The Watson Family is going on a road trip. The data in the table shows the relationship between speed and fuel economy for their car. The data can be modeled by the quadratic function y=-0.0075x^2 +0.575x + 11.5, where x represents the speed in miles per hour and y represents the fuel economy in miles per gallon (MPG). Which speed rounded to the nearest whole number will give them the best fuel economy? A. 40 mph

B. 23 mph

C. 32 mph

D. 38 mph

It keeps saying image is to big so I'll type
Table:
Speed (miles per hour)
30
40
50
Fuel economy (miles per gallon)
22.0
22.5
21.5

1 x=22.52

2: 65/39=604+39x

65x-39x=604

26x=604

x=604/26

×=23.23

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

the weight of the object inside the box!