Ac=ce and d is the midpoint of ce. if ce = 10x+18 de = 7x-1 and bc = 9x-3 find ab

The length of AB is 26units

The midpoint is a point that divides the line into two equal parts.

Given the following expressions

CE = 10x+18

DE = 7x-1

BC = 9x-3

if D is the midpoint of CE, then:

CD + DE = CE

Also CD = DE

DE + DE = CE

2DE = CE

2(7x-1) = 10x+18

14x-2 = 10x+18

14x-10x = 18+2

4x = 20

x = 20/4

x = 5

Also, we can make use of the expression:

AB + BC = AC

AB = AC - BC

Given the following:

BC = 9x - 3

CE = 10x + 18

Recall that AC=CE, hence AC = 10x + 18

AB = 10x+18-(9x-3)

AB = 10x + 18 - 9x + 3

AB = x + 18 + 3

AB = x + 21

Since x = 5

AB = 5 + 21

AB = 26

Hence the length of AB is 26

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We know the CE = 10x + 18 and DE = 7x - 1 and D is the midpoint of CE

⇒ CE = 2 * DE

⇒ 10x + 18 = 2 * (7x - 1)

⇒ 10x + 18 = 14x - 2

⇒ -4x = -20

⇒ x = 5

Now we also know that BC = 9x - 3 and AC = CE = 10x + 18

⇒ AB = AC - BC

⇒ AB = 10x + 18 - (9x - 3)

⇒ AB = x + 21

Substituting the value of x,

⇒ AB = 5 + 21

⇒ AB = 26

Hence, the value of AB is 26 units.

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05