Aregular prism has two congruent rectangles as its bases. how can one base be transformed to carry onto the other?
one base must be translated to carry onto the other base
one base must be rotated to carry onto the other base
it is impossible to carry one base onto the other base
one base must be reflected to carry onto the other base

One base must be translated to carry onto the other base

Step-by-step explanation:

A regular prism has two congruent rectangles as its bases. Since the bases of the prism are congruent and oriented the same way, neither reflection nor rotation will work to carry one base onto the other. It doesn't matter how many sides a geometric shape has.

Therefore the correct option is:

One base must be translated to carry onto the other base.

-60.75

step-by-step explanation:

just add the numbers then put the negative sign on it

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