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Point B is on line segment AC. Given AC = 2x + 7, BC = x, and

AB= 5x9, determine the numerical length of AB.

User Flashburn
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1 Answer

7 votes

Answer:

Explanation:

To determine the length of AB, we need to find the value of x.

We are given that AC = 2x + 7, BC = x, and AB = 5x + 9.

Since B is on the line segment AC, the sum of lengths AB and BC should equal the length of AC. Therefore, we can set up the equation:

AB + BC = AC

Substituting the given values, we have:

(5x + 9) + x = 2x + 7

Simplifying the equation:

6x + 9 = 2x + 7

Bringing like terms to one side:

6x - 2x = 7 - 9

4x = -2

Dividing both sides by 4:

x = -2/4

Simplifying:

x = -1/2

Now that we have the value of x, we can substitute it back into the expression for AB to find its numerical length:

AB = 5x + 9 = 5(-1/2) + 9 = -5/2 + 9 = (18 - 5)/2 = 13/2 = 6.5

Therefore, the numerical length of AB is 6.5.

User Mikel Urkia
by
8.4k points

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