Answer:
See below
Step-by-step explanation:
Quadratic equations with one solution are:
![(x+2)^2 = 0, \:\: (2x-8)^2 = 0](https://tex.z-dn.net/?f=%20%28x%2B2%29%5E2%20%3D%200%2C%20%5C%3A%5C%3A%20%282x-8%29%5E2%20%3D%200)
Quadratic equations with two solutions are:
![(2x-11)^2 = 1](https://tex.z-dn.net/?f=%20%282x-11%29%5E2%20%3D%201%20)
Quadratic equations with no solution are:
![(x+2)^2 = - 4, \:\: x^2 + 6 = - 3](https://tex.z-dn.net/?f=%20%28x%2B2%29%5E2%20%3D%20-%204%2C%20%5C%3A%5C%3A%20x%5E2%20%2B%206%20%20%3D%20-%203)
The outlier, 78, is removed from the data set shown. 23, 23, 25, 27, 34, 34, 35, 41, 45, 45, 78 How does this affect the range?
KATRIN_1 [288]
Hello.
The range with 78 is 55
without 78 is 22
So the range goes down
Have a nice day
The growth of the population
Answer:
b-5
Step-by-step explanation:
because you are using the coupon which means to subtract since you are saving $ 5 from b dollars
Answer:
Option d. (-2,-5)
Step-by-step explanation:
we know that
The equation of a vertical parabola in vertex form is equal to
![y=a(x-h)^{2} +k](https://tex.z-dn.net/?f=y%3Da%28x-h%29%5E%7B2%7D%20%2Bk)
where
a is a coefficient
(h,k) is the vertex of the parabola
In this problem we have
![y=x^{2} +4x-1](https://tex.z-dn.net/?f=y%3Dx%5E%7B2%7D%20%2B4x-1)
This is the equation of a vertical parabola open up
The vertex is minimum
Convert the equation in vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
![y+1=x^{2} +4x](https://tex.z-dn.net/?f=y%2B1%3Dx%5E%7B2%7D%20%2B4x)
Complete the square. Remember to balance the equation by adding the same constants to each side.
![y+1+4=x^{2} +4x+4](https://tex.z-dn.net/?f=y%2B1%2B4%3Dx%5E%7B2%7D%20%2B4x%2B4)
![y+5=x^{2}+4x+4](https://tex.z-dn.net/?f=y%2B5%3Dx%5E%7B2%7D%2B4x%2B4)
Rewrite as perfect squares
![y+5=(x+2)^{2}](https://tex.z-dn.net/?f=y%2B5%3D%28x%2B2%29%5E%7B2%7D)
-----> equation in vertex form
therefore
The vertex is (-2,-5)