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thanks so much! 

Thanks for jumping in and cleaning up what i left behind the curtain so to speak.  Good thread!

To do this we will need to know the values of x and y.  My favorite way to do this it to rearrange equation 2 so that it says y=2-4x.  We can then substitute this into equation one and simplify as follows:

6x-3(2-4x)=30

6x-6+12x=30

18x-6=30

18x=36

x=2

With this information in hand we can subsititue it into the first equation i mentioned y=2-4(2)=-6

Therefore x+y=2+(-6)=-4

That's the question I thought you might ask !!!

We're trying to "match" terms so that, when we subtract one equation from the other, a variable "disappears."

Note that we could have mutiplied x + y = 1 by 6 on both sides giving 6x + 6y = 6

And, if  I  subtracted this from 5x + 6y = 6  notice that the "y's" would have disappeared, thusly

  5x + 6y = 6    ⇒    5x  + 6y  =  6

-[6x + 6y = 6]  ⇒   - 6x -  6y  = -6

----------------         ----------------

                              -1x         =   0            so ... x = 0  

And we could have found "y" by substituting 0 in for "x"  into the equation x + y = 1.....we would then find that y =1  ....just like before !!

This is an topic in Algebra (I don't know if you've encountered that or not)...so, if you haven't, don't worry about it too much....!!

The domain of this is all real numbers as there is no number you can use as an input that will make this function "fail".  The range will be all real numbers greater than six as the exponential part, 5^x, can never be equal to zero nor can it be negative, however as x increases it grows unbounded above. The addition of 6 shifts it's rainge up six and that is why it is all realy numbers greater than six for the range of the function.

Using what you've given me along with this formula (which I hope is the correct one!!), we have

P =  [(.07) (4148)] / [ 1 - (1 + .07)^-16] = $439.097  = $439.10

BTW.....It might be easiest to evaluate the numerator and denominator separately and then perform the division.....

CPhill ive undertood the method and how u got the answer but still i have one  doubt left , its that how do we know that we have to multiply every term by 5 to get the answer??!!

Here's what jboy314 did, rosala

He took this equation ..... 9x + 9y = 9     and divided every term by 9.....so we have

9x/9  +  9y/9   = 9/9      and this gives us  

x + y  = 1       then, he multiplied every term by 5 ..(the reason for this will be clear in a second).. so we have

5x + 5y  = 1     Notice carefully, what happens if I take this equation and subtract it from  5x + 6y =6, we have:

         5x + 6y  = 6       ⇒    5x   + 6y  =  6   

-      (5x + 5y  = 5)      ⇒   -5x   -  5y  = -5

-----------------------           -----------------

                                                     y  =  1       

( Notice how the 5x terms cancelled each other !!!! That's why it's called the "elimination" method...jboy314  saw that he could eliminate  "x"  by multiplying x + y = 1 by 5 and then subtracting it from the other equation !!!! )

Now, all we need to do is to substitute  1 for y in any of the equations to find "x"...using x + y = 1 is easiest..so we have

x + (1) = 1      subtract 1 from both sides

   -   1  = -1

---------------

x         =   0

So  x = 0    and   y =1   are our solutions  !!!

density = mass / volume   ......so we have...

density = 5g / 10cm^3  =  .5g/cm^3

Thank u CPhill!

jboy314 pls can u show its working becoz i think i may understand much nicely then !btw u explained it really very nicely but i am still unable to get it maybe becoz i have the habbit of seeing the working !lol! CPhill i saw jboy314 before answering really very good to some questions!so jboy314 if u dont mind pls can u show me the working !

Makes perfect sense to me, rosala.....3 points and a "thumb"........!!!!

Nice explanation, jboy314.....3 points and a thumbs-up from me.....

BTW...welcome to the forum....I don't believe I've seen you here before.....

Reinout the -4 and 8 do not count as it says "between " !

so between -4 and 8 we have :

$$-3,-2,-1,0,1,2,3,4,5,6,7$$

so if we count these integers we have 11 intergers between -4 and 8  !

so i hope uve understood how we found out these intergers !if not then pls ask !

y=1 x=0

The way we get this is called solving by elimination.  First take the equations with the nines and divide both sides by 9, this produces x+y=1.  We then multiply this by five to get 5x+5y=5.  Subtracting this from the fist equation gives us y=1.  By substituting y=1 back into either equation we get our value for x.  For example:

y+x=1

1+x=1

x=0

Well, I think we can beat the End of Day Wraps =)

Well...if we started with 80 and had 3 left, we must have used 77.

So, 77/7 = 11 per day.....

as 3 4/10 is a mixed fraction so to input it in a calculator u will have to change it into just a fraction !so for that well change it like this 10 x 3 + 4 =34  , now our fraction is 34/10 so if u put this in a calculator u will get ur answer as 3.4 ! so just input 34/10 to get ur answer !i hope u have understood now !if any doubt pls tell !

On the first square we would have 2^0 = 1.

On the second square we would have 2^1 = 2

So, on the nth square, we would have  2^(n-1) grains.

So, on the 64th square, we would have 2^(64-1) = 2^(63) grains

4/10 is the fraction expression of .4.

Just type in 3.4

There is a little hidden plus sign between the 3 and the 4/10.  If you type 3+(4/10) in your calculator you will get 3.4, the correct decimal for this mixed fraction.

This is a very complicated question but I will answer it to the best of my ability

First we need to add some things and change a few variables

(Jolly Cooperation)² * (Solaire / (Sun * Medal))(Praise)

Now we carry the amount of medals to get max rank

(Solare: Praise the sun + Jolly Cooperation)³⁰ 

 This means it will take a total of 30 medals, 1 sun and 1 Jolly solaire to achive cooperation 

Does this answer your question?

$${\mathtt{24}}{\mathtt{\,\times\,}}{\mathtt{2}} = {\mathtt{48}}$$

$${\mathtt{48}}{\mathtt{\,\small\textbf+\,}}{\mathtt{24}}{\mathtt{\,\small\textbf+\,}}{\mathtt{35}}{\mathtt{\,\small\textbf+\,}}{\mathtt{13}} = {\mathtt{120}}$$
There are 120 students in total.

Chess board have 64 squares, then the result is 2⁶⁴ = 18.446.744.073.709.551.616

FV=4148; n=16, i=0.07

can someone tell me how to solve for PMT?  I get the first part correct but I keep getting the result wrong when I do the division so I cant make it to the second part