Question

RS=8y+4, ST=4y+8, and RT=15y-9.

Answer 1

Throughout this entire problem, I'm going to assume that point S is on line RT. 

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Part A)

Because S is on line RT, this means that RS + ST = RT by the segment addition postulate. Make the proper substitutions (aka replacements) and solve for y

RS + ST = RT
(8y+4) + (4y+8) = 15y-9
8y+4 + 4y+8 = 15y-9
(8y+4y)+(4+8) = 15y-9
12y+12 = 15y-9
12y+12-12y = 15y-9-12y
12 = 3y-9
12+9 = 3y-9+9
21 = 3y
3y = 21
3y/3 = 21/3
y = 7

The value of y is y = 7

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Part B)

Since y = 7 (from part A above), we can find the following

RS = 8*y+4
RS = 8*7+4
RS = 56+4
RS = 60
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ST = 4*y+8
ST = 4*7+8
ST = 28+8
ST = 36
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RT = 15*y-9
RT = 15*7-9
RT = 105-9
RT = 96
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Note how RS+ST = 60+36 = 96 and how this is equal to RT = 96 above, so that helps confirm the right answer. It helps confirm that RS+ST = RT.