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Home » Thus, the sum of the distinct prime factors is \(\boxed12\). - go-checkin.com

Thus, the sum of the distinct prime factors is \(\boxed12\). - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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#### 96Question: What is the sum of all values of $ x $ for which $ \s...
Solution: The equation $ \sqrt{(x - 3)^2} = 2x - 5 $ simplifies to $ |...
$ x - 3 = 2x - 5 $ → $ -3 + 5 = 2x - x $ → $ x = 2 $.
$ -(x - 3) = 2x - 5 $ → $ -x + 3 = 2x - 5 $ → $ 3 + 5 = 3x $ → $ x = \...
Check validity: For $ x = 2 $, $ |2 - 3| = 1 $ and $ 2(2) - 5 = -1 $....
Only $ x = \frac{8}{3} $ is valid. The sum is $ \boxed{\dfrac{8}{3}} $...
Question: How many positive 3-digit numbers are divisible by 7 but not...
Solution: First, find 3-digit numbers divisible by 7: The smallest is...
Next, find numbers divisible by both 7 and 5 (i.e., 35): Smallest 3-di...
Subtract: $ 128 - 26 = 102 $. The answer is $ \boxed{102} $.

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