Answer:
![f(x)=x^2+16](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2%2B16)
Step-by-step explanation:
By the conjugate rule, if -4i is a root, then so is +4i. So we have 2 roots, thus, we have a second degree polynomial (namely, a quadratic). If
x = -4i, then
x + 4i is a root.
If
x = 4i, then
x - 4i is a root.
Having (x - 4i)(x + 4i) as roots, we can now FOIL them together to get a polynomial of least degree.
FOILing gives us
![x^2+4ix-4ix-16i^2](https://tex.z-dn.net/?f=x%5E2%2B4ix-4ix-16i%5E2)
Notice that the +4ix and the -4ix cancel each other out, leaving you with
![x^2-16i^2](https://tex.z-dn.net/?f=x%5E2-16i%5E2)
Since
![i^2=-1](https://tex.z-dn.net/?f=i%5E2%3D-1)
we can make the substitution:
![x^2-16(-1)](https://tex.z-dn.net/?f=x%5E2-16%28-1%29)
which simplifies to
![x^2+16](https://tex.z-dn.net/?f=x%5E2%2B16)
In function notation form:
![f(x)=x^2+16](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2%2B16)
Answer:
Infinite or 2
Step-by-step explanation:
Since, we can take any side we want, infinite number of triangles can be formed.
However, if more than one similar triangles aren't allowed, then the value is (3-1)! = 2! = 2.
Answer:
2 bags
Step-by-step explanation:
Let the number of bags be b.
Let the number of candies in each bag be c.
The number of bags was 9 less than the number of candies in each bag. That is:
b = c - 9
She bought 22 candies.
This means that The number of candy in each bag multiplied by the numbe of each bag is 22:
b * c = 22
bc = 22
=> (c - 9) * c = 22
![c^2 - 9c = 22\\\\c^2 - 9c - 22 = 0\\\\c^2 - 11c + 2c - 22 = 0\\\\c(c - 11) + 2(c - 11) = 0\\\\(c + 2) (c - 11) = 0\\\\=> c = -2, c = 11](https://tex.z-dn.net/?f=c%5E2%20-%209c%20%3D%2022%5C%5C%5C%5Cc%5E2%20-%209c%20-%2022%20%3D%200%5C%5C%5C%5Cc%5E2%20-%2011c%20%2B%202c%20-%2022%20%3D%200%5C%5C%5C%5Cc%28c%20-%2011%29%20%2B%202%28c%20-%2011%29%20%3D%200%5C%5C%5C%5C%28c%20%2B%202%29%20%28c%20-%2011%29%20%3D%200%5C%5C%5C%5C%3D%3E%20c%20%3D%20-2%2C%20c%20%3D%2011)
Since the number of candies can only be a positive number, c = 11.
Therefore:
b = 11 - 9
b = 2
Katy bought 2 bags of candy containing 11 candies each.
Answer:
4/9 is the answer
Step-by-step explanation:
Answer:
D.
Step-by-step explanation:
You cannot plan your thoughts if you are just thinking out loud.