Answer:
So the answer is 
Step-by-step explanation:
Given,
Using
four times and
one time getting to 
If we are write this way then easily get the answer;

Add together
by making a common denominator of
and also add
in the second set of parenthesis to yield 


(By Cross-reduce and multiply the fractions)

∴ 
Answer:
21
Step-by-step explanation:
Chickens - 2x
cows - 4x
goats = 4x
2x+4x+4x+210
10x=210
x=21
CHECK:
21 chickens = 42 legs
21 cows = 84 legs
21 goats = 84 legs
42+84+84=210 legs
Answer:
x = -1
Step-by-step explanation:
6 − 4x = 6x − 8x + 8
Combine 6x and −8x to get −2x.
6 − 4x = −2x + 8
Add 2x to both sides.
6 − 4x + 2x = 8
Combine −4x and 2x to get −2x.
6 − 2x = 8
Subtract 6 from both sides.
−2x = 8 − 6
Subtract 6 from 8 to get 2.
−2x = 2
Divide both sides by −2.

Divide 2 by −2 to get −1.

Hope this helps and have a great day! =D
If period of

is one-half the period of

and
<span>

has a period of 2π, then

and

.
</span>
To find the period of sine function

we use the rule

.
<span /><span />
f is sine function where f (0)=0, then c=0; with period

, then

, because

.
To find a we consider the condition

, from where

.
If the amplitude of

is twice the amplitude of

, then

has a product factor twice smaller than

and while period of

<span> </span> is 2π and g(0)=0, we can write

.
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

.