Question

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

Explanation:

Step1: Set \(LM = NP\)

Since \(LM\) and \(NP\) are congruent chords (indicated by the tick - marks), we have the equation \(41−2x=7x + 5\).

Step2: Solve for \(x\)

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

Step3: Find \(LM\)

Substitute \(x = 4\) into the formula for \(LM\): \(LM=41-2x\).
\(LM=41-2\times4\).
\(LM=41 - 8\).

Answer:

\(33\)