Question

2 numeric 1 point if ( rs = 59 ) and ( overline{st}=10x - 31 ), find ( x ). answer 9

Explanation:

Step1: Use the property of congruent chords

In a circle, if two chords are congruent, then their lengths are equal. So, \(RS = ST\).

Step2: Set up the equation

Since \(RS = 59\) and \(ST=10x - 31\), we have the equation \(59=10x - 31\).

Step3: Solve for \(x\)

Add \(31\) to both sides of the equation: \(59 + 31=10x-31 + 31\), which simplifies to \(90 = 10x\).
Divide both sides by \(10\): \(\frac{90}{10}=\frac{10x}{10}\), so \(x = 9\).

Answer:

\(9\)