Question

=6x + 8, tu = 5x, and su = 7x + 16, what is st?
s
6x + 8
t
5x
u
7x + 16
mplify your answer and write it as a proper fraction, mixed number, or intege
submit

Explanation:

Step1: Use the segment - addition postulate

Since \(SU = ST+TU\), we substitute the given expressions: \(7x + 16=(6x + 8)+5x\).

Step2: Simplify the right - hand side of the equation

Combine like terms on the right - hand side: \((6x + 8)+5x=6x+5x + 8=11x + 8\). So the equation becomes \(7x+16 = 11x+8\).

Step3: Solve for \(x\)

Subtract \(7x\) from both sides: \(7x - 7x+16=11x - 7x+8\), which simplifies to \(16 = 4x+8\).
Subtract \(8\) from both sides: \(16 - 8=4x+8 - 8\), so \(8 = 4x\).
Divide both sides by \(4\): \(x=\frac{8}{4}=2\).

Step4: Find the length of \(ST\)

Substitute \(x = 2\) into the expression for \(ST\) (\(ST=6x + 8\)).
\(ST=6\times2+8\).
First, calculate \(6\times2 = 12\), then \(12 + 8=20\).

Answer:

\(20\)