Final answer:
To find the area of the region bounded by two equations, we find the points of intersection and integrate between the x-values to calculate the area. The answer is option D) 23.8 square units.
Step-by-step explanation:
To find the area of the region bounded by the equations y = -4x² + 9 and y = -1.25x + 7, we need to find the points of intersection between the two curves.
Setting the equations equal to each other, we get -4x² + 9 = -1.25x + 7. Rearranging, we have -4x² + 1.25x + 2 = 0.
Using the quadratic formula, we can find the x-values of the points of intersection. Then, we can integrate the expression -4x² + 9 - (-1.25x + 7) with respect to x between the x-values to calculate the area.
The answer is option D) 23.8 square units.