Graham drove 42 1/3 miles in 1 1/3 hours. a. how many miles did he drive in one hour? b. how many hours did he take to drive one mile?

change to  improper fractions

42 1/3

(3* 42 +1) /3 = 127/3

1 1/3 = (3*1 +1) /3 = 4/3

127/3 divided by 4/3

copy dot flip

127/3 * 3/4

127/4

31 3/4 miles per hour

He drove 31  3/4 miles in one hour

31 3/4 miles  1 mile

    =

1 hours             x hour

using cross products

31 3/4 * x =1*1

x = 1/  127/4 (copy dot flip)

x = 1 * 4/127

x = 4/127

it takes 4/127 of 1 hour (approx .03 hours)

the answer for this question is : 360°

step-by-step explanation:

we have been given a triangle   we need to tell which one of these is a triangle below to map onto itself.

360° rotation is the complete rotation which eventually leads to the same figure which is given.

the correct will be, that is 360° that will cause the triangle below to map onto itself.

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