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Home » From the second equation, express \( y \) in terms of \( x \): \( y = 5x - 7 \). - DNSFLEX

From the second equation, express \( y \) in terms of \( x \): \( y = 5x - 7 \). - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 The function \( f(x) = 2x^2 - 8x + 5 \) has a minimum value. What is this minimum value?

📌 This is a parabola opening upwards. Vertex at \( x = -\frac{b}{2a} = -\frac{-8}{2 \cdot 2} = 2 \).

📌 \( f(2) = 2(4) - 8(2) + 5 = 8 - 16 + 5 = -3 \).

📌 So, the minimum value is \( -3 \).

📌 A geometric sequence has first term 4 and common ratio \( \frac{3}{2} \). What is the sum of the first 5 terms?

📌 Sum of geometric sequence: \( S_n = a \frac{r^n - 1}{r - 1} \),

📌 \( a = 4 \), \( r = \frac{3}{2} \), \( n = 5 \).

📌 \( S_5 = 4 \cdot \frac{(\frac{3}{2})^5 - 1}{\frac{3}{2} - 1} = 4 \cdot \frac{\frac{243}{32} - 1}{\frac{1}{2}} = 4 \cdot \frac{\frac{211}{32}}{\frac{1}{2}} = 4 \cdot \frac{211}{32} \cdot 2 = 8 \cdot \frac{211}{32} = \frac{1688}{32} = 52.75 \).

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