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Quadratic equations describe the motion of a baseball after it connects with a bat, and the acceleration of gravity at the Earth's orbit.

If \((x + 4)(3x - 1) = ax^2 + bx + c,\) what is the value of \(a + b + c?\)

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If \(bx^2 + 32x = 4x(x - a),\) what is the value of \(ab\, ?\)

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What is the maximum possible area for the rectangle shown?

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