Point (11,4) is directly below point (11,20) so a segment drawn between these two points would make a right angle.
Answer:
negative correlation
Step-by-step explanation:
Both equations have
as the left hand side.
Then, in a situation like
![y=a,\quad y=b](https://tex.z-dn.net/?f=y%3Da%2C%5Cquad%20y%3Db)
we can deduce
, since they both equal ![y](https://tex.z-dn.net/?f=y)
So, we can set up the equation
![4x^2-6x+4=x+1 \iff 4x^2-7x+3 = 0](https://tex.z-dn.net/?f=%204x%5E2-6x%2B4%3Dx%2B1%20%5Ciff%204x%5E2-7x%2B3%20%3D%200)
The solutions are
![x=\dfrac{3}{4},\quad x=1](https://tex.z-dn.net/?f=%20x%3D%5Cdfrac%7B3%7D%7B4%7D%2C%5Cquad%20x%3D1%20)
From the second equation we know that y is one more than x, so we have
![x=\dfrac{3}{4} \implies y = \dfrac{7}{4},\quad x=1 \implies y=2](https://tex.z-dn.net/?f=%20x%3D%5Cdfrac%7B3%7D%7B4%7D%20%5Cimplies%20y%20%3D%20%5Cdfrac%7B7%7D%7B4%7D%2C%5Cquad%20x%3D1%20%5Cimplies%20y%3D2%20)
Answer:
Please see attachment
Step-by-step explanation:
Please see attachment
Answer:
Diane has a booth at the state fair that sells bags of popcorn she has found that her daily costs are approximated by the function c(x) =x squared -20x+150
a) How many bags of popcorn must Diane sell to minimize her cost?
b) What is Diane’s minimum cost?
a) 10
b) 50
Step-by-step explanation:
According to the quadratic equation given in the question ,
![C(X)=x^{2} -20x+150](https://tex.z-dn.net/?f=C%28X%29%3Dx%5E%7B2%7D%20-20x%2B150)
the cost will be minimum at
![x= -\frac{b}{2a}](https://tex.z-dn.net/?f=x%3D%20-%5Cfrac%7Bb%7D%7B2a%7D)
comparing x^{2} -20x+150[/tex] with the standard quadratic equation ![ax^{2} +bx^{2} +c](https://tex.z-dn.net/?f=ax%5E%7B2%7D%20%2Bbx%5E%7B2%7D%20%2Bc)
we get
a= 1, b = -20, c=150
now
![x=-\frac{(-20)}{2(1)} \\x= 10](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7B%28-20%29%7D%7B2%281%29%7D%20%5C%5Cx%3D%2010)
Hence to minimize her cost, she must sell
a) x= 10 popcorns
and her minimum cost is
b) ![C(10)= (10)^{2} -20(10)+150\\C(10) = 100-200+150\\C(10) = 50](https://tex.z-dn.net/?f=C%2810%29%3D%20%2810%29%5E%7B2%7D%20-20%2810%29%2B150%5C%5CC%2810%29%20%3D%20100-200%2B150%5C%5CC%2810%29%20%3D%2050)