Answer:
really?
Step-by-step explanation:
Answer: 50 calories
Step-by-step explanation:
One serving of a certain brand of microwave popcorn provides 150 calories, 90 of which are from fat. The fraction that comes from fat:
= 90/150 = 3/5
One serving of a certain brand of low-sodium pretzels provides 120 calories, 12 of which are from fat. The fraction that comes from fat here:
= 12/120 = 1/10
The fat that are provided by a 100 calorie serving of the microwave popcorn would be:
= 3/5 × 100
= 60
The fat that are provided by a 100-calorie serving of the pretzels would be:
= 1/10 × 100 = 10
The difference from fat that are provided by a 100 calorie serving of the microwave popcorn than are provided by a 100-calorie serving of the pretzels would be:
= 60 - 10
= 50 calories
Answer: ![a = -2](https://tex.z-dn.net/?f=a%20%3D%20-2)
![b = 8](https://tex.z-dn.net/?f=b%20%3D%208)
Step-by-step explanation:
Given :
![x^{2} +ax](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2Bax%3Cb)
re - writing the equation , we have
![x^{2} +ax-b](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2Bax-b%3C0)
we need to find the value of a and b for which -2<x < 4 , this means that the roots of the quadratic equation are -2<x < 4.
The formula for finding the quadratic equation when the roots are known is :
- sum of roots(x) + product of root = 0
sum of roots = -2 + 4 = 2
product of roots = -2 x 4 = -8
substituting into the formula , we have:
, which could be written in inequality form as
![x^{2} -2x-8](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-2x-8%3C0)
comparing with
, it means that :
![a = -2](https://tex.z-dn.net/?f=a%20%3D%20-2)
![b = 8](https://tex.z-dn.net/?f=b%20%3D%208)
Answer:
24/35 or 0.6857142
Step-by-step explanation:
Answer: The required value is
![(f-g)(x)=x^2+8.](https://tex.z-dn.net/?f=%28f-g%29%28x%29%3Dx%5E2%2B8.)
Step-by-step explanation: The given functions are:
![f(x)=2x^2+1,\\\\g(x)=x^2-7.](https://tex.z-dn.net/?f=f%28x%29%3D2x%5E2%2B1%2C%5C%5C%5C%5Cg%28x%29%3Dx%5E2-7.)
We are given to find the value of ![(f-g)(x).](https://tex.z-dn.net/?f=%28f-g%29%28x%29.)
We know that, if s(x) and t(x) are any two functions of a variable x, then we have
![(s-t)(x)=s(x)-t(x).](https://tex.z-dn.net/?f=%28s-t%29%28x%29%3Ds%28x%29-t%28x%29.)
Therefore, we have
![(f-g)(x)\\\\=f(x)-g(x)\\\\=(2x^2+1)-(x^2-7)\\\\=2x^2+1-x^2+7\\\\=x^2+8.](https://tex.z-dn.net/?f=%28f-g%29%28x%29%5C%5C%5C%5C%3Df%28x%29-g%28x%29%5C%5C%5C%5C%3D%282x%5E2%2B1%29-%28x%5E2-7%29%5C%5C%5C%5C%3D2x%5E2%2B1-x%5E2%2B7%5C%5C%5C%5C%3Dx%5E2%2B8.)
Thus, the required value is
![(f-g)(x)=x^2+8.](https://tex.z-dn.net/?f=%28f-g%29%28x%29%3Dx%5E2%2B8.)