The length of a rectangle is 36 centmeters and the width is 9
centimeters. A similar rectangle has
a width of 3 centimeters.
what is
the length of the decond triangle?

12cm

Step-by-step explanation:

They are similar, so we can set an equation of:

the ratio of length and width of the big triangle equal to the ratio of length and width of the small(second) triangle.

36:9 = x:3

36/9 = x/3

9x = 3(36)           by use the cross multiply

9x = 108

x = 12 cm

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

image for option 4

step-by-step explanation:

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