Question

1. solve for x. type a response

Explanation:

Step1: Apply the secant-secant rule

The secant-secant rule states that if two secant segments are drawn from a point outside the circle, then the product of the length of one secant segment and its external part is equal to the product of the length of the other secant segment and its external part. So, we have \((x + 8)\times8=(11 + 9)\times9\).

Step2: Simplify the right - hand side

First, calculate the right - hand side of the equation. \(11 + 9=20\), so the equation becomes \((x + 8)\times8=20\times9\). Then \(20\times9 = 180\), and our equation is \(8(x + 8)=180\).

Step3: Solve for x

Divide both sides of the equation \(8(x + 8)=180\) by 8: \(x + 8=\frac{180}{8}=\frac{45}{2}=22.5\). Then subtract 8 from both sides: \(x=22.5 - 8 = 14.5\).

Answer:

\(x = 14.5\)