The figure shows the letter M and four of its transformed images—A, B, C, and D: A coordinate plane is shown. A figure M has endpoints at 3 comma 1, 3 comma 3, 5 comma 1 and 5 comma 3. Figure A is shown with endpoints at negative 2 comma 1, negative 2 comma 3, negative 4 comma 1 and negative 4 comma 3. Figure B has endpoints at negative 2 comma negative 1, negative 2 comma negative 3, negative 4 comma negative 1 and negative 4 comma negative 3. Figure C has endpoints at 0 comma negative 1, 0 comma negative 3, 2 comma negative 1 and 2 comma negative 3. Figure D has endpoints at 3 comma negative 1, 5 comma negative 1, 3 comma negative 3 and 5 comma negative 3. Which of the four images was formed by a reflection of the letter M? A B C D

answer: sine

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

b, 20 yards

step-by-step explanation:

step-by-step explanation:

f(gx)=f(1/x+2)

=(1/x+2)+2

=(1+2x)/2+2

=(1+2x+4)/2

= (2x+5)/2