Respuesta :

lublana

Answer:

de=11

Step-by-step explanation:

We are given that b is the midpoint of ac

ac=cd, ab=3x+4,ac=11x-17 and ce=49

We have to find the value of de

b is the midpoint of ac therefore we have

ab=bc

ac=ab+bc=ab+ab=2ab

[tex]11x-17=2(3x+4)[/tex]

[tex]11x-17=6x+8[/tex]

[tex]11x-6x=8+17=25[/tex]

[tex]5x=25[/tex]

[tex]x=\frac{25}{5}=5[/tex]

Then , substitute the value of x

[tex]ab=3(5)+4=19[/tex]

ac=[tex]11(5)-17=55-17=38=cd[/tex]

ce=cd+de

49=38+de

[tex]de=49-38[/tex]

de=11

akposevictor

The measure of segment DE is 11.

Given:

[tex]AB = 3x+4\\AC = 11x-17\\CE=49[/tex]

See image in the attachment below showing the information given in the question.

Since B is the midpoint of AC, therefore:

[tex]AB = AC[/tex]

[tex]2(AB) = AC[/tex]

Substitute

[tex]2(3x+4)=11x-17[/tex]

Solve for x

[tex]6x +8=11x-17\\17 + 8 = 11x-6x\\25 = 5x\\[/tex]

Divide both sides by 5

[tex]5 = x\\x=5[/tex]

Find DE:

[tex]DE = CE - CD[/tex] (Segment Addition Postulate)

[tex]AC = CD = 11x-17[/tex]

Plug in the value of x

[tex]CD = 11(5) -17 = 38[/tex]

[tex]CE = 49 (given)[/tex]

Substitute

[tex]DE = 49 - 38\\DE = 11[/tex]

Therefore the length of DE = 11.

Learn more about segments here:

https://brainly.com/question/16553579

Ver imagen akposevictor

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