Question

Please answer this question (10) GIVING BRAINLIEST!!

Answer 1

Answer:

I used the method of replacement on the sistem of equations.

The final answer I got was y=5

Answer 2

Answer:  y = 5

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Explanation:

For any rectangle, the diagonals are always the same length. We can use congruent triangles to prove this.

This means AC = BD.

Also, the diagonals of a rectangle cut each other in half (bisect). This indicates the following two equations

• AP = PC
• BP = DP

We'll use that second equation along with BP = -2x+23 and DP = 3y-6 to form the equation -2x+23 = 3y-6. This will be used later.

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By the segment addition postulate, we know that

BP+DP = BD

(-2x+23)+(3y-6) = BD

BD = -2x+3y+17

Since the diagonals are equal, we also know that AC = -2x+3y+17

We are given that AC = 2x+4

Equating the two right hand sides leads to the equation 2x+4 = -2x+3y+17

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The conclusion of each the last two sections was the following two equations

• -2x+23 = 3y-6
• 2x+4 = -2x+3y+17

We have two equations and two unknowns. We have enough info to be able to find x and y.

Let's isolate 3y in the first equation

-2x+23 = 3y-6

3y-6 = -2x+23

3y = -2x+23+6

3y = -2x+29

Then we can plug this into the second equation

2x+4 = -2x+3y+17

2x+4 = -2x+(3y)+17

2x+4 = -2x+(-2x+29)+17 .... replace 3y with -2x+29

Now solve for x

2x+4 = -2x+(-2x+29)+17

2x+4 = -2x-2x+29+17

2x+4 = -4x+46

2x+4x = 46-4

6x = 42

x = 42/6

x = 7

We then use this to find y

3y = -2x+29

3y = -2(7)+29

3y = -14+29

3y = 15

y = 15/3

y = 5