On a graph there is a line that has an equation of y = -1/3x - 3. Another line runs perpendicular through that line and passes through the point (-12, 15). What is the
equation of the line in slope intercept form?

Step-by-step explanation:

step 1. slope intercept form: y = mx + b

step 2. a line perpendicular to y = (-1/3)x - 3 has slope m = 3

step 3. using point slope and (-12, 15) then y - 15 = 3(x - (-12))

step 4. y - 15 = 3x + 36

step 5. y = 3x + 51 (slope intercept form).

1/3

step-by-step explanation:

to find this, you can divide 12 by 4 which is 3 or you can multiply 4 until you reach 12 (4x3=12). both should give you 3, meaning theres three times less bananas than there are oranges.

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