Question

Find x and XY if Y is between X and Z, XY = x2 - x inches, XZ = 12 inches, and YZ = 8x - 6 inches.

X =
XY ="

Answer 1

The value of X is 10 inches.

The value of XY is 80 inches.

Step-by-step explanation:

We can use the given information to set up two equations:

XY = x^2 - x

XZ = XY + YZ

Substituting the second equation into the first equation, we get:

x^2 - x = 12 + 8x - 6

Simplifying this equation, we get:

x^2 - 9x - 6 = 0

Factoring this equation, we get:

(x - 10)(x + 0.6) = 0

Therefore, x = 10 or x = -0.6. Since x cannot be negative, we know that x = 10.

Substituting x = 10 into the first equation, we get:

XY = 10^2 - 10

Simplifying this equation, we get:

XY = 90 - 10

Therefore, XY = 80 inches.