Answer:
6
Step-by-step explanation:
I am not completely sure.
3x
if x=4 then it would be 12
if x=6 then it would be 18
if x=9 then it would be 27
if x=10 then it would be 30
the side is shorter than 19 but definitely longer than 6. To me, it looks like a little more than double, more of triple and 6 times 3 is 18.
Answer: 50m
Step-by-step explanation:
"Combinations" isn't really the right word, because a combination doesn't take order of elements into account, and the outcome of a race certainly does depend on order. "Permutations" would be the correct term.
If 4 students are competing, then the race has
4! = 4 • 3 • 2 • 1 = 24
possible outcomes.
Answer:
![7x+5y-48=0](https://tex.z-dn.net/?f=7x%2B5y-48%3D0)
Step-by-step explanation:
Refer the attached figure .
We are given a line AB
Point A![=(x_1,y_1) = (-3,-1)](https://tex.z-dn.net/?f=%3D%28x_1%2Cy_1%29%20%3D%20%28-3%2C-1%29)
Point B![=(x_2,y_2) = (4,4)](https://tex.z-dn.net/?f=%3D%28x_2%2Cy_2%29%20%3D%20%284%2C4%29)
Formula for slope 'm' when two points are given :
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Substituting thew values
![m=\frac{4-(-1)}{4-(-3)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B4-%28-1%29%7D%7B4-%28-3%29%7D)
![m=\frac{5}{7}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B5%7D%7B7%7D)
Since we are given that AB is perpendicular to BC
So, By property - perpendicular slopes are negative reciprocals of each other.
![\Rightarrow m_1\times m_2 =-1](https://tex.z-dn.net/?f=%5CRightarrow%20m_1%5Ctimes%20m_2%20%3D-1)
![\Rightarrow \frac{5}{7}\times m_2 =-1](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B5%7D%7B7%7D%5Ctimes%20m_2%20%3D-1)
![\Rightarrow m_2 = \frac{-7}{5}](https://tex.z-dn.net/?f=%5CRightarrow%20m_2%20%3D%20%5Cfrac%7B-7%7D%7B5%7D)
So, Slope for line BC : ![m_2 = \frac{-7}{5}](https://tex.z-dn.net/?f=m_2%20%3D%20%5Cfrac%7B-7%7D%7B5%7D)
Point B = (4,4)
Formula of equation of line : ![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
![y-4=\frac{-7}{5}(x-4)](https://tex.z-dn.net/?f=y-4%3D%5Cfrac%7B-7%7D%7B5%7D%28x-4%29)
![5(y-4)=-7(x-4)](https://tex.z-dn.net/?f=5%28y-4%29%3D-7%28x-4%29)
![5y-20=-7x+28](https://tex.z-dn.net/?f=5y-20%3D-7x%2B28)
![7x+5y-20-28=0](https://tex.z-dn.net/?f=7x%2B5y-20-28%3D0)
![7x+5y-48=0](https://tex.z-dn.net/?f=7x%2B5y-48%3D0)
Hence the equation of line BC : ![7x+5y-48=0](https://tex.z-dn.net/?f=7x%2B5y-48%3D0)
90 counterclockwise hope I’m right