as a computer technician, andre makes $20 per hour to diagnose a problem and $25 per hour to fix a problem…

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).

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).

Answer

Answer:

  • B. The line (x + y<10) has a negative slope and a positive (y)-intercept.
  • C. The line representing (20x + 25y\geq200) is solid and the graph is shaded above the line.

Explanation:

Step1: Analyze (20x + 25y\geq200)

Rewrite in slope - intercept form (y\geq-\frac{4}{5}x + 8). Slope (m =-\frac{4}{5}<0), (y) - intercept (b = 8>0), and since (\geq) is used, the line is solid and shaded above.

Step2: Analyze (x + y<10)

Rewrite as (y<-x + 10). Slope (m=-1<0), (y) - intercept (b = 10>0), and since (<) is used, the line is dashed and shaded below.

Step3: Check point ((4,5))

For (20x+25y), substitute (x = 4) and (y = 5): (20\times4+25\times5=80 + 125=205\geq200). For (x + y), (4 + 5=9<10). But the region for (x + y<10) is shaded below the line, so ((4,5)) is not in the overlapping region.