1. Find the x and y intercept for the function 3x-4y=12

Step-by-step explanation:

To easily solve this problem we need to know two facts:

Slope-intercept form

Since 3x - 4y = 12

         3x - 12 = 4y

                  y = ³/₄ x - 3

         ∴ y-intercept is (0, -3)

Solve for x when y = 0

Since 3x - 4y = 12

         3x - 4(0) = 12

                    x = 4

∴ x-intercept is (4, 0)

We can check our answer by graphing the line and seeing if it passes through the intercepts we calculated. Since it does (see graph below), then the answers we calculated are correct.

10 b/c 5*2 =10

step-by-step explanation:

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