Question

I need help with #22

Answer 1

Answer:

$4 = y \\ 4 = x$

Step-by-step explanation:

The isosceles triangle containing the side of y + 12 is congruent to 3x² - 32 [base angles are congruent], and if you look closer, they are also equivalent to all three sides of the equilateral triangle adjacent to the isosceles triangle. So, we will be working with alot gadgets here, if you know what I mean. Anyway, this is how we start out:

$5y - 4 = y + 12$

-5y - 5y

___________________

-4 = -4y + 12

-12 - 12

____________

-16 = -4y

___ ___

-4 -4

4 = y [Plug this back into both equations to get the value of 16.]

Next, you will set 3x² - 32 equal to 16:

$16 = 3{x}^{2} - 32$

+32 + 32

_________________

48 = 3x²

__ ___

3 3

16 = x²

4 = x [In this case, we want the NON-NEGATIVE root because inputting a -4 for x will not give us identical answers.]

I am joyous to assist you anytime.