Answer:
[tex] MP = 29 [/tex]
Step-by-step explanation:
Given:
[tex] MN = 17 [/tex]
[tex] NP = 3y [/tex]
[tex] MP = 5y + 9 [/tex]
[tex] MN + NP = MP [/tex] (segment addition postulate)
[tex] 17 + 3y = 5y + 9 [/tex] (substitution)
[tex] 3y = 5y + 9 - 17 [/tex] (subtracting 17 from each side)
[tex] 3y = 5y + 8 [/tex]
[tex] 3y - 5y = 5y - 8 - 5y [/tex] (Subtracting 5y from both sides)
[tex] -2y = 5y - 8 - 5y [/tex]
[tex] -2y = - 8 [/tex]
[tex] y = 4 [/tex] (dividing both sides by -2)
[tex] MP = 5y + 9 [/tex]
Plug in the value of y
[tex] MP = 5(4) + 9 = 20 + 9 [/tex]
[tex] MP = 29 [/tex]
