[PLEASE HELP] The area of Bethany's garden will be 48 square feet once she expands it. She is not going to change the measurement on one side, but the other side will be 8 feet longer than before. The equation that models this situation and can be used to determine the possible dimensions of Bethany's garden is x^2 +8x -48. Factor to determine the possible dimensions of Bethany's new garden.

4 ft by 12 ft

Step-by-step explanation:

x^2 +8x -48

Set this equal to 0 to solve for the values of x

x^2 +8x -48=0

What two values multiply to -48 and add to 8

12*-4 = -48

12+-4 = 8

(x+12) (x-4) = 0

Using the zero product property

x+12 = 0   x-4=0

x=-12           x=4

We cant have a negative length

x=4

The area is 48

48/4 = 12

The other dimension is 12

12 feet × 4 feet

Step-by-step explanation:

x² + 8x - 48 = 0

x² + 12x - 4x - 48 = 0

x(x + 12) - 4(x + 12) = 0

(x - 4)(x + 12) = 0

x = 4, -12

x = 4

New dimensions:

4 + 8 = 12

48/12 = 4

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

yes.. it's proven to be 36.