Answer !
point c' is the image of c(-4, -2) under a reflection across the y-axis. what are the coordinates of c'?
(khan academy)

(4,-2)

Step-by-step explanation:

If we are reflecting a point across the y-axis, that point must be on the same horizontal line that the pre-mage is was, this means the y coordinate must remain the same.  Now we want the points on both sides of the y-axis to have the same distance.  x and -x have the same distance from 0. This means you will need to take the opposite of x.

So a point (x,y) being reflected over the y-axis will give (-x,y).

( x  , y)->(-x,y) means we have:

(-4,-2 )->(4,-2)

You can graph this to confirm it looks like a reflection through the y-axis.

3

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