Consider the graph of the linear function h(x) = -6 + 2/3 x. which quadrant will the graph not go through and why.

The answer is b guys

Step-by-step explanation:

There are four quadrants.

I.  x>0, y>0

II. x<0, y>0

III. x<0, y<0

IV. x>0, y<0

note that for any x<0, h(x) < 0 (that corresponds to III)

Why?

So, the graph not go through II.

Note that, if x = 3, h(3) = -4 < 0, (that corresponds to IV), and if x = 12, h(12) = 2> 0, that corresponds to I.

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