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See W/A here and press "show details":

https://www.wolframalpha.com/input/?i=use+long+division++%5Cfrac%7Bx%5E4-2x%5E3%2B3x%5E2-4x%2B6%7D%7Bx%5E2%2B2x-1%7D

Well, I tried it and got an answer, but when I expanded the answer, it wasn't the original equation.

I got (x²+2x-1)(x²-4x+10)-28x+4.

I don't know what I did wrong though so that's what I was hoping you could help with. (That answer is in polynomial form, with -28x+4 being my remainder.)

Try watching and learning from this clip:

Thanks a lot! That really helps :-)

6 people

there is no head of the tabel so the first person is just a place marker so there are really only 5 people whose positions matter.

But John and sam are tied together so thet are the equaivalent of one person.

so that is only 4 people.

4!     *2   because it could be john, sam or sam, john. 

2*3*4*2 = 48 permutations.

thank you very much!

Simplify the following:
sqrt(-i)

Express -i as a square using -i = (1 - 2 i + i^2)/2, then look to factor.
-i = 1/2 - i - 1/2 = (1 - 2 i - 1)/2 = (1 - 2 i + i^2)/2 = (-i + 1)^2/2:
 sqrt(1/2 (-i + 1)^2 ) 

For all n>=0, sqrt(m/n) = (sqrt(m))/(sqrt(n)).
sqrt(1/2 (1 - i)^2) = (sqrt((1 - i)^2))/(sqrt(2)):
(sqrt((1 - i)^2))/(sqrt(2))

For all complex z with Re(z)>0, sqrt(z^2) = z.
Cancel exponents. sqrt((1 - i)^2) = -i + 1:
(1 - i)/sqrt(2)

Multiply numerator and denominator of (-i + 1)/sqrt(2) by sqrt(2).

Rationalize the denominator. (-i + 1)/sqrt(2) = (-i + 1)/sqrt(2)×(sqrt(2))/(sqrt(2)) = ((-i + 1) sqrt(2))/(2):

((-i + 1) sqrt(2))/(2)   [Courtesy of Mathematica 11 - Home Edition]

If you are an advanced mathematics student you will start learning this at the very end of high school. (around 16-18 years old) or at university.  Most students will never learn this.

There will be two answers on the complex plane. I have not worked them out yet.

This is my initial attempt to make sense of it:

$\sqrt{-i}=\sqrt{-1}*\sqrt i=i*\sqrt i = i^\frac{3}{2}=(\sqrt{-1})^\frac{3}{2}=((-1)^\frac{1}{2})^\frac{3}{2}=(-1)^\frac{3}{4}$

But wolframalpha says that one of the answer presentations is    $-(-1)^\frac{3}{4}$

This is not a "Complex Math Problem" !!. You just need a different calculator that can handle very big numbers: 

  (57943^5/479073519*59278794-(576^2)+52794378)^507 

=1.2692702773 6389262913........................ x  10^11,614

Yeah...if I can't get this correct after an edit....forget it  !!!!!!

LOL!!!!!!!

Glad it was helpful!!  

CPhill is too tired today !!

$660.00 - $178.23 + $363.82 =$845.59

This is true for all real numbers except 0

Let   a  be any real number except  0

Note that

a^n-n    =   aⁿ  / aⁿ    =   1 =    a⁰   

Since the opening ratio was 15:3 or 5:1, it, therefore, follows that they repaired:

225/5 =45 bikes. So, the total sold and repaired at the opening was:

225 + 45 = 270 Bikes. If they sold and repaired the same number of bikes today, then the ratio would be: 11/[11+7] x 270 =165 bikes repaired today.

I'm assuming that the total number repaired and sold now is the same  as  when they first opened

Let the total number sold and repaired originally  = N

So.....225  is 15/18  =  5/6 of this....so.....

(5 / 6 )  N  =  225      multiply  both sides by  6/5

N  =  225 (6/5)  =  270

So......the number repaired now  =   11 / 18 *  270  =  165

okay 7:11 is the new rate which they sell and repair bikes.

we know that they will sell 225 in the future. so we have to think how they did get ot 225 so quickly. So, we also think that 7 times something is 225 (because it's the future goal). we can figure it out by doing reverse multiplication, which is division---> so,  225/7= 32.14

 Now you just do 32.14 x 11 which equals 353.54 bikes repaired.

you can't really repair 353.54 so you round , that leads you to 353 bikes repaired.

you're welcome, hope i didn't get anything wrong  

First turn these into percents, divid them by 100.

204.69/100= 2.0469%

149.94/100= 1.4994%

then to find the difference between them you would get the bigger percent and minus the smaller percent.

2.0469-1.4994= .5475 is the difference between them.

don't u mean 178.23?

God i love this website, and also i hate it. You make it seem so easy,  i wish i was good at math like you . Anyways, thank you so much for solving this math problems

-3x  =  1.5       divide both sides by -3

x  =  1.5  /  - 3       =   - 1 / 2

80%  =  .80  =   80  / 100   =  8 / 10    =   4 / 5

1 km  ≈ .621 miles

1 L  ≈ .264 gal

So......

28.5 km  = 28.5 *.621  ≈ 17.7 miles / .264 gal  ≈ 67.04 mpg

22 km  =  22 * .621  ≈ 13.66 miles / .264 gal  ≈  51.74 mpg

Cost for city driving  =  500 / 51.74  *  3.50  ≈  $33.82