This diagram shows a pre-image triangle ABC, and its image triangle A”B”C”, after a series of transformations. select from the drop-dow menus to correctly complete the statements. 1. triangle ABC is A. reflected across the y-axis B. reflected across the line y = x C. rotated 90 degrees counterclockwise about the origin
2. to become triangle A’B’C’ is A. reflected across the x-axis
B. translated 4 units down
C. rotated 180 degrees about the origin
3. to become triangle A”B”C”. because the transformations are A. both rigid B. not both rigid
4.the pre-image and image are A. congruent B. not congruent

d≈7.07in

step-by-step explanation:

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