The answers are written but I am not sure how they got them. Can someone please explain it to me? Thank you! (Worth 50 points :))

x = 2.4

I'm not sure how the answer is 4.5 but I'm pretty sure this is right unless I'm missing something

Step-by-step explanation:

So we need to find how much shorter is the short line compared to the longer one. Basically we need a scale factor, for this we can use the side lengths already given to us, 10 and 15. So u can choose either enlarge the short line or shorten the longer one.

If u want to enlarge the short line then do 15/10 which is 3/2 which u will then multiply the shorter line's equation with it, if u want to shorten the longer line then do 10/15 which is 2/3 and multiply the longer lines equation with it.

I'll be using the 3/2 one cause why not:

3/2(x + 6) = 4x + 3

3/2x + 18/2 = 4x + 3

multiply the entire equation with 2 to make 3/2 no longer a fraction

(3/2x + 18/2 = 4x + 3)2

6/2x + 18 = 8x + 6

3x + 18 = 8x + 6

subtract 18 from both sides

3x = 8x - 12

subtract 8x from both sides

-5x = - 12

divide -5 from both sides

x = 2.4

U can input x into the equation to check:

3/2(2.4 + 6) = 4(2.4) + 3

12.6 = 12.6, it's right

hi there!

question 1 answer: p/q can be terminating when q = 5^m * 2^n

question 2 answer: -1 and -1

question 3 answer: -4

question 4 answer: 5/12

hope this : )