I think the answer should be 20
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The equation y = -x^2+6x+5 is really the equation y = -1x^2+6x+5. It is in the form y = ax^2 + bx + c where
a = -1
b = 6
c = 5
We will use 'a' and 'b' in the formula below
h = -b/(2a)
h = -6/(2*(-1))
h = -6/(-2)
h = 3
The h refers to the x coordinate of the vertex. Since we know the x coordinate of the vertex (is 3), we can use it to find the y coordinate of the vertex
Simply plug x = 3 into the original equation
y = -x^2 + 6x + 5
y = -(3)^2 + 6(3) + 5
y = -(9) + 6(3) + 5
y = -9+18+5
y = 14
This is the k value, so k = 14.
In summary so far, we have a = -1, h = 3 and k = 14. Plug all this into the vertex form below
y = a(x-h)^2 + k
y = -1(x-3)^2 + 14
y = -(x-3)^2 + 14
Therefore the vertex form equation is y = -(x-3)^2 + 14
So when x = 3, the paired y value is y = 14. The point (x,y) = (3,14) is a point on the parabola. This point is either the highest or lowest point.
How can we figure out if it's the highest or lowest point? By looking at the value of 'a'. Notice how a = -1 and this is less than zero. In other words, a < 0
Since a < 0, this means the parabola opens downward forming a "frown" so to speak. That's one way to remember it: negative 'a' leads to sad face.
Anyways, this parabola opening downward means that the vertex is the highest point.
So (3,14) is the vertex
The maximum is y = 14.
Answer:
1.27
Step-by-step explanation:
When completing word problems, it's always important to first turn everything into an equation.
The volume of a rectangular box is:
![V=lhw](https://tex.z-dn.net/?f=V%3Dlhw)
Where <em>l</em> is the length, <em>h</em> is the height, and <em>w</em> is the width.
Which we can write down the equation:
![47 ft^3=(4w)(6+w)(w)](https://tex.z-dn.net/?f=47%20ft%5E3%3D%284w%29%286%2Bw%29%28w%29)
Next up, distribute:
![47=4w^2(6+w)\\47=24w^2+4w^3\\4w^3+24w^2-47=0](https://tex.z-dn.net/?f=47%3D4w%5E2%286%2Bw%29%5C%5C47%3D24w%5E2%2B4w%5E3%5C%5C4w%5E3%2B24w%5E2-47%3D0)
We have a cubic equation, you can solve it using a calculator.
We have three solutions, and they are:
![w=-5.62919529..., -1.64201009..., 1.27120539...](https://tex.z-dn.net/?f=w%3D-5.62919529...%2C%20-1.64201009...%2C%201.27120539...)
Since lengths cannot be negative, there is just one solution: ![w=1.27120539...](https://tex.z-dn.net/?f=w%3D1.27120539...)
And rounding it gives:
![w=1.27](https://tex.z-dn.net/?f=w%3D1.27)
And don't forget to put ft at the end!
Answer:
C
Step-by-step explanation:
C is the common letter in both angles