Answer/Step-by-step explanation:
Length of AC:
Given that AB = x + 2, and BC = 7x - 3, therefore,
[tex] (x + 2) + (7x - 3) = AC [/tex] (segment addition postulate)
Simply the expression for the length of segment AC
[tex] x + 2 + 7x - 3 = AC [/tex]
Collect like terms
[tex] x + 7x + 2 - 3 = AC [/tex]
[tex] 8x - 1 = AC [/tex]
Length of QR:
Given that PQ = 8y + 5, and PR = 13y + 25, therefore,
QR = (13y + 25) - (8y + 5) (PQ + QR = PR)
Simplify the expression to for the length of segment QR
QR = 13y + 25 - 8y - 5
Collect like terms
QR = 13y - 8y + 25 - 5
QR = 5y + 20
