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Alexxx
2 months ago
5

If  BD BC, BD = 5x – 26, BC = 2x + 1, and AC = 43, find AB.

Mathematics
1 answer:
Svet_ta [12.7K]2 months ago
4 0

Answer:

AB = 24.

Step-by-step explanation:

BD = 5x – 26.

BC = 2x + 1.

AC = 43.

Applying the segment addition postulate, AC = AB + BC.

Since BD is equal to BC, with BD being expressed as 5x-26 and BC as 2x+1, we can create an equation to calculate x:

5x - 26 = 2x + 1 Subtract 2x from both sides.

5x - 26 - 2x = 2x + 1 - 2x.

3x-26 = 1 Add 26 to both sides.

3x-26 + 26 = 1 + 26.

3x = 27 Divide each side by 3.

3x/3 = 27/3.

x = 9.

Thus, BC = 2x + 1 = 2(9) + 1 = 18 + 1 = 19.

Since AC = AB + BC; using the data provided along with the found BC value, we get:

43 = AB + 19 Subtract 19 from each side.

43 - 19 = AB + 19 - 19.

24 = AB.

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