Question

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

Explanation:

Step1: Recognize equal chords

In a circle, chords equidistant from the center are equal. So \( LM = NP \).
Set \( 41 - 2x = 7x + 5 \).

Step2: Solve for \( x \)

Add \( 2x \) to both sides: \( 41 = 9x + 5 \).
Subtract 5: \( 36 = 9x \).
Divide by 9: \( x = 4 \).

Step3: Find \( LM \)

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

Answer:

33