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

.
Answer:
8
Step-by-step explanation:
i have 6 apples + 2 peers
Answer:

Step-by-step explanation:
The first line has a slope of -5/3 found using the points in the slope formula.

Parallel lines have the same slope. So -5/3 is the slope of the second line. Write its equation using the point slope form
.

1.4
= 1+ 0.4
= 1+ 4/10
= 1+ (4/2) / (10/2)
= 1+ 2/5
= 1 2/5
The final answer is 1 2/5.