Answer:
a = 2, b = -9, c = 3
Step-by-step explanation:
Replacing x, y values of the points in the equation y = a*x^2 + b*x +c give the following:
(-1,14)
14 = a*(-1)^2 + b*(-1) + c
(2,-7)
-7 = a*2^2 + b*2 + c
(5, 8)
8 = a*5^2 + b*5 + c
Rearranging:
a - b + c = 14
4*a + 2*b + c = -7
25*a + 5*b + c = 8
This is a linear system of equations with 3 equations and 3 unknows. In matrix notation the system is A*x = b whith:
A =
1 -1 1
4 2 1
25 5 1
x =
a
b
c
b =
14
-7
8
Solving A*x = b gives x = Inv(A)*b, where Inv(A) is the inverse matrix of A. From calculation software (I used Excel) you get:
inv(A) =
0.055555556 -0.111111111 0.055555556
-0.388888889 0.444444444 -0.055555556
0.555555556 0.555555556 -0.111111111
inv(A)*b
2
-9
3
So, a = 2, b = -9, c = 3
Answer: 7.5 gallons
Step-by-step explanation:
300 divided by 40 is 7.5
Mark me as brainliest if this helps!
Answer: Tunnel tent.
Step-by-step explanation:
The tent which has the minimum area requires less nylon to manufacture,
Since, the area of Pup tent = Area of 3 square each having side 8 ft + Area of 2 equilateral triangle having side 8 ft
= 
= 
= 
= 
Now, the area of tunnel tent = Area of square having side 8 ft + total Area of half cylinder having radius 4 ft and height 8 ft
= ![8^2 + \frac{1}{2} [ 2\pi\times 4(4+8)]](https://tex.z-dn.net/?f=8%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%5B%202%5Cpi%5Ctimes%204%284%2B8%29%5D)
= 
= 
= 
Since, 214.72 < 247.43
Thus, Tunnel tent requires less nylon to manufacture.
