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3 years ago

Point e is between points d and f. If DE=x-4,EF=2x+5 and DF=4x-8, find x number 17 help please

Mathematics

2 answers:

Murljashka [212]3 years ago

4 0

DF =DE + EF
4x-8 = x-4 + 2x+5
4x - 8 = 3x + 1
4x - 3x = 1 + 8
x = 9

Anna007 [38]3 years ago

4 0

Answer: The required value of x is 9.

Step-by-step explanation: Given that point E is between the points D and F.

Also, DE = x - 4, EF = 2x + 5 and DF = 4x - 8.

We are to find the value of x.

Since the point E lies between the points D and F, so we must have

$DE+EF=DF\\\\\Rightarrow (x-4)+(2x+5)=4x-8\\\\\Rightarrow 3x+1=4x-8\\\\\Rightarrow 4x-3x=1+8\\\\\Rightarrow x=9.$

Thus, the required value of x is 9.

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EF is the median of trapezoid ABCD.

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Answer:

Part A) $x = 11$

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length of EF = 4x - 18 = 4(11) - 18 = 44 - 18 =26

length of AD = 3x - 18 = 3(11) - 4 = 33 - 4 =29

Step-by-step explanation:

Median of trapezium is $m=\frac{base1+base2}{2}$

In provided figure, base1 is x+12 and base2 is 3x-4

A) solve for value of x

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$4x-18=\frac{x+12+3x-4}{2}$

$4x-18=\frac{4x+8}{2}$

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$2x = 22$

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B) To find the length of BC, AD and EF , put the value of x in equation of lines

length of BC = x + 12 = x + 12 = 11 + 12 =23

length of EF = 4x - 18 = 4(11) - 18 = 44 - 18 =26

length of AD = 3x - 4 = 3(11) - 4 = 33 - 4 =29

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