Question

What is the value of x and the length of segment DE?

1. 5/9= 9/(2x+3)


2. 10x + 15 = 9(9)


x=?

length of de=?

Answer 1

Answer: 6.6 for the first x

Length of DE is 16.2

Also these are correct!

Explanation:

I just put it in

Answer 2

`x = 6.6` and
`DE = 16.2`

Explanation:

The question is incomplete as the attachment to solve segment DE is missing. However, see attached for complete question.

Given

`(5)/(9)= (9)/((2x+3))`

Required

Find x

Length of DE

To find x, we need to first simplify the given equation

`(5)/(9)= (9)/((2x+3))`

Multiply both sides by
`9(2x+3)`

`(5)/(9) * 9(2x + 3) = (9)/((2x+3)) * 9(2x + 3)`

`5(2x + 3) = 9(9)`

`10x + 15 = 81`

Subtract 15 from both sides

`10x + 15 - 15 = 81 - 15`

`10x = 66`

Divide both sides by 10

`(10x)/(10) = (66)/(10)`

`x = (66)/(10)`

`x = 6.6`

From the attached;

`DE = 2x + 3`

Substitute 6.6 for x

`DE = 2(6.6) + 3`

`DE = 13.2 + 3`

`DE = 16.2`

Hence
`x = 6.6` and
`DE = 16.2`