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Home » 2Question: What is the remainder when the sum of the first 100 even numbers is divided by 7? - Midis

2Question: What is the remainder when the sum of the first 100 even numbers is divided by 7? - Midis

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Factor the numerator using the difference of squares:

📌 \[ x^2 - 9 = (x - 3)(x + 3) \]

📌 The expression simplifies to:

📌 \[ rac{(x - 3)(x + 3)}{x + 3} = x - 3 \]

📌 Restriction: \( x

📌 eq -3 \) (to avoid division by zero).

📌 #### \( x - 3 \), \( x

📌 Solve the system: \( 2x + y = 10 \) and \( x - y = 2 \).

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b = \sqrt{576} = 24 \text{ cm}
Thus, the length of the other leg is:
\boxed{24 \text{ cm}}
Problem 5:
A cube has a space diagonal of \(6\sqrt{3}\) cm. What is the volume of...
The space diagonal \(d\) of a cube with side length \(s\) is given by:
d = s\sqrt{3}
d = 6\sqrt{3}
s\sqrt{3} = 6\sqrt{3} \quad \Rightarrow \quad s = 6 \text{ cm}
The volume \(V\) of a cube is:

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