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Question:** The sum of the first n natural numbers is given by the formula \( S = rac{n(n+1)}{2} \). What is the sum of the first 50 natural numbers?
\( S = rac{50(50+1)}{2} = rac{50 imes 51}{2} = rac{2550}{2} = 1275 \)
#### 1275
Question:** A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Is this triangle a right triangle?
Since \( 7^2 + 24^2 = 25^2 \), it is a right triangle.
Question:** A train travels 300 km in 4 hours. If it maintains the same speed, how long will it take to travel 450 km?
Speed = Distance / Time = 300 km / 4 hours = 75 km/h
Time to travel 450 km = Distance / Speed = 450 km / 75 km/h = 6 hours
Question:** Solve the equation \( 3x - 7 = 2x + 5 \).
\( 3x - 2x - 7 = 5 \)