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:
d ≈ 21.26 units
Step-by-step explanation:
calculate the distance d using the distance formula
d =
with (x₁, y₁ ) = (- 3, 8 ) and (x₂, y₂ ) = (13 - 6 )
d =
=
=
=
=
≈ 21.26 units ( to 2 dec. places )
Answer:
Step-by-step explanation:
We know the property of derivative:
Given function :
Differentiate both sides with respect to x , we get
[By Chain rule]
[Since , where a is scalar and ]
Hence, the derivative of the given function is .
Answer:
See below.
Step-by-step explanation:
Part A: A system will have no solution when the graphs are parallel and do not intersect.
Part B: A system will have no solution when the equations have the exact same slope. The same slope means they are parallel and do not intersect. This is done easiest in slope-intercept form.
Answer:
2x + 6
Step-by-step explanation: