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Home » x(x - 2)(x - 3) = 0. - Portal da AcÃºstica

x(x - 2)(x - 3) = 0. - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

📌 Here, \(a = 2\), \(b = -4\), \(c = -6\)

📌 Discriminant: \(b^2 - 4ac = (-4)^2 - 4 \times 2 \times (-6) = 16 + 48 = 64\)

📌 \(x = \frac{4 \pm \sqrt{64}}{4} = \frac{4 \pm 8}{4}\)

📌 Solutions: \(x = \frac{12}{4} = 3\) and \(x = \frac{-4}{4} = -1\)

📌 A train travels 180 miles in 3 hours. What is the average speed of the train in miles per hour?

📌 Average speed = Total distance / Total time = \(180 \text{ miles} / 3 \text{ hours} = 60 \text{ mph}\)

📌 The area of a triangle is given by \(A = \frac{1}{2}bh\). If a triangle has a base of 10 cm and a height of 12 cm, what is its area?

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Largest = \( x + 4 = 64 \)
A car rental company charges $45 per day plus $0.20 per mile. If Sarah...
Daily cost: \( 3 \times 45 = 135 \) dollars.
Mileage cost: \( 150 \times 0.20 = 30 \) dollars.
Total = \( 135 + 30 = 165 \) dollars.
A rectangular field has a length 4 meters more than twice its width. I...
Let width = \( w \). Then length = \( 2w + 4 \).
Area: \( w(2w + 4) = 104 \)
Expand: \( 2w^2 + 4w = 104 \)
Divide by 2: \( w^2 + 2w = 52 \)

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