The graph shows the solution to a system of inequalities: Solid line joining ordered pairs 0, 3.75 and 15, 0. Shade the portion of the graph below the line in the first and second quadrant.

Which of the following inequalities is modeled by the graph?

x + 4y ≥ 15; y ≥ 0
x − 4y ≥ 15; y ≥ 0
x + 4y ≤ 15; y ≥ 0
−x − 4y ≥ 15; y ≥ 0

24

step-by-step explanation:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.