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Let x be the amount of water in tank A

Let m be the amount of water needed to fill tank A

So  the total capacity of tank A is (x+m)

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Let y be the amount of water in tank B

Let n be the amount of water needed to fill tank B

and the total capacity of tank B is (y+n)

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We are being asked to find (n+m)

Now the capacity ratio of tank A to tank B is 7:3  so

$$\begin{array}{rll}
\frac{x+m}{y+n}&=&\frac{7}{3}\\\\
3(x+m)&=&7(y+n)\\\\
\end{array}$$

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now there is x litres in tank A and m litres are needed to fill tank B so  

x-n=33 litres  ==>  x=33+n

Likewise

y-m=9 lites ==>  y=9+m

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$$\begin{array}{rll}
3(x+m)&=&7(y+n)\qquad \mbox{substituting for x and y we get;}\\
3(33+n+m)&=&7(9+m+n)\\
3*33+3(m+n)&=&7*9+7(m+n)\\
99+3(m+n)&=&63+7(m+n)\\
36&=&4(m+n)\\
9&=&m+n\\
\end{array}$$

so the amount of water to fill up both tanks completely is 9L

sin(2arctan(12/5))

I always do these by drawing the triangle

$$let\:\theta = atan\:\frac{12}{5}$$

sin(2arctan(12/5))

$$\\Sin(2 atan(12/5))\\
=sin(2\theta)\\
=2sin\theta cos\theta\\
=2\times \frac{12}{13}\times \frac{5}{13}\\
=\frac{120}{169}$$

Excellent, ND  !!!!

Points and Thumbs  !!!

(1 + 2 x^1/3  + x^2/3) 

This is as

$$1+2\sqrt[3]x+\sqrt[3]{x^2}\\\\
OR\\\\
1+2\sqrt[3]x+\left(\sqrt[3]x\right)^2\\\\$$

We don't know the length of any of the sides, but we know that the total length of the four sides is 1060 feet, and that two sides are 180 ft longer than the other two.

We can write this as an algebraic equation!

x + x + x + 180 + x + 180 = 1060

4x + 360 = 1060

     - 360     -360         ---Subtract 360 from both sides

4x =  800

x = 200

So the width of the field is 200, and the legnth is 180 ft. longer than the width, so the legnth of the field is 380 feet!

I believe your wanting us to simplify this.

-3(3x-(5x-3))

-3((3x-5x-(-3))

-3((3x-5x+(+3))     ---Minus a negative is the same as plus a positive

-3(-2x+3)

6x-9

To check that both the simplified version and the original will give you the same answer when the value of x is put it, put a random value for x in both of them. Let's put in 5 for x.

Original version:

-3(3x-(5x-3))

-3(3(5)-(5(5)-3))

-3(15-(25-3))

-3(15-22)

-3(-7)

21

Simplified version:

6x-9

6(5) - 9

30 - 9

21

There we go, it works!

50*6 = 300

300/10 = 30

30-6 = 24

24 + 36 = 60

OK....so we have......

(1 + x^1/3)² =

(1 + x^1/3) * (1 + x^1/3)   =

(1 + 2 x^1/3  + x^2/3)     ....... remember, by the laws of exponents,  aⁿ * aⁿ = a²ⁿ....so x^1/3 * x^1/3 = x^2/3  !!!

Good thinking, ND.....yep, that a=b thing gets past most people - unless you're alert........!!!!

Mary is 24.  She is twice as old as Ann was when Mary was as old as Ann is now. How old is Ann?

I'll admit, rosala....this one IS a "stumper."  I think the verbiage in the problem is the confusing thing....until Alan and Melody explained it...I didn't see it, either.

Using what they said......

Mary's age now = 24

So...some years ago (let's call this "x") Mary was as old as Ann is now.  And let's call Ann's current age "A" Therefore:

24 - x  = A  .......Let's call this "Equation 1"

And, as Alan has noted, x years ago, Ann's age was just, A - x.     

Now here's the tricky part............"Mary.... is twice as old as Ann was"......

Let's stop right there........"is twice as old as Ann was" means that Ann's age at the time, (A - x), times 2 must equal  Mary's age now - (24)  !!!

OR, equation-wise......

(A - x) * 2 = 24     ........divide by 2 on both sides......

(A - x ) = 12     .........add x to both sides.......

A = 12 + x    Let's call this "Equation 2"

And remember, from Equation 1, we have that 24 - x = A

Therefore Equation 1  must equal Equation 2 because A = A....so we have.....

24 - x = 12 + x       ......add x to both sides......

24 = 12 + 2x          ......subtract 12 from both sides.......

12 = 2x                   ......divide both sides by 2.....

x = 6

Therefore, since A = 12 +x, then 12 + 6 = 18 and that's Ann's current age!!!

P.S.....The complex wording of this problem makes it almost indecipherable. I might have stated it thusly:

Mary is 24.  Ann is younger. When Mary was Ann's current age, Ann was half of Mary's current age. How old is Ann??

Yeah...I think that works...!!!        

I figured out the flaw in this problem after looking it up on a website.

The equation they have here is a bit different, but it's the same concept.

Does the following formulation of the question help you rosala?

Mary is now 24 years old.

Ann is now A years old.

When Mary was A years old, Ann was B years old.

Mary is now 2*B years old.

How old is Ann now?

(x^2 - x - 6) / (x^2 - 4)    factoring the top and bottom, we  have

(x-3) (x+2) /[ (x-2) (x+2)]   "cancelling"  (x+2) on top and bottom, we have

(x-3) / (x-2)

Oh thats surprising!i didnt even know that there would be such serious error in this ! ill try to find out but for that ill have to translate this !this language is going above my head!

Well, I do know what this means....your basically just manipulating the equation algebraically...

It all seems legit, but there has to be an error somewhere, because 2 ≠ 1.

I'm not quite sure, maybe someone else on the forum has an explanation for this problem.

NinjaDevo im not a teacher but still i too cant understand this!do u know what does this mean !

Anonymous ur teacher will be able to undersatand this if she knows Portugese so take care that ur teacher doent know !lol!

Rosala has a point. It's never necessarily good to "beat" your teacher.

Here's something you can use to "trick" your teacher though. Maybe see if they can find the fault in this!

Thanks, ND......!!!

CPhill is right, it's always a good habit to double check (or verify) your answers.

You are probably aware of how to do this, but I'll show you how to do it if your not familiar.

To check it, you simply put in the values of x and y into one of the equations like so:

4x-7y=43         ---This is the second equation that was given

4(2) - 7(-5) = 43

8 - (-35) = 43   

8 + (+35) = 43              ---Subtracting a minus ifs the same thing as adding a postitive

43 = 43

And 43 does equal 43, so we know our answer is right!

Danke or Thank You CPhill !

Thumbs Up and Points, rosala!!!

So the amount with you is $300   and the costs of the items are  $200 , $50 , $15 and $15 .

total amount of things = 200+50+$15 +15 =280

so now we will minus the cost of all the things to the money u have 

=300 - 280 =20   so now u are left with $20 which means that ur amount is enough for the things!

So if u have $300 you will have enough money to but things that cost $200,$50 , $15 and $15  

so that was your correct answer !

i hope uve understood by now but if not then pls ask!

i hope this helps!

Thank you CPhill! BTW i was just trying to find what her question was actually and i didnt know i answered her unknowingly !lol! 

Set it up vertically

  ₁

  55

+39  

------

  94

so 55+39 = 94

I think Christina just wanted somone to verify this....you have done so, rosala !!!