Gerald is constructing a line parallel to line l through point p. he begins by drawing line m through points p and q. he then draws a circle centered at q, which intersects line l at point n and line m at point s. keeping the compass measure, he draws a congruent circle centered at point p, which intersects line m at point t.

which next step will create point r, such that when a line is drawn through points p and r, the line will be parallel to line l?

Found the missing image and choices. Here are the choices:
Use the compass to construct a circle centered at Q through point P.

Using the compass measure between points S and N, draw an arc to the right of line m, centered at T, intersecting the edge of circle P.

Using the compass measure between points S and N, draw an arc above line l, centered at N, intersecting the edge of circle Q. 

Use the compass to construct a circle centered at P through point Q.

MY ANSWER:
Using the compass measure between points S and N, draw an arc above line l, centered at N, intersecting the edge of circle Q. 

The value of the measure is needed because it will also be the value on the parallel line to be drawn on Circle P.

a. geometricb. g[h] = (3/4)·g[h-1]; g[1] = 384c. g[h] = 384·(3/4)^(h-1)d. g[12] ≈ 16.2183 gallonse. g[12] ≈ 64.8732 quarts

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

Apples are more expensive by 11/3