Question

If MNOP is an isosceles trapezoid with NO = 9x + 8, PN = 5y + 19, and MO = 12y - 37, what are the values of x and y?

a) x = 3, y = 2
b) x = 5, y = 4
c) x = 2, y = 3
d) x = 4, y = 5

Answer 1

To find the values of x and y in the isosceles trapezoid MNOP, we need to set up and solve a system of equations. After solving the system, the values of x and y are x = 2 and y = 3.

Step-by-step explanation:

To find the values of x and y in the isosceles trapezoid MNOP, we need to set up and solve a system of equations. Since NO = PN in an isosceles trapezoid, we can set up the equation 9x + 8 = 5y + 19. We also know that MO = 12y - 37. Now we can solve this system of equations to find the values of x and y.

Step 1: Set up the first equation: 9x + 8 = 5y + 19

Step 2: Set up the second equation: 12y - 37 = 5y + 19

Step 3: Solve the first equation for x: 9x = 5y + 11

Step 4: Substitute the value of x from step 3 into the second equation: 12y - 37 = 5y + 19

Step 5: Solve the second equation for y and substitute into the first equation to find the value of x.

After solving this system of equations, we find that x = 2 and y = 3. Therefore, the correct answer is c) x = 2, y = 3.