Point slope form follows the equation y-y₁=m(x-x₁), so we want it to look like that. Starting off with m, or the slope, we can find this using your two points with the formula

. Note that y₁ and x₁ are from the same point, but it does not matter which point you designate to be point 1 and point 2. Thus, we can plug our numbers in - the x value comes first in the equation, and the y value comes second, so we have

as our slope. Keeping in mind that it does not matter which point is point 1 and which point is point 2, we go back to y-y₁=m(x-x₁) and plug a point in (I'll be using (10,5)). Note that x₁, m, and y₁ need to be plugged in, but x and y stay that way so that you can plug x or y values into the formula to find where exactly it is on the line. Thus, we have our point slope equation to be

Feel free to ask further questions!
Answer:
Part 1) The expression for the perimeter is
or 
Part 2) The perimeter when z = 15 ft. is 
Step-by-step explanation:
Part 1)
we have

Find the roots of the quadratic equation
Equate the equation to zero

Complete the square
Group terms that contain the same variable, and move the constant to the opposite side of the equation

Factor the leading coefficient


Complete the square. Remember to balance the equation by adding the same constants to each side


Rewrite as perfect squares

-----> root with multiplicity 2
so
The area is equal to
![A=625(z-0.12)(z-0.12)=[25(z-0.12)][25(z-0.12)]=(25z-3)^{2}](https://tex.z-dn.net/?f=A%3D625%28z-0.12%29%28z-0.12%29%3D%5B25%28z-0.12%29%5D%5B25%28z-0.12%29%5D%3D%2825z-3%29%5E%7B2%7D)
The length side of the square is 
therefore
The perimeter is equal to



Part 2) Find the perimeter when z = 15 ft.
we have

substitute the value of z

Answer:
The expected value of X is 2 with a standard deviation of 1.34.
Step-by-step explanation:
For each speaker, there are only two possible outcomes. Either it is defective, or it is not. The probability of a speaker being defective is independent of other speakers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:

The standard deviation of the binomial distribution is:

Stereo speakers are manufactured with a probability of 0.1 of being defective
This means that 
Twenty speakers are randomly selected.
This means that 
Let the random variable X be defined as the number of defective speakers. Find the expected value and the standard deviation.


The expected value of X is 2 with a standard deviation of 1.34.