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What is the center of the circle x2 + y2 + 8x - 12y + 27 = 0?

What you need to do is complete the squares

\(x^2 + y^2 + 8x - 12y + 27 = 0\\ x^2 + y^2 + 8x - 12y=-27\\ (x^2 + 8x+ number1)+ (y^2 - 12y+number2)=-27+number 1 +number2\\ \)

You have to find the numbers that turn those expressions into perfect squares.

Can you do that?

108:8=6  stacks

6*8=48    yellow sheets

108+48=156  sheets

Kevin have 156 sheets.

There are some little bars in the right hand side of the display on the calculator.

click on that.  It will display a drop down menu that will have what you want :)

Thanks Rom,

Asker, if you have problems with Rom's instructions and you need more help then you need to say so.  

But think about it a little first :))

\(\mbox{First solve for y in terms of x using the second equation.}\\ \mbox{Then plug that expression for y into the first equation and solve for x.}\)

Just expand the LHS using the cos(A-B) identity (which I expect is in the formulary page on this site (or you can google it)

and simplify to show it equals sin x

Maybe you can explain where your problems lies?

16.95+.05*A=22.95+.02*A i need help please

One reason that this looks so intimidating is it has all those decimals.    Yuck!

If you multiply both sides by 100 they will all 'disappear'   Magic!

Do that first, if you still do not know what to do next then post again (on this thread) but maybe it will look more normal then and you will be able to finsih it yourself.  

Don't let the large numbers intimidate you.  Think about what you would do if the nmumbers were little and less scary and then do the same thing!   :)

Why is the 1.5 in brackets.  The meaning is not clear.

I've never seen this treated so I thought I'd take a deeper look.

\(c = r_c e^{\imath \theta_c} \\ c^\imath = \left( r_c e^{\imath \theta_c}\right)^\imath = r_c^\imath e^{\imath^2 \theta_c} = r_c^\imath e^{-\theta_c} \\ \mbox{Now what is }r_c^\imath? \\ r_c = e^{\ln(r_c)} \\ r_c^\imath = \left(e^{\ln(r_c)}\right)^\imath = e^{\imath \ln(r_c)} \\ \mbox{so }c^\imath = e^{\imath \ln(r_c)} e^{-\theta_c}= \\ e^{-\theta_c}\left(\cos(\ln(r_c))+\imath \sin(\ln(r_c))\right) \\ \mbox{Letting }c=\imath \\ r_c=1, \theta_c=\dfrac \pi 2 \\ \imath^\imath = e^{-\frac \pi 2} \left(\cos(\ln(1)) + \imath \sin(\ln(1))\right) = \\ e^{-\frac \pi 2}\left(\cos(0)+\imath \sin(0)\right)=e^{-\frac \pi 2} \\ \mbox{which is in agreement with Melody's answer}\)

Thanks guest, that is a good answer, I just want to add to it. :)

why is 82 divided by 0.25 equals to a bigger number?

This means.  How many quarters are there in 82 wholes.

Well there are 4 quarters in 1 whole thing

there are 4*2=8 quarters in 2 whole things

so there must be 4*82 quarters in 82 whole things.   :))

If you need more help, show us what you have attempted and we can help you more. :)

I just googled standard form of an equation to see how easy it was to find.  It was very east :)

http://www.mathwarehouse.com/algebra/linear_equation/standard-form-equation-of-a-line.php

Next time you could google things like this for yourself  :)

Thanks for answering guest, but this is not an equation.  There is no Left hand side.

10!4/log5(5678)

=10!*    4/log5(5678)

Why have you got 5(5678)  the meaning of this is not clear to me. 

Oh, thanks guet, I just read what you put and yes yourinterpretation of that bit sound likely.

So, is the question

\(10!\times 4\div log_5\;5678\)

I think the web.0calc will handle this as is but most calcs cannot do log base 5

You have to change it using the chage of base rule.

You can find that on our formulary page.  :)

5 + 2(m -1)

You have to expand 2(m-1) first. and then add the 5 afterwards.  Can you do that?

Here is a similar question, you can copy the technique

3(x-5) = 3*x+3*-5 = 3x+ - 15 = 3x-15

If you get stuck then post your attempt :)

Is it:5 + 2(m -1) or 5 = 2(m -1)?

I believe it is 5=2(m-1) that you want. Did you try to solve it, and if so what happened? How would you multiply the right hand side? Once you get that right, then it should be very simple. The easiest way to go is to move all pure numbers to one side and leave the variable "m" on the other side. Just remember that when you move numbers from one side of the equation to the other, you must change the sign of + to - or vice versa. Let us see if you can come up with the right answer. Good luck.

Hi Michael and guest,

I thought it was interesting too.

Here is a proof.

Source form Wikipedia.

I think the unit of teampature should be in kelvin.To do that You need to add 273.15 to the tempature in unit of degree of celsius

T=273.15+C 

You know what "i" stands for? Of course, it stands for  √−1. So, what made you ask this question? Is it an assignment or just curiosity on your part? Or, are you studying "Complex numbers?" It's an interesting question, however!. But, I'm afraid that you may get lost in the explanation. It has a numerical value of: e^(-Pi/2)=0.207879576.........etc.

2178

Did you look in your Algebra book and see what an equation in "standard form" looks like? Do that first and then rearrange this equation to look like the " standard" ones in your book. Just remember that when you move one variable from one side of the equation to the other, you must change the sign in front of that variable. If it is a "+", then it becomes a "-" and vice versa.
 

This one might be a difficult one for you. But, you must have seen before, right?. We want to find the value of the exponent x. You have to raise the right hand side to an exponent that will give the left hand side, or 2,600?. What will happen if you take the log of 2,600 and the log of 2760 and divide one by  the other? Try it and see what you get. Hint: your answer must be less than 1. Good luck.

why is 82 divided by 0.25 equals to a bigger number?

Why? Because of this: .25 as a decimal=1/4. And if you divide 82 / 1/4, we turn it into multiplication like this: 82 X 4/1=328. Notice that when I turned into multiplication, I flipped 1/4 to 4/1. And that's the main reason for the answer getting bigger.

Just add the two fractions first. Once you get your result, then just put x in front and you are done. if you have difficulty with fractions, then use a calculator. A fraction such as 3/5, just means divide 3 by 5. Just try it on a calculator and see what you get for 3/5 as a decimal.

The perimeter of a tennis court is 228 ft. The length is 42 ft more than the width. What are the dimensions?

A tennis court is a rectangle. What is the formula for the perimeter of a rectangle? It must be in your textbook. Look it up. We don't have the width, but what if we set it to be:W? Obviously, the length will be W + 42. Once you have the formula, just plug in all these numbers and solve for W. Your equation should look something like this: 2[ a +(a+42)]=Perimeter. Try it and good luck.

Hallo Omi67,

Super Erklärung!  Aber bei Antwort #4 hat  sich ein Vorzeichenfehler eingeschlichen:

\(\int f(x) dx = x*ln(x)^2 -2*(x*ln(x)-x) + C = x*ln(x)^2 -2*x*ln(x)-(-2x) + C \)

also

\(x*\left ( ln(x)^2 -2*ln(x)\color{green}{+}2 \right ) + C \)

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