Math

QuestionFind WYW Y given that WW is the midpoint of segment VYV Y, with VW=9x+7V W=9 x+7 and WY=16x28W Y=16 x-28.

Studdy Solution

STEP 1

Assumptions1. Point WW is the midpoint of Segment VYV Y . The length of segment VWV W is given by 9x+79 x+7
3. The length of segment WYW Y is given by 16x2816 x-28
4. Since WW is the midpoint, the lengths of VWV W and WYW Y are equal

STEP 2

Since WW is the midpoint, we know that VW=WYV W = W Y. We can set up the equation as follows9x+7=16x289 x+7 =16 x-28

STEP 3

To solve for xx, we need to get all the xx terms on one side of the equation and the constants on the other side. We can do this by subtracting 9x9x from both sides16x9x=7+2816 x -9 x =7 +28

STEP 4

implify the equation to find the value of xx7x=357 x =35

STEP 5

To isolate xx, divide both sides of the equation by 77x=357x = \frac{35}{7}

STEP 6

Calculate the value of xxx=5x =5

STEP 7

Now that we have the value of xx, we can substitute it into the equation for WYW Y to find the length of WYW YWY=16x28W Y =16 x -28

STEP 8

Substitute x=5x =5 into the equationWY=16(5)28W Y =16(5) -28

STEP 9

Calculate the value of WYW YWY=8028=52W Y =80 -28 =52So, the length of segment WYW Y is52 units.

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