Please help me with the questions please ASAP ASAP please ASAP help

A. x = 2, y = 12

Step-by-step explanation:

You can solve this problem using similar triangles; you know the triangles are similar because each of the two legs of the triangles are cut in half, meaning the line 5x - 3 is parallel to x + 12. Because of the nature of this figure (the line that is length 5x - 3 cuts the triangle exactly halfway), you can write an equation to find x:

2(5x - 3) = x + 12 (this is a property of triangles when a line is parallel to a base and intersects the triangle at half of that base's height. The line would be half the base)

10x - 6 = x + 12 (simplify)

9x - 6 = 12 (subtract x from both sides)

9x = 18 (add 6 to both sides)

x = 2 (divide both sides by 9)

At this point, you could just click A since that's the only problem where x = 2, but for the sake of properly explaining this problem, I'll continue to find y.

In the image, y + 8 is equal to 2y - 4, shown by the short lines intersecting each side signifying congruence. Now, you can write an equation for this and solve:

y + 8 = 2y - 4

8 = y - 4 (subtract y from both sides)

y - 4 = 8 (switch it around so y is on the left; you don't have to do this, but I think it makes the problem more comfortable to solve)

y = 12 (add 4 to both sides)

a. she will receive a refund of $278.

step-by-step explanation: