Combining Like Terms To add like terms in
order to simplify an
expression

Terms whose variables
and the power to
which the variable is
raised are the same

a letter used to take
the place of an
unknown value

All positive whole
numbers, their
opposites, and zero

I'm a bit confused.. Is this supposed to be asking a question about Combining Like Terms or is it like, telling what it is or something. I'm just clueless lol, It's good if your just telling people what it is if anyone needs help with it though! Not many people do that!

answer is : muchas/tipicas

have a nice day!

~recklesschicken

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