Point E is on line segment DF. Given DE = 2x, EF = 2x – 6, and DF = 3x + 5, determine the numerical length of EF.

EF =

EF is 16.  

Step-by-step explanation:

So we know that Point E is somewhere on Line DF. In other words, DE plus EF must equal DF. In an equation, this is:

We are given that DE is 2x, EF is 2x-6, and DF is 3x+5. So, substitute:

Now, solve for x.

On the right, combine like terms:

Subtract 4x from both sides:

Subtract 5 from both sides:

Divide both sides by -1:

Now that we know x is 11, substitute this back into the equation for EF to find EF.

Substitute 11 for x:

Multiply:

Subtract:

And we're done!

13

step-by-step explanation:

distance formula is d=√(x2-x1)^2   +   (y2-y1)^2

the answer is here: : )

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