Answer:
n^2/(n + 5)
Step-by-step explanation:
The numerators are 1^2, 2^2, 3^2, 4^2, etc.
The denominators are 6, 7, 8, 9, etc.
The nth numerator is n^2.
The nth denominator is n + 5.
Answer: n^2/(n + 5)
Answer:
6.08 kg bag unit price: $1.72
7.48 kg bag unit price: $1.86
6.08 kg bag is the better buy
Step-by-step explanation:
To find unit price, divide the price by the amount. 10.47 divided 6.08 equals 1.7203947. Round it to the nearest cent to get 1.72. So, the unit price for the first bag is $1.72. Next divide 13.88/7.48 to get 1.85561. Round it to the nearest cent to get 1.86. So, the unit price for the second bag is $1.86 per kg. The better buy is the cheaper one, so the 6.08 kg bag is a better deal. Hope this helped!
The function in vertex form is
⇒ 3rd answer
Step-by-step explanation:
The vertex form of the quadratic function f(x) = ax² + bx + c is
f(x) = a(x - h)² + k, where
- a is the coefficient of x²
- (h , k) are the coordinates of the vertex point
, wher b is the coefficient of x- k = f(h), that means value f(x) when x = h
∵ f(x) = x² + x + 1
∴ a = 1 , b = 1
∵ ![h=\frac{-b}{2a}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B-b%7D%7B2a%7D)
- Substitute the values of a and b to find h
∴ ![h=\frac{-1}{2(1)}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B-1%7D%7B2%281%29%7D)
∴ ![h=\frac{-1}{2}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B-1%7D%7B2%7D)
Substitute the value of x in f(x) by the value of h to find k
∵ f(
) = ![(\frac{-1}{2})^{2}+\frac{-1}{2}+1](https://tex.z-dn.net/?f=%28%5Cfrac%7B-1%7D%7B2%7D%29%5E%7B2%7D%2B%5Cfrac%7B-1%7D%7B2%7D%2B1)
∴ f(
) = ![\frac{1}{4}-\frac{1}{2}+1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D-%5Cfrac%7B1%7D%7B2%7D%2B1)
∴ f(
) = ![\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D)
- k is the value of f(x) when x = h
∵ h = ![\frac{-1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B2%7D)
∴ k = f(
)
∴ k = ![\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D)
Substitute the values of a, h and k in the vertex form
∵ f(x) = a(x - h)² + k
∵ a = 1 ,
, ![k=\frac{3}{4}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B3%7D%7B4%7D)
∴ ![f(x)=1(x-\frac{-1}{2})^{2}+\frac{3}{4}](https://tex.z-dn.net/?f=f%28x%29%3D1%28x-%5Cfrac%7B-1%7D%7B2%7D%29%5E%7B2%7D%2B%5Cfrac%7B3%7D%7B4%7D)
∴ ![f(x)=(x+\frac{1}{2})^{2}+\frac{3}{4}](https://tex.z-dn.net/?f=f%28x%29%3D%28x%2B%5Cfrac%7B1%7D%7B2%7D%29%5E%7B2%7D%2B%5Cfrac%7B3%7D%7B4%7D)
The function in vertex form is ![f(x)=(x+\frac{1}{2})^{2}+\frac{3}{4}](https://tex.z-dn.net/?f=f%28x%29%3D%28x%2B%5Cfrac%7B1%7D%7B2%7D%29%5E%7B2%7D%2B%5Cfrac%7B3%7D%7B4%7D)
Learn more:
You can learn more about the quadratic functions in brainly.com/question/9390381
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Answer: download photo math
Step-by-step explanation: