Answer:
a) 6 ways
b) 6 ways
Step-by-step explanation:
a) for all of the letters
for the first letter, we have 3 options
for the second, we have 2 options
for the third, we have 1 option
So the number of options will be;
3 * 2 * 1 = 6
b) for the first, we have 3 options, for the second, we have 2 options
so the number of options will be 3 * 2 = 6 options
Answer:
52
Step-by-step explanation:
Simplify the expression (Steps shown below).
Answer:
y = -1/3x -2
Step-by-step explanation:
Answer:
Y=-4/5x+3/5y
Step-by-step explanation: first get the gradient
3--1/-3-2
=4/-5
y-3/x+3=4/-5
-5y+15=4x+12
-5y=4x-3
y=4/-5x+3/5
Check the picture below.
the distance from 1,2 to 1,8 is simply 6 units, we can read that off the grid. Now let's see what the other distances are, and add them all up to get the perimeter.
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{2})\qquad C(\stackrel{x_2}{5}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AC=\sqrt{(5-1)^2+(5-2)^2}\implies AC=\sqrt{4^2+3^2} \\\\\\ AC=\sqrt{25}\implies AC=5 \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%20%5C%5C%5C%5C%20A%28%5Cstackrel%7Bx_1%7D%7B1%7D~%2C~%5Cstackrel%7By_1%7D%7B2%7D%29%5Cqquad%20C%28%5Cstackrel%7Bx_2%7D%7B5%7D~%2C~%5Cstackrel%7By_2%7D%7B5%7D%29%5Cqquad%20%5Cqquad%20d%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20AC%3D%5Csqrt%7B%285-1%29%5E2%2B%285-2%29%5E2%7D%5Cimplies%20AC%3D%5Csqrt%7B4%5E2%2B3%5E2%7D%20%5C%5C%5C%5C%5C%5C%20AC%3D%5Csqrt%7B25%7D%5Cimplies%20AC%3D5%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\bf B(\stackrel{x_1}{1}~,~\stackrel{y_1}{8})\qquad C(\stackrel{x_2}{5}~,~\stackrel{y_2}{5}) \\\\\\ BC=\sqrt{(5-1)^2+(5-8)^2}\implies BC=\sqrt{4^2+3^2} \\\\\\ BC=\sqrt{25}\implies BC=5 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{perimeter}{6+5+5\implies 16}~\hfill](https://tex.z-dn.net/?f=%5Cbf%20B%28%5Cstackrel%7Bx_1%7D%7B1%7D~%2C~%5Cstackrel%7By_1%7D%7B8%7D%29%5Cqquad%20C%28%5Cstackrel%7Bx_2%7D%7B5%7D~%2C~%5Cstackrel%7By_2%7D%7B5%7D%29%20%5C%5C%5C%5C%5C%5C%20BC%3D%5Csqrt%7B%285-1%29%5E2%2B%285-8%29%5E2%7D%5Cimplies%20BC%3D%5Csqrt%7B4%5E2%2B3%5E2%7D%20%5C%5C%5C%5C%5C%5C%20BC%3D%5Csqrt%7B25%7D%5Cimplies%20BC%3D5%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20%5Cstackrel%7Bperimeter%7D%7B6%2B5%2B5%5Cimplies%2016%7D~%5Chfill)
