AC CE and D is the midpoint of CE. IF CE 10x + 18, DE =7x -1, and BC = 9x - 2, find AB, AB =
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Answer:
Step-by-step explanation:
D is the midpoint of CE, then
CD = DE = 0.5CE = 0.5(10x+18) = 5x + 9
So: 5x + 9 = 7x - 1
-9 -9
5x = 7x - 8
-7x -7x
-2x = -8
÷(-2) ÷(-2)
x = 4
AC = CE = 10x + 18 = 40 + 18 = 58
BC = 9x - 2 = 36 - 2= 34
AB = AC - BC = 58 - 34 = 24
D is the midpoint of CE, so if you draw a line with those three points, it'll look like C-D-E.
Since DE = 7x-1, which also means CD = 7x-1.
CD + DE = CE, so (7x-1)+(7x-1) = 10x+18.
Therefore, x = 5 and CE = 68.
Since AC is congruent to CE, AC = 68.
Assuming the point B is somewhere between AC.
Since BC = 9x-2 and x = 5, which means BC = 43.
AC - BC = AB, so 68 - 43 = 25.
Therefore, AB = 25