Answer:
The function rule is

Step-by-step explanation:
The given ordered pairs are (0,-1), (1,0),(2,3),(3,8),(4,15)
We can observe the following pattern.





When we generalize this pattern, we obtain:

This is the function equation.
The function rule is

Answer:
35
Step-by-step explanation:
40=1/2(115-x)
80=115-x
-35=-x
x=35
The triangle formed by the vertices would be equilateral if the sides of the triangle coincide with the diagonals of the square face that defines the cube. See the attached sketch if that description is unclear.
Count the number of equilateral triangles that are possible. Such a triangle will always use up 3 vertices of the cube, and separate 1 vertex from the remaining 4. This means there are as many equilateral triangles as there are corners in the cube: 8.
Count the total number of triangles that can be made. From the 8 available vertices, we only need 3. If we fix 3 vertices, it doesn't matter in which order we connect them to make a triangle, so we count the number of combinations of 8 vertices taking 3 at a time, which is

Then the probability of forming an equilateral triangle is 8/56 = 1/7.
85) I gonna do substitution to solve them.
First lets find number of boys.
boys = x
girls = x - 5
27 = x + x - 5 --) 27 = 2x - 5 --) 32 = 2x --) 16 = x
There are 16 boys.
Now do the opposite with girls.
boys = x + 5
girls = x
27 = x + x + 5 --) 27 = 2x + 5 --) 22 = 2x --) 11 = x
There are 11 girls.
86) I gonna do subsitution to solve this problem too.
x + y = 82
6x + 2y = 284
First find # of car magnets
y = -x + 82
6x + 2( -x + 82 ) = 284 --) 6x - 2x + 164 = 284 --) 4x + 164 = 284 --) 4x = 120 --)
x = 30
There are 30 car magnets.
x = -y + 82
6( -y + 82 ) + 2y = 284 --) -6y + 492 + 2y = 284 --) -4y + 492 = 284 --) -4y = -208 --) 4y = 208 --) y = 52
There are 52 bumper stickers