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Multiply 12 by (3/5)

12/1 * 3/5

= (12*3) / (1*5)

= 36/5 or 7 and 1/5 or 7.2

You use the reciprocal of (3/5) because a number to a negative exponent is the same as 1 over the number to the positive form of the exponent.

So - (3/5) ^ -2 is the same as - (1/(3/5)) ^ 2.

So:

$${\mathtt{\,-\,}}\left({\left({\frac{{\mathtt{3}}}{{\mathtt{5}}}}\right)}^{-{\mathtt{2}}}\right) = {\mathtt{\,-\,}}{\frac{{\mathtt{25}}}{{\mathtt{9}}}} = -{\mathtt{2.777\: \!777\: \!777\: \!777\: \!777\: \!8}}$$

And $${\mathtt{\,-\,}}\left({\left({\frac{{\mathtt{5}}}{{\mathtt{3}}}}\right)}^{{\mathtt{2}}}\right) = {\mathtt{\,-\,}}{\frac{{\mathtt{25}}}{{\mathtt{9}}}} = -{\mathtt{2.777\: \!777\: \!777\: \!777\: \!777\: \!8}}$$

let the number be x

double the number is 2x

subtract it from 24 and you get

24-2x

Well the quartz has displaced  186-107.5 = 78.5ml

1ml=1cm cubed

So the volume of the quartz is 78.5cm^3

5x-x^2

you cannot simplify

What does this question mean please Geno?

24.1294560865187199

nearest hundreth means 2 decimal places

Look at the first 3 decimal places - the rest is of no conseqence     24.129

The nine is a big number (5,6,7,8,9 are all big numbers)

So the 2 in the second place goes up to 3

the answer is 24.13

Try looking at this thread and see if you can work it out

y=-3x-4

The y interecept is -4.   This is just a point  (0,-4)  So mark this on the y axis.

now

The gradient is        $$-3\; =\; \frac{-3}{1}$$

Now if a line has a negative gradient this means that the top of it will be on the LEFT hand side of the page.

Starting at the y intercept.   Go up 3 spaces.  Then go side ways 3 spaces in the LEFT (or neg) direction.

Mark the point where you end up.  

Join the points and you have your line.   

You should write the equation of the line on the line  

I think that you want an equal sign in your first equation.

Do you want these solved simultaneously?

-5x+y=-2         (1a)   change this to     y=5x-2    (1b)   (I added 5x to both sides)

-3x+6y=-12      (2a)

Now substitute 1b into 2a

-3x+6(5x-2)=-12

simplify and when you get a valuse for x sub it back inot one of the original equations to get a value for y.

Will  you be right to do it now?    

I'm no where near knowing how to do this graph thing. I'm so lost and confused :/

c)

$$\\\displaystyle\lim_{x\rightarrow \infty}\;\;\frac{sin(x^2)+10}{x^2+10}\\\\
Now\\
-1\le sin(x^2)\le 1\\
9\le sin(x^2)+10\le 11\\
$Therefore the numerator is a positive number between 9 and 11$\\
$Therefore$\\
\\\displaystyle\lim_{x\rightarrow \infty}\;\;\frac{sin(x^2)+10}{x^2+10}=0$$

What is the equation?

This is actually pretty simple to figure out. One only needs to find the square root (√) button on their calculator, press it and then enter the value you wish to dicover the square root of, in this case 1023. If one follows the aforementioned process, one with arrive at the conclusion that the square root of 1023 = 31.9843711834389516... or ≈ 31.9844.

Hope this helped!

Well, this a fairly simple question, so here we go.

Since pi is an irrational number (has an infinite amount of decimals), the most accurate way to answer this question is basically to rewrite it as:

(7*7*7)/-π = 343/-π

But that's kind of useless, so one can simply punch that into their calculator and find:

343/-π=-109.1802909610402003... or ≈-109.18

Hope this helped!

Do you mean:  31/4 ?

To get the numerator:  7x4 + 3  =  31

5x  =  25

Divide both sides by 5:

5x/5  =  25/5

   x    =  5

I'm going to assume that the first equation is:  -5x + y  =  -2

I will try to eliminate the y-terms by multiplying the first equation by -6:

-5x + y  =  -2          --->   multiply x -6   --->     30x - 6y  =  12

-3x + 6y  =  -12      --->                                   -3x + 6y  =  -12

       Adding down the columns:                          27x         =  0

                                                                                x  =  0

IF x = 0, (first equation) -5x + y  =  -2     --->     -5(0) + y  =  -2     --->     y  =  -2.

Answer:  x = 0,  y = -2

Well, for this question, one must evoke the BEDMAS order of operations. I see no brackets nor exponents, so division and multiplication first: 

π*π+π/π-π rewritten (π*π)+(π/π)-π

Now one must deal with the brackets:

(π*π)+(π/π)-π becomes π²+1-π   

And if you plunk that into a calculator you should find π²+1-π=7.7280117474995654...

Hope this helped!

Thank you Chris,

I haven't finished with this question yet but I have put it in the Sticky Thread "Great answers to Learn from"  :)

To divide fractions, multiply by the reciprocal:

5/7 ÷ -8/14  =  5/7 x -14/8  =  -70/56  =  -35/28  =  -5/4 

Here's why 0^0 is undefined.....

Normally  a^n /a^n = a^(n-n) = a^0 =1

So....   0^a/0^a  should be  0^(a - a) = 0^0 =1....however, the problem is that we divided by 0 originally (0^a)....and that's undefined

Factor out the common term: 2^2013:

Since:  2^2014 = 2·2^2013

So:  2^2014 - 2^2013

  =   2·2^2013 - 2^2013

  =  2^2013·( 2 - 1 )

  =  2^2013·(1)

  =  2^2013

Yes Geno you may be right.  I was thinking about this as well.  My initial thought was that it was undefined but then I hunted about on the net and found people disagreed with me.

There seemed to be a concesous of opinion that 0^0 was defined as 1  ( this is just one site that said this - there were others)

If you want to find the value of log(to the base 16) 19, use the change-of-base formula:

log(to the base 16) 19  = log(19) / log(16) = 1.06198...

You could also use natural logs and have  ln(19) / ln(16) = 1.06198...