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:
The correct options are 2 and 4.
Step-by-step explanation:
From the given box plot it is clear that





We know that these number divides the data in four equal parts.



25% of the data values lies between 50 and 110. Therefore option 1 is incorrect.
Seventy-five percent of the data values lies between 20 and 50. Therefore option 2 is correct.
It is unlikely that there are any outliers. This statement is not true because the is a huge difference between third quartile and maximum value.
Therefore option 3 is incorrect.
The interquartile range is

Therefore option 4 is correct.
The range is
Range = Maximum-Minimum

Therefore option 5 is incorrect.
2(x+3)= 3x-1
2x+6=3x-1
X=7
Therefore
YM = 7+3= 10
And by definition of midpoint YM=MZ so MZ=10
angles in a triangle need to equal 180 degrees
so x = 180 - 47 - 58
x = 180-105
x= 75 degrees
ANSWER

EXPLANATION
The given function is;

The constant term is 11.
The coefficient of the leading term is 5.
The factors of 11 are ±1,±11
The factors of 5 are ±1,±5
According to the Rational roots Theorem,
the potential roots are obtained by expressing the factors of the constant term over the coefficient of the leading term.
