Question

what is the value of x and the length of segment de?

1. \\( \frac { 5 } { 9 } = \frac { 9 } { 2 x + 3 } \\)
2. \\( 10 x + 15 = 9 ( 9 ) \\)

\\( x = \\)
length of \\( \overline { d e } = \\) units

Explanation:

Step1: Solve the equation \(10x + 15=9\times9\)

First, calculate \(9\times9 = 81\). So the equation becomes \(10x+15 = 81\).
Then, subtract 15 from both sides: \(10x=81 - 15\).
\(10x=66\).

Step2: Find the value of \(x\)

Divide both sides of \(10x = 66\) by 10. \(x=\frac{66}{10}=6.6\).

Step3: Find the length of \(DE\)

Substitute \(x = 6.6\) into \(2x+3\).
\(2x+3=2\times6.6 + 3\).
\(2\times6.6+3=13.2 + 3=16.2\).

Answer:

\(x = 6.6\); Length of \(\overline{DE}=16.2\) units