Which of the following is equivalent to 6x 2 + x - 12 ?

1 answer:

4 0

$6x^2+x-12=6x^2-9x+8x-12=3x(2x-3)+4(2x-3)\\\\=(2x-3)(3x+4)\\\\other\ method:\\\\6x^2+x-12\\a=6;\ b=1;\ c=-12\\\Delta=b^2-4ac\to\Delta=1^2-4\cdot6\cdot(-12)=1+288=289\\\\x_1=\frac{-b-\sqrt\Delta}{2a};\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{289}=17$

$x_1=\frac{-1-17}{2\cdot6}=\frac{-18}{12}=-\frac{3}{2};\ x_2=\frac{-1+17}{2\cdot6}=\frac{16}{12}=\frac{4}{3}\\\\6x^2+x-12=6(x+\frac{3}{2})(x-\frac{4}{3})=2\cdot3(x+\frac{3}{2})(x-\frac{4}{3})\\\\=2(x+\frac{3}{2})\cdot3(x-\frac{4}{3})=(2x+3)(3x-4)$

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7 0

3 years ago

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The nurse needs to mix 2% solution with 10% solution to get 10 ml of the prescribed 6% solution. What amount of each solution do

xenn [34]

<em>Volumes of 2% Solution = </em><em>5 ml</em>

<em>Volumes of 10% Solution = </em><em>5 ml</em>

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<h3>Further explanation</h3>

Simultaneous Linear Equations could be solved by using several methods such as :

<em>Elimination Method</em>
<em>Substitution Method</em>
<em>Graph Method</em>

If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.

Let us tackle the problem!

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<em>Volumes of 2% Solution = x</em>

<em>Volumes of 10% Solution = y</em>

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<em>Total Volume = 10 ml</em>

$\boxed{x + y = 10}$ → <em>Equation 1</em>