Need a quick answer please

The length of DE is 11

Step-by-step explanation:

Let us solve the question

∵ B is the midpoint of AC

∴ AB = BC

∵ AB = 3x + 4

∴ BC = 3x + 4

∵ AC = AB + BC

→ Substitute the expressions of AB and BC

∴ AC = 3x + 4 + 3x + 4

→ Add the like terms

∵ AC = (3x + 3x) + (4 + 4)

∴ AC = 6x + 8

∵ AC = 11x - 17

→ Equate the right sides of the AC

∴ 11x - 17 = 6x + 8

→ Subtract 6x from both sides

∵ 11x - 6x - 17 = 6x - 6x + 8

∴ 5x - 17 = 8

→ Add 17 to both sides

∵ 5x - 17 + 17 = 8 + 17

∴ 5x = 25

→ Divide both sides by 5

∴ x = 5

→ Substitute the value of x in AC to find its length

∵ AC = 11(5) -17 = 55 - 17

∴ AC = 38

∵ AC = CD

∴ CD = 38

∵ CE = 49

∵ CE = CD + DE

→ Substitute the lengths of CE and CD

∴ 49 = 38 + DE

→ Subtract 38 from both sides

∵ 49 - 38 = 38 - 38 + DE

∴ 11 = DE

∴ The length of DE is 11

mathpapa

step-by-step explanation:

the formula of a midpoint between a abd b: