Which expression can be used to determine the number of people who can sit as a group if y tables are joined to form 1 long table? Justify in words why your answer is correct.
a) 4(y + 1)
b) 369 + 1)
c) 2(2y + 1)
d) 6y

c) 2(2y+1)

Step-by-step explanation:

This is because when the tables are together there can be 4 people at each table, plus 1 at either end. Whatever equation you have must have +2 in it, to account for the ends of the tables. The number of tables (y) must be multiplied by 4 because there are always 4 people per table. The number of tables is unknown so 4y must be in your equation.

2(2y+1) simplifies to 4y+2, which is the equation we want.

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!