Question

7 numeric 1 point if ( lm = 41 - 2x ) and ( np = 7x + 5 ), find ( lm ). answer

Explanation:

Step1: Set up the equation

Since \(LM = NP\) (chords of equal length in a circle), we have \(41-2x=7x + 5\).

Step2: Solve for \(x\)

Add \(2x\) to both sides: \(41=7x + 5+2x\), which simplifies to \(41 = 9x+5\).
Subtract \(5\) from both sides: \(41 - 5=9x\), so \(36 = 9x\).
Divide both sides by \(9\): \(x=\frac{36}{9}=4\).

Step3: Find \(LM\)

Substitute \(x = 4\) into \(LM=41-2x\).
\(LM=41-2\times4=41 - 8=33\).

Answer:

\(33\)