1 x 72<span>, </span>2 x 36<span>, </span>3 x 24,4 x 18<span>, </span>6 x 12<span>, or </span><span>8 x 9</span>
Answer:
I think you are missing something from the question, but if you were to find out how much you would get paid for a certain amount of hours from $12 per hour, then the formula would be:
Step-by-step explanation:
Let h = no. of hours worked
$12 * h
![\large\begin{array}{l} \textsf{a) }\mathsf{(f\circ g)(x)}\\\\ =\mathsf{f\big[g(x)\big]}\\\\ =\mathsf{\big[g(x)\big]^2-6\cdot g(x)+2}\\\\ =\mathsf{\big[\sqrt{x}\big]^2-6\sqrt{x}+2}\\\\\\ \therefore~~\boxed{\begin{array}{c}\mathsf{(f\circ g)(x)=x-6\sqrt{x}+2} \end{array}}\qquad\checkmark \end{array}](https://tex.z-dn.net/?f=%5Clarge%5Cbegin%7Barray%7D%7Bl%7D%20%5Ctextsf%7Ba%29%20%7D%5Cmathsf%7B%28f%5Ccirc%20g%29%28x%29%7D%5C%5C%5C%5C%20%3D%5Cmathsf%7Bf%5Cbig%5Bg%28x%29%5Cbig%5D%7D%5C%5C%5C%5C%20%3D%5Cmathsf%7B%5Cbig%5Bg%28x%29%5Cbig%5D%5E2-6%5Ccdot%20g%28x%29%2B2%7D%5C%5C%5C%5C%20%3D%5Cmathsf%7B%5Cbig%5B%5Csqrt%7Bx%7D%5Cbig%5D%5E2-6%5Csqrt%7Bx%7D%2B2%7D%5C%5C%5C%5C%5C%5C%20%5Ctherefore~~%5Cboxed%7B%5Cbegin%7Barray%7D%7Bc%7D%5Cmathsf%7B%28f%5Ccirc%20g%29%28x%29%3Dx-6%5Csqrt%7Bx%7D%2B2%7D%20%5Cend%7Barray%7D%7D%5Cqquad%5Ccheckmark%20%5Cend%7Barray%7D)
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![\large\begin{array}{l} \textsf{b) }\mathsf{(g\circ f)(-2)}\\\\ =\mathsf{g\big[f(-2)\big]}\\\\ =\mathsf{\sqrt{f(-2)}}\\\\ =\mathsf{\sqrt{(-2)^2-6\cdot (-2)+2}}\\\\ =\mathsf{\sqrt{4+12+2}}\\\\ =\mathsf{\sqrt{18}}\\\\ =\mathsf{\sqrt{3^2\cdot 2}}\\\\ =\mathsf{3\sqrt{2}}\\\\\\ \therefore~~\boxed{\begin{array}{c}\mathsf{(g\circ f)(-2)=3\sqrt{2}} \end{array}}\qquad\checkmark \end{array}](https://tex.z-dn.net/?f=%5Clarge%5Cbegin%7Barray%7D%7Bl%7D%20%5Ctextsf%7Bb%29%20%7D%5Cmathsf%7B%28g%5Ccirc%20f%29%28-2%29%7D%5C%5C%5C%5C%20%3D%5Cmathsf%7Bg%5Cbig%5Bf%28-2%29%5Cbig%5D%7D%5C%5C%5C%5C%20%3D%5Cmathsf%7B%5Csqrt%7Bf%28-2%29%7D%7D%5C%5C%5C%5C%20%3D%5Cmathsf%7B%5Csqrt%7B%28-2%29%5E2-6%5Ccdot%20%28-2%29%2B2%7D%7D%5C%5C%5C%5C%20%3D%5Cmathsf%7B%5Csqrt%7B4%2B12%2B2%7D%7D%5C%5C%5C%5C%20%3D%5Cmathsf%7B%5Csqrt%7B18%7D%7D%5C%5C%5C%5C%20%3D%5Cmathsf%7B%5Csqrt%7B3%5E2%5Ccdot%202%7D%7D%5C%5C%5C%5C%20%3D%5Cmathsf%7B3%5Csqrt%7B2%7D%7D%5C%5C%5C%5C%5C%5C%20%5Ctherefore~~%5Cboxed%7B%5Cbegin%7Barray%7D%7Bc%7D%5Cmathsf%7B%28g%5Ccirc%20f%29%28-2%29%3D3%5Csqrt%7B2%7D%7D%20%5Cend%7Barray%7D%7D%5Cqquad%5Ccheckmark%20%5Cend%7Barray%7D)
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Tags: <em>composite function composition evaluate algebra</em>
Answer:
Midpoint of a line segment with the endpoints A(a1, a2), B(b1, b2) is M(1/2*(a1 + b1), 1/2*(a2 + b2))
So,
(1/2*(-4 + 7), 1/2*(-3 + (-5))) = (1/2*3, 1/2*(-8)) = (1.5, -4)
Answer D is correct.
1/4 because 6/24 can be simplified all the way down to 1/4
