A triangle's area is given by the expression 3x^2-x+12 The height is 6x. The base of the triangle is the quotient of the area and (1)/(2) of the height. I 6x Which expression represents the base of the triangle? (x)/(2)-(1)/(6)+(4)/(x) x-(1)/(3)+4x (x)/(2)-(1)/(6)+4x x-(1)/(3)+(4)/(x)

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A triangle's area is given by the expression 3x^2-x+12 The height is 6x. The base of the triangle is the quotient of the area and (1)/(2) of the height. I 6x Which expression represents the base of the triangle? (x)/(2)-(1)/(6)+(4)/(x) x-(1)/(3)+4x (x)/(2)-(1)/(6)+4x x-(1)/(3)+(4)/(x)

Answer 1

To find the expression that represents the base of the triangle, we will use the formula for the area of a triangle:\[\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}\]Given that the area of the triangle is \(3x^2 - x + 12\) and the height is \(6x\), we can set up the equation:\[3x^2 - x + 12 = \frac{1}{2} \times \text{base} \times 6x\]Step 1: Simplify the right side of the equation by multiplying the base by \(6x\) and then by \(\frac{1}{2}\):\[3x^2 - x + 12 = \text{base} \times 3x\]Step 2: Solve for the base by dividing both sides of the equation by \(3x\):\[\text{base} = \frac{3x^2 - x + 12}{3x}\]Step 3: Simplify the expression by dividing each term by \(3x\):\[\text{base} = \frac{3x^2}{3x} - \frac{x}{3x} + \frac{12}{3x}\]\[\text{base} = x - \frac{1}{3} + \frac{4}{x}\]Therefore, the expression that represents the base of the triangle is:\[x - \frac{1}{3} + \frac{4}{x}\]This matches the last option:\(x-\frac{1}{3}+\frac{4}{x}\)

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A triangle's area is given by the expression 3x^2-x+12 The height is 6x. The base of the triangle is the quotient of the area and (1)/(2) of the height. I 6x Which expression represents the base of the triangle? (x)/(2)-(1)/(6)+(4)/(x) x-(1)/(3)+4x (x)/(2)-(1)/(6)+4x x-(1)/(3)+(4)/(x)

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