Domain:
This function is a polynomial, i.e. a sum of powers of a variables, each with its coefficient. Polynomials are defined for every possible value of the variable, so the domain is the whole real number set: 
Range:
A polynomial of degree 2 represents a parabola. Since the leading coefficients, i.e. the coefficient of the term with highest degree, is positive (in this case, it's 3), the parabola is concave up. It means that it has a minimum, and it's unbounded from above. So, the range is something like 
. To find the minimum, let's start with the "standard" parabola 
, and transform it to the one of this exercise. has minimum 0, and thus its range is 
. When you multiply it times three, its shape narrows, but the range wont change: 
. Finally, when you subtract 5, you shift everythin down 5 units. This transformation affects the range, since you have 
Image of -3:
To compute 
, simply plug 
in the formula:
Numbers associated with 43:
We want to see which x value we must choose to get a y value of 43. So, the equation is
Answer:
(3x - 1 )° is equals to 71 degreesthe statement will be 3x - 1 degree is equal to 71 degree put the like terms together 3 x is equals to 71 degrees + 1 degrees then it'll be 3 x is equals to 72 then divide both sides by 3 will get x is equals to 24 degrees
Given:
x: [1 2 3 4 5 6 7]
y: [9 9.5 10.25 11.25 12.5 14 15.75]
Let the function which models the data be
y(x) = ax² + bx + c
Apply the function to the first three data points
a + b + c = 9 .(1)
4a + 2b + c = 9.5 (2)
9a + 3b + c = 10.25 (3)
Subtract (1) from (2).
3a + b = 0.5
or
b = 0.5 - 3a (4)
Subtract (1) from (3).
8a + 2b = 1.25 (5)
Substitute (4) into (5).
8a + 2(0.5 - 3a) = 1.25
2a = 0.25
a = 0.125
From (4),
b = 0.5-3*0.125 = 0.125
From (1),
c = 9 - 0.125 - 0.125 = 8.75
The function is
y = 8.75 + 0.125x + 0.125x²
Check that the function works for x=4,5,6,7.
From the calculator, obtain
y(4) = 11.25 Correct
y(5) = 12.5 Correct
y(6) = 14 Correct
y(7) = 15.75 Correct
The graph of the function is shown below.
Answer: y = 8.75 + 0.125x + 0.125x²
Answer:
A = 24
Step-by-step explanation:
We can see that the face of the given rectangular prism shows the width 4 and the height of 6. If we cut the figure at any point along the length 20, such that the cross section is parallel to the face, the cross section, which occurs at x length, will always have the same dimensions, that are 4 and 6.
So the area of the cross section which is parallel to the face of the given rectangular prism is given by:
A = 6 × 4
A = 24
Answer:
15
Step-by-step explanation:
we know that the boys in total cost 75 dollars and the girls cost 90.
75 and 90 share but one common factor and that is 15.
Therefore, we can conclude that the tickets cost $15.
