Answer:

Step-by-step explanation:
You can use the work they gave you and continue from there:

First, simplify the numerator:

Finally, simplify the denominator:

Answer:
-2y+6
Step-by-step explanation:
Multiply (y-3) by -2
Answer:

Step-by-step explanation:
Given

Required
Determine the period
A sine function is represented as:

Where

By comparing:
and 

So:

So, we have:



Hence, the period of the function is 
Answer:
It will take 60 seconds for the signs to light up at the same time again.
Step-by-step explanation:
Given:
One sign lights up every 10 seconds
One sign lights up every 12 seconds
They have just lit up at the same time.
To find in how many seconds will it take for the signs to light up at the same time again.
Solution:
In order to find the time in seconds will it take for the signs to light up at the same time again, we need to find the least common multiple of the the times for which the given signs light up.
The numbers are 10 and 12.
To find the LCM, we will list the multiples of each and check the least common multiple.
The multiples of 10 and 12 are :


thus, we can see that 60 is the least common multiple.
Thus, the signs will light up at the same time time after every 60 seconds.
Step-by-step explanation:
When it says y varies directly with x it just means that y and x are proportional/equal to each other. The constant of variation and the constant of proportionality are the same thing just different way of saying it so they can confuse you and make your life miserable. Since y and x are proportional to each other and the constant of proportionalty is -5 to make an equation that represents a line you use the formula y=mx+b. That is the slope of the line. With that formula let's first plus in the x so we have y=m2+b. The formula for direct variation is y=kx as well that's good to know and it's good to memorize all these formulas. Math becaomes easier when you have the process down pat and you just need to plug numbers into different equations, expressions, and scenarios. Do m = [y1 - y2] / [x1 - x2] and you'll get the answer.