A function 

 is periodic if there is some constant 

 such that 

 for all 

 in the domain of 

. Then 

 is the "period" of 

.
Example:
If 

, then we have 

, and so 

 is periodic with period 

.
It gets a bit more complicated for a function like yours. We're looking for 

 such that

Expanding on the left, you have

and

It follows that the following must be satisfied:

The first two equations are satisfied whenever 

, or more generally, when 

 and 

 (i.e. any multiple of 4).
The second two are satisfied whenever 

, and more generally when 

 with 

 (any multiple of 10/7).
It then follows that all four equations will be satisfied whenever the two sets above intersect. This happens when 

 is any common multiple of 4 and 10/7. The least positive one would be 20, which means the period for your function is 20.
Let's verify:


More generally, it can be shown that

is periodic with period 

.
 
        
        
        
1)
Let the number of fish sandwiches sold br represented by x
Then the number of grilled cheese sold is 2X
and the number of cheeseburgers 3(2x)
x + 2x + 3(2x) = 225
and solve
2) 
Let x represent the no. of pounds of peanuts
Then x + 14 represents the no of pounds of the mixture
And
(2.25)x + (3.25)(14) = (2.65)(x + 14
and solve
3) Try on your own
plz mark me as brainliest :)
 
        
             
        
        
        
Answer:
46in
Step-by-step explanation:
brainiest is appreciated
 
        
                    
             
        
        
        
Composing functions means that the input of the outer functions is the output of the inner function.
In fact, you can rewrite the circle notation as

So, we can substitute g(x) with its expression:

And since f(x)=x+5, we simply have to add 5 to its input:

Similarly, we have, substituting f with its expression,

And since g(x)=4x+2, we have to multiply the input by 4 and add 2:

 
        
             
        
        
        
Answer: D) 1.47x + 1.61y = 229.11
Explanation: The amount of beverages and candy sold combined (addition) should be set equal to the targeted goal per game ($229.11).