When asked to graph the line for y = 2/5x + 3, Mallory drew the line shown.

What mistake did Mallory make in graphing the line of the equation?

A. She reversed the sign of the slope.

B. She reversed the sign of the y-intercept.

C. She reversed the numerator and denominator of the slope.

D. Her line should go through the origin.

A

Step-by-step explanation:

Using desmos we can see that the slope is positive and increasing while Mallory made a negative slope.

yrguevfytbrtuyr4

step-by-step explanation:

tduressqwzyx86diyvkghvtufvgycyvgtytc4

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