Answer:
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!
