Question

question 20 of 25
which of the following systems of inequalities would produce the region
indicated on the graph below?

a. ( y leq -x + 4 ); ( y < x + 2 ); ( y geq 0 ); ( x geq 0 )
b. ( y leq -x + 4 ); ( y > x + 2 ); ( y geq 0 ); ( x geq 0 )
c. ( y geq -x + 4 ); ( y < x + 2 ); ( y geq 0 ); ( x geq 0 )
d. ( y leq -x + 4 ); ( y geq x + 2 ); ( y geq 0 ); ( x geq 0 )

Explanation:

Step1: Analyze the solid line \( y = -x + 4 \)

The line \( y=-x + 4 \) has a y - intercept of 4 and an x - intercept of 4. The shaded region is below this line, so the inequality should be \( y\leq -x + 4 \) (since the line is solid, the inequality includes equality).

Step2: Analyze the dashed line \( y=x + 2 \)

The line \( y = x+2 \) has a y - intercept of 2. The shaded region is below this dashed line, so the inequality should be \( y

Step3: Analyze \( x\geq0 \) and \( y\geq0 \)

The shaded region is in the first quadrant (to the right of \( x = 0 \) and above \( y=0 \)), so \( x\geq0 \) and \( y\geq0 \) are part of the system.

Answer:

A. \( y\leq -x + 4;y