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Question 5(Multiple Choice Worth 1 points) (08.01 MC) Finn removes the plug from a trough to drain the water. The volume, in gallons, in the trough after it has been unplugged can be modeled by f(x)=12x^2-13x+3 where x is the ti following equations will reveal the time in minutes when the trough is empty? f(0)=12(0)^2-13(0)+3 0=(3x-1)(4x-3) f(x)=12(x-3)^2-1 f(x)=12(x-1)^2-3

Pergunta

Question 5(Multiple Choice Worth 1 points)
(08.01 MC)
Finn removes the plug from a trough to drain the water. The volume, in gallons, in the trough after it has been unplugged can be modeled by
f(x)=12x^2-13x+3 where x is the ti
following equations will reveal the time in minutes when the trough is empty?
f(0)=12(0)^2-13(0)+3
0=(3x-1)(4x-3)
f(x)=12(x-3)^2-1
f(x)=12(x-1)^2-3

Question 5(Multiple Choice Worth 1 points) (08.01 MC) Finn removes the plug from a trough to drain the water. The volume, in gallons, in the trough after it has been unplugged can be modeled by f(x)=12x^2-13x+3 where x is the ti following equations will reveal the time in minutes when the trough is empty? f(0)=12(0)^2-13(0)+3 0=(3x-1)(4x-3) f(x)=12(x-3)^2-1 f(x)=12(x-1)^2-3

Solução

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OtávioEspecialista · Tutor por 3 anos

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The correct equation that will reveal the time in minutes when the trough is empty is \(0 = (3x - 1)(4x - 3)\).

Explicação

## Step 1<br />The problem involves a quadratic function, which is a function of the form \(f(x) = ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants. In this case, the function is \(f(x) = 12x^2 - 13x + 3\), which models the volume of water in the trough after it has been unplugged.<br /><br />## Step 2<br />The trough is empty when the volume of water is zero, which means we need to find the values of \(x\) for which \(f(x) = 0\). This is equivalent to solving the equation \(12x^2 - 13x + 3 = 0\).<br /><br />## Step 3<br />The equation \(12x^2 - 13x + 3 = 0\) can be factored into \((3x - 1)(4x - 3) = 0\). This is because the product of two factors equals zero if and only if at least one of the factors is zero.<br /><br />## Step 4<br />Setting each factor equal to zero gives us the solutions \(x = 1/3\) and \(x = 3/4\). These are the times in minutes when the trough is empty.
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