Answer:
The V-shaped graph opens downward, and its vertex lies at (1, 12).
Step-by-step explanation:
- first, plot the graph of f(x),
- take some 5 random negative and positive x values and then find corresponding f[x] values.plot f(x) on y-axis. now, plot these points on the graph and finally join all the points. this gives u the required graph.
- I have plotted the graph and uploaded it.
refer it.
- by seeing the graph, we can easily say that,The V-shaped graph opens downward, and its vertex lies at (1, 12).
ANSWER
![x ^{2} = - 4(y - 1).](https://tex.z-dn.net/?f=x%20%5E%7B2%7D%20%20%3D%20%20-%204%28y%20-%201%29.)
EXPLANATION
Since the parabola has the (0, 0) and the directrix at y=2.
The equation is of the form
![{(x - h)}^{2} = - 4p(y - k)](https://tex.z-dn.net/?f=%20%7B%28x%20-%20h%29%7D%5E%7B2%7D%20%20%3D%20%20-%204p%28y%20-%20k%29)
where (h,k) is the vertex.
The vertex is half way between the directrix and the focus.
The vertex will be at (0,1)
and is the distance from the vertex to the focus which is 1.
![{(x - 0)}^{2} = - 4(1)(y - 1)](https://tex.z-dn.net/?f=%7B%28x%20-%200%29%7D%5E%7B2%7D%20%20%3D%20%20-%204%281%29%28y%20-%201%29)
![x ^{2} = - 4(y - 1)](https://tex.z-dn.net/?f=x%20%5E%7B2%7D%20%20%3D%20%20-%204%28y%20-%201%29)
Cos(x) = 1 at 0 and 2pi 360 and -360 is the same angle as 2pi so all of the above if you start at 0 and make a complete circle (360) you will be back at point 0.
Answer:
The town recreation department ordered 66 baseballs and 24 bats.
Step-by-step explanation:
Let the number of baseball be 'x'.
Also Let the number of bats be 'y'.
Given:
Total items bought = 100
Now we can say that;
Total items bought is equal to sum of number of baseball and number of bats.
Framing in equation form we get;
![x+y =100 \ \ \ \ equation \ 1](https://tex.z-dn.net/?f=x%2By%20%3D100%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%201)
Also Given:
Cost of each baseball = $4.50
Cost of each bat = $20
Total purchase = $822
Now we can say that;
Total Purchase is equal to to sum of number of baseball multiplied by Cost of each baseball and number of bats multiplied by Cost of each bat.
framing in equation form we get;
![4.5x+20y =822 \ \ \ \ equation\ 2](https://tex.z-dn.net/?f=4.5x%2B20y%20%3D822%20%5C%20%5C%20%5C%20%5C%20equation%5C%202)
Multiplying equation 1 by 4.5 we get;
![4.5(x+y) =100\times4.5\\\\4.5x+4.5y = 450 \ \ \ \ equation \ 3](https://tex.z-dn.net/?f=4.5%28x%2By%29%20%3D100%5Ctimes4.5%5C%5C%5C%5C4.5x%2B4.5y%20%3D%20450%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%203)
Now Subtracting equation 3 from equation 2 we get;
![(4.5x+20y)-(4.5x+4.5y) = 822-450\\\\4.5x+20y-4.5x-4.5y =372\\\\15.5y = 372](https://tex.z-dn.net/?f=%284.5x%2B20y%29-%284.5x%2B4.5y%29%20%3D%20822-450%5C%5C%5C%5C4.5x%2B20y-4.5x-4.5y%20%3D372%5C%5C%5C%5C15.5y%20%3D%20372)
Dividing both side by 15.5 we get;
![\frac{15.5y}{15.5}= \frac{372}{15.5}\\ \\y =24](https://tex.z-dn.net/?f=%5Cfrac%7B15.5y%7D%7B15.5%7D%3D%20%5Cfrac%7B372%7D%7B15.5%7D%5C%5C%20%20%5C%5Cy%20%3D24)
Substituting the value of y in equation 1 we get;
![x+y =100\\\\x+24 =100\\\\x =100-24 =66](https://tex.z-dn.net/?f=x%2By%20%3D100%5C%5C%5C%5Cx%2B24%20%3D100%5C%5C%5C%5Cx%20%3D100-24%20%3D66)
Hence the town recreation department ordered 66 baseballs and 24 bats.
X=95°(right opposite angle)
As X is right opposite to 95°,meaning that it would be 95° as well.
Please do remember that any angles that are right opposite to each other would be equal.
hope it helps!