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Home » Thus, the roots of the equation are \(\boxed{1 \text and 3}\). - Anadea

Thus, the roots of the equation are \(\boxed{1 \text and 3}\). - Anadea

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 A hydrologist is solving the equation \(3x - 7 = 2x + 5\) to determine the equilibrium flow rate. Find the value of \(x\).

📌 Start by isolating \(x\) in the equation \(3x - 7 = 2x + 5\).

📌 Subtract \(2x\) from both sides:

📌 Thus, the value of \(x\) is:

📌 \]Question: Find the vertex of the parabola modeling the growth rate of a climate-dependent species, given by $ y = -2x^2 + 8x - 5 $.

📌 Solution: The vertex form of a parabola $ y = ax^2 + bx + c $ has its vertex at $ x = -\frac{b}{2a} $. Here, $ a = -2 $, $ b = 8 $, so $ x = -\frac{8}{2(-2)} = 2 $. Substituting $ x = 2 $ into the equation: $ y = -2(2)^2 + 8(2) - 5 = -8 + 16 - 5 = 3 $. Thus, the vertex is at $ (2, 3) $. \boxed{(2, 3)}

📌 Question: Solve for $ v $ in the equation $ \frac{1}{2}mv^2 = \frac{3}{4}kT $, where $ m $ is mass, $ k $ is Boltzmann’s constant, and $ T $ is temperature, to express $ v $ in terms of $ k $, $ T $, and $ m $.

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