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
the formula for area of a rectangle is
Area = length x width
since both the length and the width of the rectangle lie on the same x and y axis, we can find the distance between the width and the distance between the length by subtracting
(-4,9) (-4,-3)
these points lie on the same x axis, so they create a vertical line
9-(-3) = 12
12 units is the distance between them
(-4,-3) (-1,-3)
these points lie on the same y axis, so they create a horizontal line
-1-(-4) = 3
3 units is the distance between them
now that we have the length and the width, we can find the area
A = 12 x 3
A = 36 units²
Answer:
5/33
Step-by-step explanation:
Answer:
E
Step-by-step explanation:
If you add 22 onto the sum of all the points and divide by the amount of games (6), you get 12.
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