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3 years ago

If b is the midpoint of ac, ac=cd, ab=3x+4, ac=11x-17, and ce=49, find de

Mathematics

2 answers:

Anton [14]3 years ago

7 0

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

$11x-17=2(3x+4)$

$11x-17=6x+8$

$11x-6x=8+17=25$

$5x=25$

$x=\frac{25}{5}=5$

Then , substitute the value of x

$ab=3(5)+4=19$

ac= $11(5)-17=55-17=38=cd$

ce=cd+de

49=38+de

$de=49-38$

de=11

IrinaK [193]3 years ago

5 0

First, we draw our line.

|------------------------------------------------------------------------------------|

a e

Next, break up this line into segments using the information.

|----------------------|----------------------|--------------------|------------------|

a b c d e

The entire line is 29.

ab + bc + cd + de = ae

ab + bc + cd + de = 29

You also know that

bd = bc + cd

Due to midpoint theorem,

ab = bc

cd = de

Then,

2ab + 2cd = 29

The equations we will use are

bd = bc + cd eq1

2bc + 2cd = 29 eq2

Dividing both sides of the equation in eq2 yields

bc + cd = 14.5

bd = bc + cd

bd = 14.5

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