In this system of equations, I'll do elimination. Ok, so what we are trying to do is to eliminate a variable, but we can't. So since -2y is negative, and y has a coefficient of 1 and is positive, let's multiply the first whole equation by 2.
2 times (3x+y=11) is 6x+2y=22. (I just used distributive property.) Now let's add from left to right.
6x plus x is 7x, 2y plus -2y is 0, and 22 plus 6 is 28. Now we have this simple equation, 7x=28. We can simply divide each side by 7, to get x as 4. So x=4 in this set of equations. Now all we need to do is plug x in the equation then solve for y. For this system of equations, I'll use the first equation, because it is easier. So I'll plug x as 4 into the equation to get 12+y=11. Now we can simply solve for y. 11-12 is -1, so y must equal -1. So y=-1. Therefore, x=4 and y=-1. Hope I helped.
Answer:
1/64, 1/256, 1/1024
Step-by-step explanation:
To get from 16 to 4 we multiply by 1/4
To get from 4 to 1 we multiply by 1/4
Each time we multiply by 1/4
The next term would be 1/16 * 1/4
1/16 * 1/4 = 1/64
The take that term 1/64 and multiply by 1/4
1/64*1/4 = 1/256
Finally take 1/256 and multiply by 1/4
1/256*1/4 =1/1024
Use the polynomial remainder theorem. If

is a polynomial of degree

, then we can divide by a linear term

to get a quotient

and remainder

of the form

Then when

, we get

. In other words, the value of

at

tells you the value of the remainder upon dividing

by

.
So given that

, and the remainder upon dividing

by

is -8, we know that

, so


Since

is a polynomial (not a rational expression), then we know that

divides

exactly. In particular, the remainder term of this quotient is 0. We can use long or synthetic division to determine

. I prefer typing out the work for synthetic division:
-1 | 1 -4 15 k + 8
. | -1 5 -20
- - - - - - - - - - - - - - - - - -
. | 1 -5 20 k - 12
The remainder here has to be 0, so

.
Finally, we can get the remainder upon dividing

by

by evaluating

, which gives

.
Answer:
2.25
Step-by-step explanation:
Just add it up, IDK if it's the full answer because you had 3 dots (...).