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what is the good score for psat - Decision Point

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Sum: \( x + (x+2) + (x+4) = 3x + 6 = 90 \).

📌 Solve: \( 3x = 84 \), so \( x = 28 \).

📌 Largest integer is \( x+4 = 32 \).

📌 #### 321. The sum of two consecutive even integers is 146. What is the larger integer?

📌 Let the smaller even integer be \( x \). Then the larger even integer is \( x + 2 \).

📌 The equation is \( x + (x + 2) = 146 \).

📌 Simplify: \( 2x + 2 = 146 \)

📌 Subtract 2: \( 2x = 144 \)

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Use the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).
Here, \(a = 2\), \(b = -8\), \(c = 6\).
\(x = \frac{8 \pm \sqrt{(-8)^2 - 4 \times 2 \times 6}}{4} = \frac{8 \p...
\(x = \frac{8 \pm 4}{4}\), so \(x = 3\) or \(x = 1\).
A box has dimensions 2 units by 3 units by 4 units. If each dimension...
Original volume is \(2 \times 3 \times 4 = 24\) cubic units.
New dimensions are 4, 6, and 8 units.
New volume is \(4 \times 6 \times 8 = 192\) cubic units.
\(n(n+1) = 420\).
Solving \(n^2 + n - 420 = 0\) using the quadratic formula:

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