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I need help with this

I need help with this-example-1

1 Answer

3 votes

Answers:

a = 4

YZ = 20

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Step-by-step explanation:

Y is between X and Z (not necessarily at the midpoint). This means the three points are on the same line. Going from left to right we have X, Y and Z in that exact order.

Put another way, segment XZ is cut into smaller pieces XY and YZ.

The smaller pieces XY and YZ add back up to the largest segment XZ.

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XY + YZ = XZ

( XY ) + ( YZ ) = XZ

( 7a ) + ( 5a ) = 6a+24 ..... substitution

7a+5a = 6a+24

12a = 6a+24

12a-6a = 24 ....... subtracting 6a from both sides

6a = 24

a = 24/6 ....... dividing both sides by 6

a = 4 is the first answer we're after

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Use this value of 'a' to find the length of each segment

XY = 7a = 7*4 = 28

YZ = 5a = 5*4 = 20 is the second answer we want

XZ = 6a+24 = 6*4+24 = 48

Note how XY+YZ = 28+20 = 48 to match with XZ = 48 we got in the previous line above.

User Stefan Jung
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