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Home » x^2 + 3x = \left(x + \frac32\right)^2 - \frac94 - AMAZONAWS

x^2 + 3x = \left(x + \frac32\right)^2 - \frac94 - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 #### 144 units

📌 The length of a diagonal of a square is 10 cm. What is the perimeter of the square?

📌 The diagonal \(d\) of a square with side \(s\) is given by \(d = s\sqrt{2}\).

📌 Solving for \(s\), we have \(s = \frac{10}{\sqrt{2}} = \frac{10 \times \sqrt{2}}{2} = 5\sqrt{2}\) cm.

📌 The perimeter is \(4s = 4 \times 5\sqrt{2} = 20\sqrt{2}\) cm.

📌 Approximating \(\sqrt{2} \approx 1.414\), the perimeter is \(20 \times 1.414 = 28.28\) cm.

📌 #### 28.28 cm

📌 If a train travels 150 km in 2 hours and then 200 km in 3 hours, what is its average speed for the entire trip?

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Thus, solutions are $30^\circ, 90^\circ, 150^\circ$.
\boxed{30^\circ}, \boxed{90^\circ}, \boxed{150^\circ}
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Numbers greater than 7 on a 10-sided die: 8, 9, 10 → 3 outcomes
Probability of success (rolling >7): $ p = \frac{3}{10} = 0.3 $
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Number of trials $ n = 4 $
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