Question

solve for x. round your answer to the nearest tenth if necessary.
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(image of triangle nlm with segment np = 4.6, nm = np + x, no = 5.7, ol = 4.3, and segment op parallel to lm)

Explanation:

Step1: Identify the theorem

Since \( OP \parallel LM \), by the Basic Proportionality Theorem (Thales' theorem), \(\frac{NP}{PM}=\frac{NO}{OL}\).
Let \( NP = 4.6 \), \( PM = x \), \( NO = 5.7 \), \( OL = 4.3 \).

Step2: Set up the proportion

Substitute the values into the proportion: \(\frac{4.6}{x}=\frac{5.7}{4.3}\).

Step3: Cross - multiply to solve for \( x \)

Cross - multiplying gives \( 5.7x=4.6\times4.3 \).
First, calculate \( 4.6\times4.3 = 19.78 \).
Then, solve for \( x \): \( x=\frac{19.78}{5.7}\approx3.5 \).

Answer:

\( x\approx3.5 \)