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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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The first number plus the second number equals 83, the first number
timama [110]

Answer:

I hope this helps

Step-by-step explanation:

So the way to handle a problem like this is to rewrite the three numbers in terms of their relationship to one of the three numbers.  Let's call the numbers x, y, and z, where x is the first number, y is the second, and z is the third.

We know x + y + z = 83.

Since the third number is twice the second, we say that z = 2y.

Since the second number is seven less than the first, we say that y = x - 7.  We can rewrite this as x = y + 7.

Now all three can be written in terms of y.

x + y + z = 83

(y + 7) + y + 2y = 83

4y + 7 = 83

4y = 76

y = 19

The second number is 19.  The first is 19 + 7 or 26, and the third is 2 times 19 or 38.

A check reveals that 26 + 19 + 38 = 83.

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3 years ago
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mrs_skeptik [129]

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3 years ago
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Given that f(x) = 2x + 5 and g(x) = x − 7, solve for f(g(x)) when x = −3.
Gnesinka [82]
F(x)=2x+5, g(x)=x-7

f(g(x))=2(x-7)+5=2x-14+5=2x-9

When x= -3:

2\cdot (-3)-9=-6-9=\boxed{-15}

<em>:)</em>

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3 years ago
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Bezzdna [24]
Y = 3x + 1

Because,
slope intercept form is y=mx+b
Where y is the y values, m is slope, x is x values, and b is y-intercept

First, to find the slope use rise/run, so rise (from 10 to 13) is 3 and run is (from 3 to 4) is 1, 3/1=3

Next to find y-intercept plug in the slope and some x and y values,
10=3(3)+b
10=9+b
1=b
So then the equation is y=3x+1 you can check by plugging stuff in and also I graphed it so I’ll add a picture

This is my first time answering questions so if I got something wrong ask or something hope this helps :)

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3 years ago
Which graph represents the compound inequality?
Marrrta [24]

Answer:

The second graph represent the compound inequality

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