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Applying the segment addition postulate, the value of y is: 4.
According to the segment addition postulate, since points R, S, and T are collinear points, therefore, the following equation is true:
RS + ST = RT
Given the following lengths:
RS = 4y + 5
ST = 3y + 6
RT = 39
Plug in the values into RS + ST = RT
(4y + 5) + (3y + 6) = 39
4y + 3y + 5 + 6 = 39
7y + 11 = 39
7y + 11 - 11 = 39 - 11
7y = 28
7y/7 = 28/7
y = 4
Thus, applying the segment addition postulate, the value of y is: 4.
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