If F is the midpoint of DE, DF = 3x+5 and FE = 5x-19 , Find DF

41

Step-by-step explanation:

when there is midpoint it bisects the segment(cuts it in equal halfs)

3x+5 = 5x-19

3x + 24 = 5x

24 = 2x

12 = x

3(12) + 5 =

36 + 5

41

The value of segment DF is 41 units.

Step-by-step explanation:

If we know that F is the midpoint of DE, we can conclude that DF and FE have the same value.  This lets us set up the following equation:

DF = FE, which when we substitute in our given values is:

3x + 5 = 5x - 19

The next step is to solve this equation.  We should start by subtracting 3x from both sides of the equation.

5 = 2x - 19

Then, we can add 19 to both sides of the equation.

24 = 2x

Finally, we can divide both sides by 2.

x = 12

Now that we have a value for x, we need to find the length of DF.  To do this, we can just plug in our value for x into the given expression for DF and simplify.

DF = 3x + 5 = 3(12) + 5 = 36 + 5 = 41

Therefore, the correct answer is 41.

Hope this helps!

i think it might be a but you might want a second opinion

dilation scale factor 2: starting with δabc, draw the dilation image of the triangle with a center at the origin and a scale factor of two. notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). dilation with scale factor 2, multiply by 2.