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jolli1 [7]
3 years ago
9

Geometry

Mathematics
1 answer:
Kobotan [32]3 years ago
5 0

Answer: UV = 52

Concept:

Additive property of length, or the segment addition postulate, states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.

Solve:

<u>Given information</u>

TU = 4x

UV = 2x + 14

TV = 7x - 5

<u>Given expression deducted from the additive property of length</u>

TV = TU + UV

<u>Substitute values into the expression</u>

7x - 5 = 4x + 2x + 14

<u>Combine like terms</u>

7x - 5 = 6x + 14

<u />

<u>Subtract 6x on both sides</u>

7x - 5 - 6x = 6x + 14 - 6x

x - 5 = 14

<u>Add 5 on both sides</u>

x - 5 + 5 = 14 + 5

x = 19

<u>Find UV by substituting the value of x</u>

UV = 2x + 14 = 2 (19) + 14 = \boxed{52}

Hope this helps!! :)

Please let me know if you have any questions

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