If

is the variable of the horizontal axis, then you can solve for

to get the equation of the line in slope-intercept form in the

plane:

i.e. a line with slope

through the origin, which means it is contained in the first and third quadrants. Since the terminal side of

has a negative sine, the angle must lie in the third quadrant.
Because the slope of the line is

, you can choose any length along the line to make up the hypotenuse of a right triangle with reference angle

. Any such right triangle will have

, regardless of whether the angle is the first or third quadrant. But since

is known to lie in the third quadrant, and so

and

are both negative, you have
There are 21 black socks and 9 white socks. Theoretically, the probability of picking a black sock is 21/(21+9) = 21/30 = 0.70 = 70%
Assuming we select any given sock, and then put it back (or replace it with an identical copy), then we should expect about 0.70*10 = 7 black socks out of the 10 we pick from the drawer. If no replacement is made, then the expected sock count will likely be different.
The dot plot shows the data set is
{5, 5, 6, 6, 7, 7, 7, 8, 8, 8}
The middle-most value is between the first two '7's, so the median is (7+7)/2 = 14/2 = 7. This can be thought of as the average expected number of black socks to get based on this simulation. So that's why I consider it a fair number generator because it matches fairly closely with the theoretical expected number of black socks we should get. Again, this is all based on us replacing each sock after a selection is made.
Hello there!
3x - y = 3
-x + y = 3
We need to solve 3x - y = 3 for y
Let start by adding -3x to both sides
3x - y = 3
3x - 3x - y = 3 - 3x
-y = 3 - 3x
We cannot leave the variable with a negative sign. We must multiply both sides by -1
-y * -1= (3 - 3x)-1
y = 3x - 3
Substitute 3x -3 for y in -x+y=3
-x + y = 3
-x + 3x - 3 = 3
2x - 3 = 3
2x = 3 + 3
2x = 6
x = 6/2
x = 3
Now substitute 3 for x in y=3x -3
y = 3x - 3
y = 3(3) - 3
y= 9 - 3
y= 6
Thus,
The answer is x=3 and y=6
It is always my pleasure to help students like you :)
As always, I am here to help!
I’ll assume the c is b. (1/2) x (5) x (2) x (2) is 10