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My name is Ann [436]
2 years ago
15

A parabola can be drawn given a focus of (-9, -7) and a directrix of x = 9. Write

Mathematics
1 answer:
Slav-nsk [51]2 years ago
4 0

Check the picture below, so the parabola looks more or less like so, with a vertex at (0 , -7), let's recall the vertex is half-way between the focus point and the directrix.

so this horizontal parabola opens up to the left-hand-side, meaning that the "P" distance is a negative value.

\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=0\\ k=-7\\ p=-9 \end{cases}\implies 4(-9)(x-0)~~ = ~~[y-(-7)]^2 \\\\\\ -36x=(y+7)^2\implies x=-\cfrac{1}{36}(y+7)^2

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Answer:

One of the negatives must go

Step-by-step explanation:

6 0
2 years ago
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Which fraction has the value that's equal to 3/4
mamaluj [8]

One of the fractions that’s equal to \frac{3}{4} is \frac{12}{16}

<u>Solution:</u>

Given that , we have to find fractions which has the same value as that of the fraction \frac{3}{4}

Now, we know that, there are several fractions with values equal to \frac{3}{4}

To find them, just multiply the numerator and denominator by the same number.

\begin{array}{l}{3 \times 2=6} \\\\ {4 \times 2=8}\end{array}

Therefore, \frac{6}{8} is equal to \frac{3}{4}

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Hence, one of the fractions that’s equal to \frac{3}{4} is \frac{12}{16}

4 0
3 years ago
The table represents a linear function?
Llana [10]
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How are you doing? I know this is kind of late, but here goes nothing! Yes, it is a linear equation, you know this because, the input always will result with the same output. Plus, since it has a slope, which is 10 by the way, it also confirms that this is linear! Linear means, that if you put these plots on a line, it will create a straight line! Hope I helped!

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lukranit [14]
I'd say first isolate the "x"
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so we get "x" equals three times "y" plus two which is then divided by two and subtracted by three.

after that I would simply divide both sides by three as shown below

x/3=( 3*(y+2)/2  -3)/3

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Olivia finished the race in 40.64 seconds. patty finished the race in 40.39 seconds. miguel finished the race in 41.44 seconds.
ANEK [815]
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Patty had the lowest time, so therefore, Patty finished the race in the least amount of time.
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