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Home » Love It or Hate It: The Cross Ring That’s Trending Like Wildfire! - Crosslake

Love It or Hate It: The Cross Ring That’s Trending Like Wildfire! - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question: If \( x + rac{1}{x} = 5 \), what is the value of \( 2x^2 + rac{2}{x^2} \)?

📌 Solution: Square both sides: \( x^2 + 2 + rac{1}{x^2} = 25 \), so \( x^2 + rac{1}{x^2} = 23 \). Multiply by 2: \( 2x^2 + rac{2}{x^2} = 46 \). oxed{46}

📌 Question: Find the intersection of the lines \( y = 3x + 1 \) and \( y = -2x + 11 \).

📌 Solution: Set \( 3x + 1 = -2x + 11 \). Solve for \( x \): \( 5x = 10 \) â \( x = 2 \). Substitute into \( y = 3(2) + 1 = 7 \). The intersection is \( (2, 7) \). oxed{(2, 7)}

📌 Question: If \( m(m + n) = 24 \) and \( m + n = 8 \), what is the value of \( m \)?

📌 Solution: Substitute \( m + n = 8 \) into the first equation: \( m \cdot 8 = 24 \), so \( m = 3 \). oxed{3}Question: A sequence of six real numbers forms an arithmetic progression. The sum of the first three terms is 12, and the sum of the last three terms is 30. What is the sum of all six terms?

📌 Solution: Let the six terms of the arithmetic progression be $ a - 2d, a - d, a, a + d, a + 2d, a + 3d $.

📌 The sum of the first three terms is:

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\(10 \times 3 = 30\) cm
A sphere has a surface area of \(144\pi\) square centimeters. What is...
The formula for the surface area of a sphere is:
\(4\pi r^2\)
\(4\pi r^2 = 144\pi\)
Simplify and solve for \(r^2\):
\(r^2 = \frac{144}{4} = 36\)
Find \(r\):
\(r = \sqrt{36} = 6\) cm
A right triangle has legs of 9 cm and 12 cm. What is the length of the...

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Subtracting 1 from both sides, \( x = 4 \).
#### \( x = 4 \)
Find the area of a circle with a circumference of 31.4 units.
The formula for circumference is \( C = 2\pi r \).
So, \( 31.4 = 2\pi r \).
Solving for \( r \), \( r = rac{31.4}{2\pi} pprox rac{31.4}{6.28} =...
The area \( A = \pi r^2 = \pi imes 5^2 = 25\pi \).
#### Area = \( 25\pi \) square units
If \( \log_2(x) + \log_2(8) = 5 \), find \( x \).
Using the property \( \log_b(a) + \log_b(c) = \log_b(ac) \),

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