Answer:
All the intervals that contain the number
are solution of the problem
Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to
![f(x)=a(x-h)^{2}+k](https://tex.z-dn.net/?f=f%28x%29%3Da%28x-h%29%5E%7B2%7D%2Bk)
where
(h,k) is the vertex of the parabola
In this problem we have
![f(x)=(x+3)(x+1)](https://tex.z-dn.net/?f=f%28x%29%3D%28x%2B3%29%28x%2B1%29)
Convert to vertex form
![f(x)=x^{2}+x+3x+3](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E%7B2%7D%2Bx%2B3x%2B3)
![f(x)=x^{2}+4x+3](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E%7B2%7D%2B4x%2B3)
Group terms that contain the same variable, and move the constant to the opposite side of the equation
![f(x)-3=x^{2}+4x](https://tex.z-dn.net/?f=f%28x%29-3%3Dx%5E%7B2%7D%2B4x)
Complete the square. Remember to balance the equation by adding the same constants to each side.
![f(x)-3+4=x^{2}+4x+4](https://tex.z-dn.net/?f=f%28x%29-3%2B4%3Dx%5E%7B2%7D%2B4x%2B4)
![f(x)+1=x^{2}+4x+4](https://tex.z-dn.net/?f=f%28x%29%2B1%3Dx%5E%7B2%7D%2B4x%2B4)
Rewrite as perfect squares
![f(x)+1=(x+2)^2](https://tex.z-dn.net/?f=f%28x%29%2B1%3D%28x%2B2%29%5E2)
-------> equation in vertex form
The vertex is the point ![(-2,-1)](https://tex.z-dn.net/?f=%28-2%2C-1%29)
The x-coordinate of the vertex is ![-2](https://tex.z-dn.net/?f=-2)
Answer:
-7k + 14
Step-by-step explanation:
(k² - 7k + 2) - (k² - 12)
k² - 7k + 2 - k² + 12
k² - k² - 7k + 2 + 12
-7k + 14
Answer:
![27\ containers](https://tex.z-dn.net/?f=27%5C%20containers)
Step-by-step explanation:
step 1
Find the volume of one container (cylinder) is equal to
![V=\pi r^{2}h](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E%7B2%7Dh)
we have
-----> the radius is half the diameter
![h=6\ cm](https://tex.z-dn.net/?f=h%3D6%5C%20cm)
substitute
![V=(3.14)(2^{2})(6)=75.36\ cm^{3}](https://tex.z-dn.net/?f=V%3D%283.14%29%282%5E%7B2%7D%29%286%29%3D75.36%5C%20cm%5E%7B3%7D)
step 2
By proportion
Find the the minimum number of identical containers that Sue would need to make
of ice
![\frac{1}{75.36}=\frac{x}{2,000}\\ \\x=2,000/75.36\\ \\x= 26.5\ containers](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B75.36%7D%3D%5Cfrac%7Bx%7D%7B2%2C000%7D%5C%5C%20%5C%5Cx%3D2%2C000%2F75.36%5C%5C%20%5C%5Cx%3D%2026.5%5C%20containers)
Round to the nearest whole number
![26.5=27\ containers](https://tex.z-dn.net/?f=26.5%3D27%5C%20containers)
I tried answering i hope this helps!