There are 73 students in the eighth grade class at Garfield Middle
School. Eleven do not participate in after-school activities. Of the
remaining students, 35 participate in volleyball (V) and 39 are
members of the Student Council (SC). How many students
participate in both volleyball and student council? Fill in the
correct numbers in the Venn diagram and explain your answer.

12 students are in both Volleyball and Student Council.

To find this, take 73 and take away 11 to get 62.This is because 11 students don't participate in any activities.

Next, add together 35 and 39 to get 74. Then, subtract 62 from 74 to get 12 which equals the number of people in both activities.

To check this, subtract 12 from 35 and 39. In doing so, you will get 23 and 27. Now add 23, 27, 11, and 12. This will give you 73, which is the number of students in the 8th grade.

Below is a picture of a Venn Diagram to show this. I hope this helps!

(1,4) is on graph of f(x)

f(1) = 4

so 1/4 f(x)

1/4 f(1)

1/4. ×4

1

so point for function 1/4. f(x) is (1,1)

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!