Answer:
Equation of line is given by:
Step-by-step explanation:
Given points:
![(-8,-2)\ and\ (-4,6)](https://tex.z-dn.net/?f=%28-8%2C-2%29%5C%20and%5C%20%28-4%2C6%29)
Slope of line
where
and
is a point on the line
![m=\frac{6-(-2)}{-4-(-8)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B6-%28-2%29%7D%7B-4-%28-8%29%7D)
![m=\frac{6+2}{-4+8}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B6%2B2%7D%7B-4%2B8%7D)
![m=\frac{8}{4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B8%7D%7B4%7D)
∴ ![m=2](https://tex.z-dn.net/?f=m%3D2)
Point-slope equation of line is given by:
where
is a point on the line and
is slope of line.
Using point
and slope
point-slope equation of line is given by:
Simplifying.
Using distribution.
Subtracting 2 to both sides.
Thus, equation of line is
The concepts you have to learn about in here are permutations and computations. They are quite the same, but they only differ in technicalities. Permutations are arrangements where order matters, otherwise, the arrangements are called combinations. For example, if you want to choose 3 winners out of the five contestants, that is a combination problem. But if you want to choose the top 3 winners out of the five contestants, this time, it is a permutation problem because order matters by ranking.
Now, choosing members of the committee is assumed to be random, if not mentioned. So, we apply the equation for combination
n!/r!(n-r)!
where
n is the total number of species per kind
r is the number of species you pick out of the total
So, out of the 12 students, 2 are seniors and 10 are non-seniors. Now, you have to find the number of ways if r is at least 1. So that means r could be 1 or 2. Therefore, the solution would be:
(10C4+ 2C1) + (10C3 + 2C2)
10C4 means 4 committee students out of the 10 non-senior students. Note that the right side numbers after C must equal to 5 because the committee must contain 5 members. The left side numbers before C signify the total pool of species to choose from. Applying the equation
10!/4!(10 - 4)! + 2!/1!(2-1)! + 10!/3!(10-3)! + 2!/2!(2-2)!
= 333
Therefore, there are a total of 333 ways.
Answer:
I believe the answer would be step 1: 12x + 15 = 12, and step 2: 12x = -3.
Step-by-step explanation:
3(4x + 5) = 12, you would foil and do 3 times 4x which is 12x, then do 3 times 5 which is 15. So the result would be 12x + 15 = 12. And the step 2 that goes along with this answer. you would do -15 on both sides of the equal sign, so now you have 12x = 12 - 15 which is -3, so it would be 12x = -3
Answer:
D. 120
Step-by-step explanation:
Array formula: A (n, p) = n! / (n -p)!
At where:
n = Total number of elements in the set.
p = Quantity of elements per arrangement
A (5.5) = 5! / (5-5)! = (5x4x3x2x1) / 0!
By definition: 0! = 1
Then: 120/1 = 120