Answer:
6 ways - ab,ac, ba,bc and ca,cb
Step-by-step explanation:
We are given 3 letters a,b,c.
We can choose the first letter in 1 out of 3 ways.
Once the first letter has been chosen without replacement, we have two letters remaining. Another letter can be chosen from the 2 remaining letters in 2 ways. So the total number of ways of choosing the two letters is 3*2 = 6.
Listing out the possible set of choices:
Options include: ab,ac, ba,bc and ca, cb
![▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪](https://tex.z-dn.net/?f=%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA%20%20%7B%5Chuge%5Cmathfrak%7BAnswer%7D%7D%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA%E2%96%AA)
Let's calculate the slope (m) of line passing through points (2 , 5) and (3 , 4)
Consider the coordinates of the points, and now apply the formula ~
![\qquad \sf \dashrightarrow \: m = \dfrac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20%20m%20%3D%20%5Cdfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D%20)
![\qquad \sf \dashrightarrow \: m = \dfrac{4 - 5}{3 - 2}](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20m%20%3D%20%20%5Cdfrac%7B4%20-%205%7D%7B3%20-%202%7D%20)
![\qquad \sf \dashrightarrow \: m = \dfrac{ - 1}{1}](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20m%20%3D%20%20%5Cdfrac%7B%20-%201%7D%7B1%7D%20)
![\qquad \sf \dashrightarrow \: m = - 1](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20m%20%3D%20%20-%201)
Therefore, the slope if the required line Is -1
Answer:
jdj says that he will have a problem soon and I am so sorry to see her in my life now but she doesn't know anything but she has not met comedy ever here In America stills nothing surely why'd you
Answer:
x = 1 and y = 5
Step-by-step explanation:
Use substitution because you know that x = y - 4, and plug this into the first equation to get -10(y - 4) + 3y = 5, or -10y + 40 + 3y = 5. This is -7y = -35 so y = 5. Plug this into the 2nd equation to get that x = 1 and y = 5.
Answer: Third Option
yes; k = 4 and y = 4x
Step-by-step explanation:
Observe in the values of x and y given that when x decreases the variable-y also decreases.
Then the variation is direct.
Then, if between any two points of the function, the rate of variation k remains the same then the variation is constant.
We can test whether these conditions are met by using the given points.
(-2, -8) and (-4, -16)
The rate of variation k for these points is:
![k = \frac{y_2-y_1}{x_2-x_1}\\\\k =\frac{-16-(-8)}{-4-(-2)}\\\\k = \frac{-16+8}{-4+2}\\\\k =4](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5C%5C%5Ck%20%3D%5Cfrac%7B-16-%28-8%29%7D%7B-4-%28-2%29%7D%5C%5C%5C%5Ck%20%3D%20%5Cfrac%7B-16%2B8%7D%7B-4%2B2%7D%5C%5C%5C%5Ck%20%3D4)
Now we calculate the variation rate for the points
(-4, -16) and (-6, -24)
![k = \frac{y_2-y_1}{x_2-x_1}\\\\k =\frac{-24-(-16)}{-6-(-4)}\\\\k = \frac{-24+16}{-6+4}\\\\k =4](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5C%5C%5Ck%20%3D%5Cfrac%7B-24-%28-16%29%7D%7B-6-%28-4%29%7D%5C%5C%5C%5Ck%20%3D%20%5Cfrac%7B-24%2B16%7D%7B-6%2B4%7D%5C%5C%5C%5Ck%20%3D4)
The rate of variation is constant and equal to 4.
Then the answer is yes; k = 4 and y = 4x