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.