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Mariulka [41]
3 years ago
12

Factor the expression 6m-27n

Mathematics
1 answer:
coldgirl [10]3 years ago
5 0

Answer:

3(2m-9n)

Step-by-step explanation:

Find the greatest common denominator take it out and add what you have left. When you work this out you get 6m-27n

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Morgarella [4.7K]

\text{mass of freight train} = 9.98 \times  {10}^{6} kg

\text{mass of aircraft carrier} = 7.3 \times  {10}^{7}  \: kg

\text{difference of masses of aircraft and train: } \\  \\ 7.3 \times  {10}^{7}  - 9.98 \times  {10}^{6}  \\  \\  = 73 \times  {10}^{6}  - 9.98 \times  {10}^{6}

= (73 - 9.98 )\times  {10}^{6}  \\  \\  = 63.02 \times  {10}^{6}  \\  \\  = 6.302 \times  {10}^{6}  \: kg \\  \\  \approx 6.3 \times  {10}^{6}  \: kg

Approximately, aircraft carrier is 6.3 × 10^6 kg heavier than the freight train.
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A parabola can be drawn given a focus of (-11, -2) and a directrix of x= -3
fgiga [73]

Check the picture below, so the parabola looks more or less like that.

now, the vertex is half-way between the focus point and the directrix, so that puts it where you see it in the picture, and the horizontal parabola is opening to the left-hand-side, meaning that the distance "P" is negative.

\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}

\begin{cases} h=-7\\ k=-2\\ p=-4 \end{cases}\implies 4(-4)[x-(-7)]~~ = ~~[y-(-2)]^2 \\\\\\ -16(x+7)=(y+2)^2\implies x+7=-\cfrac{(y+2)^2}{16}\implies x=-\cfrac{1}{16}(y+2)^2-7

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