Select the inequality that corresponds to the following graph:
a. 4x+3y≥12
b. 3x+4y< 12
c. 3x-4y< 12
d. 4x+3y≤12

d. 4x+3y≤12

Step-by-step explanation:

To solve the problem we need to find the equation of the red line, since it is part of the inequality.

This should be like the following y=mx+b, where 'm' is the slope.

The slope can be obtained using the following equation:

If we use the points given by the graph (0,4) and (3,0) we will obtain that m=-4/3

Now, to find 'b' we just need to evaluate any point ine equation y=mx+b. iike (0,4).

4=-4/3*0 + b.

b=4

Our line has the following equation: y= -(4/3)*x +4, that can be written in standard form as 3y+4x=12

The region is below the graph, hence our inequality shoul be 3y+4x<=12.

The iqual sign part comes watching the graph, the line is drawn using solid line, hence the line is included in the region.

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).