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find the value of the variable and XP, if X Is between P and Q. XQ = 13, XP = 5x - 3, PQ = 40

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Answer to a math question find the value of the variable and XP, if X Is between P and Q. XQ = 13, XP = 5x - 3, PQ = 40

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Lurline
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108 Answers
Solution:
1. Given:
- XQ = 13
- XP = 5x - 3
- PQ = 40

2. Since X is between P and Q, according to geometry, the sum of the segments XP and XQ should equal segment PQ:
XP + XQ = PQ

3. Substitute the known values:
(5x - 3) + 13 = 40

4. Simplify and solve for x:
5x - 3 + 13 = 40
5x + 10 = 40
5x = 40 - 10
5x = 30
x = \frac{30}{5}
x = 6

5. Calculate XP using the value of x:
XP = 5x - 3 = 5(6) - 3 = 30 - 3 = 27

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