Elam is packing his room to move into a new house. A small box can hold 8 books without breaking, while a large box can hold 12 books without breaking. He has at most 160 books to pack and less than 30 boxes total. Let s represent the number of small boxes and l represent the number of large boxes. The inequalities s ≥ 0 and l ≥ 0 are part of the system that models this scenario.
Which inequalities complete the system?
s – l < 30
8s – 12l ≤ 160
s + l < 30
8s + 12l ≤ 160
s + l > 30
8s + 12l ≤ 160
s + l < 30
8s + 12l ≥ 160

it would open into a square depending on the type of envelope i’m not sure about the second part

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

15.36 per mile

but forgot to round

i am pretty sure