Answer this
the graph of the function p(x) = −0.74x2 + 22x + 75 is shown. the function models the profits, p, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands:
graph of a parabola opening down passing through points negative 3 and 9 hundredths comma zero, zero comma 75, 5 and 6 tenths comma 175, 14 and 87 hundredths comma 238 and 51 hundredths, 24 and 13 hundredths comma 175, and 32 and 82 hundredths comma zero
if the company wants to keep its profits at or above $175,000, then which constraint is reasonable for the model?
a) −3.09 ≤ x ≤ 5.6 and 24.13 < x ≤ 32.82
b) 0 ≤ x < 5.6 and 24.13 < x ≤ 32.82
c) −3.09 ≤ x ≤ 32.82
d) 5.6 ≤ x ≤ 24.13

D

Step-by-step explanation:

Actually we don't need all the points. The parabola opens down. That means it has a maximum point which is its vertex. Any parabola always symmetric about its axis of symmetry. if you see the two points: (5.6,175) and (24.13,175), these are symmetric about the axis of symmetry which is lying between them, you can conclude that between x=5.6 and x=24.13 the P value (y axis) will be higher than 175. That is what the question asking about.

d 5.6 ≤ x ≤ 24.13

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus