Question

question 8
let a be between b and c. use the segment addition postulate to solve for t. (hint: draw a picture of this description before answering the question.)
ba = 5t + 1
ac = 7t + 15
bc = 25

Explanation:

Step1: Apply segment - addition postulate

Since A is between B and C, by the Segment Addition Postulate, $BA + AC=BC$.
Substitute the given expressions: $(5t + 1)+(7t + 15)=25$.

Step2: Combine like - terms

Combine the t - terms and the constant terms on the left - hand side: $5t+7t + 1+15 = 25$, which simplifies to $12t+16 = 25$.

Step3: Isolate the variable term

Subtract 16 from both sides of the equation: $12t+16−16 = 25−16$, resulting in $12t=9$.

Step4: Solve for t

Divide both sides of the equation by 12: $t=\frac{9}{12}=\frac{3}{4}$.

Answer:

$t = \frac{3}{4}$