option D

Substitute \(x = 10\) and \(y = 19\) into \(x + y\): \(x + y=10 + 19=29>23\). So it's not a solution.

Step1: Analyze \(f(-\frac{1}{4}x - 1)+3\)

The \(-\frac{1}{4}x-1\) inside the function: The factor \(-\frac{1}{4}\) causes a horizontal stretch by a factor of 4 and a reflection across the y - axis. The \(-1\) inside the function causes a horizontal shift 1 unit to the left. The \(+3\) outside the function causes a vertical shift 3 units up.

Answer:

B. (3,2), E. (4,2), F. (1,2)

9.