Which point on the x-axis lies on the line that passes through point c and is parallel to line ab?

a. (1, 0)
b. (1, 1)
c. (0, 2)
d. (2, 0)

Option D.

Step-by-step explanation:

Consider the below figure attached with this question.

From the below figure it is clear that the coordinates of given points are A(-4,0), B(2,-3) and C(-2,2).

Slope of line AB is

The slope of two parallel lines are same.

So, the slope of required line is -1/2.

The point slope form of a line is

where, m is slope.

The equation of required line is

Substitute y=0 in the above equation to find the x-intercept of required line.

The x-intercept of required line is (2,0). Therefore, the correct option is D.

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