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Home » Find the value of \( x \) in the equation \( 3x^2 - 12x + 9 = 0 \). - AMAZONAWS

Find the value of \( x \) in the equation \( 3x^2 - 12x + 9 = 0 \). - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 The perimeter formula is \( 2l + 2w = 54 \).

📌 Substitute \( l = 2w + 5 \) into the perimeter formula: \( 2(2w + 5) + 2w = 54 \).

📌 Simplify and solve for \( w \): \( 4w + 10 + 2w = 54 \) becomes \( 6w + 10 = 54 \).

📌 Subtract 10: \( 6w = 44 \).

📌 Divide by 6: \( w = \frac{44}{6} = \frac{22}{3} \approx 7.33 \) meters.

📌 Then \( l = 2(\frac{22}{3}) + 5 = \frac{44}{3} + 5 = \frac{59}{3} \approx 19.67 \) meters.

📌 #### Width: 7.33 meters, Length: 19.67 meters

📌 A company’s profit in thousands of dollars is modeled by \( P(x) = -2x^2 + 20x - 30 \), where \( x \) is the number of units sold in hundreds. What is the maximum profit, and how many units maximize it?

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