Answer:
the value of DE is -76.5.
Explanation:
Let's break down the information given in the problem and use it to find the value of DE.
Given:
AC = CD
AB = 3x + 4
AC = 1x - 17
CE = 49
First, let's use the fact that B is the midpoint of AC. This means that AB = BC.
So, we have:
AB = BC
3x + 4 = 1x - 17
Solve for x:
2x = -21
x = -21 / 2
x = -10.5
Now that we have the value of x, let's find AC using one of the given equations:
AC = 1x - 17
AC = 1*(-10.5) - 17
AC = -10.5 - 17
AC = -27.5
Since AC = CD, CD = -27.5.
Now, let's find DE. Since CE = 49 and CD = -27.5, we can calculate DE using the following equation:
CE + ED = CD
49 + ED = -27.5
Solve for ED:
ED = -27.5 - 49
ED = -76.5