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Thanks for that website kitty<3....I discovered it, too, about 3-4 years ago...fascinating and easy to understand (which is good for an idiot like me!!).  I think - if I remember correctly - that there might be a link to the Lucas Numbers from this page......equally fascinating connections between those two series!!!

Hi Kitty,

You could have just multiplied both sides by 9 in the first place. You made it a little longer than necessary. 

Fibonacci was an Italian mathematician.  He lived from about 1170 to 1250.

He 'toyed with' lots of cool concepts!

Here is a stack of pages you can look at to help answer this question.

Fibonacci.

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibBio.html

Good job, Takahiro !!!

Points and a Thumbs-Up !!

It's what happens... when you

Actually, kitty<3, I might have "violated" the rules with the use of powers....but, then again......I didn't actually see any "rules" posted............

To answer this question you will need to break down this equation.

First of all lets try and simplify all that can be simplified.

$${\frac{{\mathtt{1}}}{{\mathtt{x}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{x}}}{{\mathtt{x}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}} = {\mathtt{1}}$$

First of all we can see a fraction that can be simplified. That is ofcourse, X Over X. Any number, if the Numerator and Denominator is identical, then it will always equal to 1. So being that, we will substitute X over X with 1.

$${\frac{{\mathtt{1}}}{{\mathtt{x}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}} = {\mathtt{1}}$$ 

Let us move over some numbers across the = sign.

$${\frac{{\mathtt{1}}}{{\mathtt{x}}}} = {\mathtt{1}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,-\,}}{\mathtt{1}}$$

Lets solve that:

$${\frac{{\mathtt{1}}}{{\mathtt{x}}}} = -{\mathtt{2}}$$

Now we must eradicate the denominator. To do that we will multiply both sides by x.

$${\frac{{\mathtt{1}}}{{\mathtt{x}}}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{\,-\,}}\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)$$

Lets solve that!

$${\frac{{\mathtt{1}}}{{\mathtt{x}}}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{\,-\,}}\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}\right) \Rightarrow {\mathtt{x}} = {\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}} \Rightarrow {\mathtt{x}} = -{\mathtt{0.5}}$$

We have jumped a step, however, you should be able to see what has been done.

x=-0.5

Lets substitute that in!

$${\frac{{\mathtt{1}}}{-{\mathtt{0.5}}}}{\mathtt{\,\small\textbf+\,}}{\frac{\left(-{\mathtt{0.5}}\right)}{-{\mathtt{0.5}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}} = {\mathtt{1}}$$

Lets solve it now and see if it work!

$${\frac{{\mathtt{1}}}{-{\mathtt{0.5}}}} = -{\mathtt{2}}$$

$${\frac{\left(-{\mathtt{0.5}}\right)}{-{\mathtt{0.5}}}} = {\mathtt{1}}$$

$${\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}} = {\mathtt{1}}$$

Is it correct?

Yes!

Therefore $${\mathtt{x}} = -{\mathtt{0.5}}$$

That's great, CPhill! :D

I just found another way by working backwards:

22/2 = 11, and 3*4 = 12, minus 1 = 11

So 22 = $$\left(\left({\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{4}}\right){\mathtt{\,-\,}}{\mathtt{1}}\right){\mathtt{\,\times\,}}{\mathtt{2}} = {\mathtt{22}}$$

(1 + 4)² - 3 =

5² - 3 = 22

Also

2³ + 14  =

8 + 14 =  22

Re:  what is 6.2% of 2,683.2

6.2% is the same as 0.062

So simply multiply 0.062 and 2683.2

You can do that on this site's calculator:

$${\mathtt{0.062}}{\mathtt{\,\times\,}}{\mathtt{2\,683.2}} = {\mathtt{166.358\: \!4}}$$

So you have: $${\frac{{\mathtt{x}}}{{\mathtt{9}}}}$$ = $${\frac{{\mathtt{1}}}{{\mathtt{81}}}}$$

Cross-multiply the equation.

x*81 = 9*1

Simplify.

81x = 9

Divide both sides by 81

x = 9/81

Simplify the fraction.

x = 1/9

Re:  quadratic formula

Which is

If you mean how to use it, it helps you find the zeros of a quadratic equation in the form $${{\mathtt{ax}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{bx}}{\mathtt{\,\small\textbf+\,}}{\mathtt{c}} = {\mathtt{0}}$$

This site can help you understand it:

http://www.purplemath.com/modules/quadform.htm

Slope: -2

Point: (3,1)

Slope-intercept form: y = mx+b

First use the point-slope formula: (y-y₁) = m(x-x₁) where (x₁,y₁) are the coordinates of the point and m = slope.

So:

y-1 = -2(x - 3)

Multiply out the -2.

y - 1 = -2x + 6

Add 1 to both sides.

y = -2x + 7

Thank you Melody!

The answer is 7z because you are multiplying 7 and z. A variable with no coefficient will always have a 1 in front of it. So think of it as 7*1(z).

The ladder positioned against the wall forms a right triangle. You are trying to find the length of the ladder, which is the hypontenuse of the triange. 24 ft is a leg length, as well as 7ft. Use the pythagorean theorem to solve this problem. A^2+b^2=C^2

24^2+7^2=C^2      Plug in the given values.

576+49=C^2          Square the pieces.

625=C^2               Combine the squared pieces.

25=C                    Take the square root of both sides.

The length of the ladder is 25 ft.

THe question is a^2+b^2=c^2 problem. Pythagorean theorem.

 a  and b are the sides that are touch the right angle and c is the side that doesn't

The house makes a right triangle 

Only if they become undead can they die again

use c^2-b^2=a^2

c is hypotenus

b is leg

a is answer

The calculator will let you take logs in bases 10, e and 2. (Hover your cursor over the "log" button to see the other two bases)

If you have this:

log_a b    ......        where a is an "uncommon" base

You can always use the change-of-base rule to evaluate the log =    log (b) / log (a)

Good question!

Two minus make a plus ONLY

1) if they are so close together that you can put a circle around them and there is nothing else in  the circle.

Think of it like this if you want

Negative numbers are cold numbers.  Like -30degrees would be very cold wouldn't it?

and Positive numbers are hot numbers.  An oven might be 180degrees. There is an invisible + in front of the 180.

So 15--2 means you are taking away cold - so it must get hotter

15--2=15+2=17

2) If you are multiplying or dividing

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NOW if you are adding or subtracting positive and negative numbers then you need to think about a number line.

10+3 means you start at 10 and go 3 places in the positive direction = 13

10-3 means you start at 10 and go 3 places in the negative direction = 7

Just continue this method with trickier negative numbers

-3-8 means you start at -3 and go 8 places in the negative direction = -11

OR to put it another way.  It is -3 degrees and it gets 8 degrees COLDER = -11 degrees

So lets look at your question

-7+-8 = If you add cold it gets colder so the question becomes

-7-8     Now if it is -7 degrees that pretty cold and you take away 8 degrees, it is going to get even colder! So the answer must be more negative.  

Start at -7 on the number line and go 8 places in the negative direction.  The answer is -15

I don't know why I am writing all this I am sure that I have done it before as a post to keep.  Not to worry.

Here is a number line that might help you. You'll have to add the negative numbers in yourself.

Here is a site that might also help.   

http://www.mathsisfun.com/positive-negative-integers.html

Think about this.......If the temperature was -8 and then it dropped another 7 degees....would it have risen 15 degrees??  No.....it would have dropped -8 + -7 = -15 degrees !!

You're getting this confused with a negative times a negative, which = a positive.

This one is harder to see......suppose you have lost 7 dollars for the last 8 weeks......then in 8 more weeks, you will have 56 dollars less...(8) times (-7). But 8 weeks ago, (-8), you had (-8) times (-7) = 56 dollars more. Does that make sense??

So, adding two negatives produces a negative, but multiplying two negatives produces a positive.

Hope that helps......

It is just 6 divided by 0.9

you can do it youself on the home page calcualtor.