The graph of the function C(x) = −0.52x2 + 23x + 92 is shown. The function models the production cost, C, in thousands of dollars for a candle company to manufacture a candle, where x is the number of candles produced, in thousands:

graph of a parabola opening down passing through points negative 3 and 69 hundredths comma zero, zero comma 92, 6 and 84 hundredths comma 225, 22 and 11 hundredths comma 346 and 33 hundredths, 37 and 39 hundredths comma 225, and 47 and 92 hundredths comma zero

If the company wants to keep its production costs under $225,000, then which constraint is reasonable for the model?

0 ≤ x < 6.84 and 37.39 < x ≤ 47.92
−3.69 ≤ x ≤ 6.84 and 37.39 < x ≤ 47.92
−3.69 ≤ x ≤ 47.92
6.84 ≤ x ≤ 37.39

h is the x-coordinate of the vertex

step-by-step explanation:

we have

in this function

the point represent the vertex of the function

so

h is the x-coordinate of the vertex

k is the y-coordinate of the vertex

the furthest the dog can be is 508 meters away from the house, and the closest he can be is 492 meters away from the house.

in 2010, the population of the state of california is 37.29 × 10⁶

step-by-step explanation:

population of los angeles = 3.79 × 10⁶

population of california = 9.84 × population of los angeles

                                        = 9.84 × 3.79 × 10⁶

                                        = 37.2936 × 10⁶

                                        = 37.29 × 10⁶

∴ in 2010, the population of the state of california is 37.29 × 10⁶