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Home » \[ z = \frac-(1 + i) \pm (1 - i)2 \] - jntua results

\[ z = \frac-(1 + i) \pm (1 - i)2 \] - jntua results

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 A parabola is given by the equation \( y = 2x^2 - 4x + 1 \). What is the vertex of the parabola?

📌 The vertex form is given by \( x = -\frac{b}{2a} \). For \( a = 2 \) and \( b = -4 \):

📌 \[ x = -\frac{-4}{2 \times 2} = 1 \]

📌 Substitute \( x = 1 \) back into the equation to find \( y \):

📌 \[ y = 2(1)^2 - 4(1) + 1 = 2 - 4 + 1 = -1 \]

📌 The vertex is \( (1, -1) \).

📌 #### (1, -1)

📌 A solution contains 30% alcohol. How much pure alcohol must be added to 200 mL of this solution to make a 50% alcohol solution?

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