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Now that is amazing!  

$$(4x^2-2x/x^2+5x+4)/(2x/x^2+2x+1)$$

I assume that you really mean

$$\\((4x^2-2x)/(x^2+5x+4))/((2x)/(x^2+2x+1) )\\\\
=\frac{4x^2-2x}{x^2+5x+4}\div\frac{2x}{x^2+2x+1}\\\\
=\frac{4x^2-2x}{x^2+5x+4}\times\frac{x^2+2x+1}{2x}\\\\
=\frac{x(x-2)}{(x+4)(x+1)}\times\frac{(x+1)(x+1)}{2x}\\\\
=\frac{(x-2)}{(x+4)}\times\frac{(x+1)}{2}\\\\
=\frac{(x-2)(x+1)}{2(x+4)}\\\\
=\frac{x^2-x-2}{2x+8}\\\\$$

$${{\mathtt{\,-\,}}\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}^{{\mathtt{5}}} = {\mathtt{\,-\,}}{\frac{{\mathtt{32}}}{{\mathtt{243}}}} = -{\mathtt{0.131\: \!687\: \!242\: \!798\: \!353\: \!9}}$$

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This reduces to 600pi = (1/2)1800*theta or 600pi = 900*theta or theta = 2pi/3

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2^4 is 16, so this reduces to 2^(6x)/2^(x^2)=1  or 2^(6x) = 2^(x^2)  so that 6x = x^2  so x = 0 or x = 6

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I assume tg(x) is tan(x) = sin(x)/cos(x).

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This is a formula due to Euler:  v = vertices, f = faces, e = edges.

Imagine a cube, for example. It has 8 vertices, 6 faces and 12 edges, so v - e + f is 8 - 12 + 6 = 2

A tetrahedron: v = 4, f = 4, e = 6:   v - e + f:  4 - 6 + 4 = 2

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When x = 2/3 then (1/4)x² - 5x + 7 becomes (1/4)(2/3)2 - 5*(2/3) + 7 → 1/9 - 10/3 + 7 → (1 - 30 + 63)/9 → 34/9 → 3 7/9

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There is no single solution because there are 2 unknows and only one equation.

There are an infinite number of solutions.

What does this formula mean?

One of Euler's formulas:  v - e + f  =  2

                                    v - 11 + 7  =  2

                                    v - 4  =  2

                                    v  =  6

Half-way between the two x-values, 3 and 0, is 1.5

Half-way between the two y-values, 0 and 2, is 1.

The midpoint is (1.5, 1)

There is no last digit to pi; it is infinitely long and doesn't repeat.

When you fold a piece of paper, it doubles in width. If you double it 51 times:  2⁵¹  ≈  2.25 x 10¹⁵.

A sheet of paper is approximately 0.1 mm.

0.1 mm x 2.25 x 10¹⁵  

=  2.25 x 10¹⁴ mm      (multiply by 0.1)

=  2.25 x 10¹³ cm        (divide by 10)

=  2.25 x 10¹¹ m         (divide by 100)

=  2.25 x 10⁸ km         (divide by 1000)

=  225, 000, 000  km

The distance from the earth to the sum is approximately  149, 600, 000 km

First, rewrite  ( 3√z - 1 ) / ( 1 - √z ) by multiplying both the numerator and denominator by -1:

                 =  ( 1 - 3√z ) / ( √z - 1 )

Now, you have:

   ( 2√z - 3 ) / ( √z - 1 )  -  1   =   ( 1 - 3√z ) / ( √z - 1 )

Multiply each term by (1 - √z ) / ( √z - 1 ) - 1

     2√z - 3  -  1 · ( √z - 1 )  =  1 - 3√z 

     2√z - 3 - √z + 1  =  1 - 3√z

                   √z - 2  =  1 - 3√z

                        4√z  =  3

                          √z  =  3/4

                            z  =  9/16

8a² - 72  =  0

Add 72 to both sides:

8a²  =  72

Divide both sides by 8:

a²  =  9

Find the square root of both sides;

a  =  3     or     a  =  -3

You put this question up yesterday and the answer is still the same.

That colon has no meaning there. Your question does not make sense.

i dont remember myself telling the story of me doing that, or you throwing me, that is a stroy to be saved for another day. In the meantime, im just gonna chill with a coke......

p.s. Coke is better than pepsi (no contest)

Melody,I think that they would be great names for ducks, .....  or geese.

If they were mine, my dog, Snoopy, would have company, and if I forgot to feed him he would have dinner!

 But don't worry I don't forget to feed Snoopy and he is very lazy anyway.  He'd just love the company   

If I had 2 ducks, I'd call them Banjo and Patterson.

Banjo Patterson is a famous Australian poet and story teller.

But they would make fabulous duck names don't you think?

The drake (if I had one) would be Banjo!   :D

1/3

Oh you probably mean the slash to be a fraction line.

in this case is should have been written as 

7 ÷ (7/3)    or   7 / (7/3)

You have to invert the 2nd one and multiply.

= 7 × (3/7)

=7×3/7

=21/7

=3

÷ and /  both mean divide.  :)

A fraction line really IS a divide sign in disguise.  I mean ALL the time.  Not just here.  :)

... and mine: Milica and Milo

It's pretty much impossible to fold a piece of paper more than about eight times, so the question is pointless.

My pet hogs:

Tubby and Fatso

Sugar and Spice