As a computer technician, Andre makes $20 per hour to diagnose a problem and $25 per hour to fix a problem. He works fewer than

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1 month ago

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As a computer technician, Andre makes $20 per hour to diagnose a problem and $25 per hour to fix a problem. He works fewer than

10 hours per week, but wants to make at least $200 per week. The inequalities 20x + 25y ≥ 200 and x + y < 10 represent the situation. Which is true of the graph of the solution set? Check all that apply. The line 20x + 25y ≥ 200 has a positive slope and a negative y-intercept. The line x + y < 10 has a negative slope and a positive y-intercept. The line representing 20x + 25y ≥ 200 is solid and the graph is shaded above the line. The line representing x + y < 10 is dashed and the graph is shaded above the line. The overlapping region contains the point (4, 5).

Mathematics

2 answers:

Leona [12.6K] · Answer 1 · 2026-02-24T06:02:48+03:00

Leona [12.6K]1 month ago

8 0

According to e d g e n u i t y, the correct answers are b, c, and e.

AnnZ [12.3K] · Answer 2 · 2026-02-24T06:04:40+03:00

For
ax + by = c
the slope is determined as -a/b
For the inequality 20x + 25y ≥ 200
slope=-20/25=-4/5
This represents a negative slope.

The y-intercept occurs when x=0.
20(0) + 25y ≥ 200
25y ≥ 200
y ≥ 8
This results in a positive y-intercept.

For x + y < 10
slope=-1/1=-1
The y-intercept can be calculated as y < 10 when x=0, resulting in y intercept at y=10.

Since this line has an equality sign, it will be a solid line.
Testing the point (0,0) indicates if the solution is above or below:
0 ≥ 200
This is false, hence, shading occurs on the opposite side of (0,0), which is above the line.

For x + y < 10, without an equality, it will be dashed.
Testing (0,0):
0 < 10
This is true, therefore shading occurs below.

Testing point (4,5)

For 20(4)+25(5) ≥ 200
80 + 125 ≥ 200
225 ≥ 200
This is true.

For 4+5 < 10
9 < 10
This is also true.

Thus, the valid statements are:
The line x + y < 10 exhibits a negative slope and a positive y-intercept.
The line defined by 20x + 25y ≥ 200 is solid, and the graph's shading is above the line.
The intersection region includes the point (4, 5).