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The ratio numbers have to be a factor of 64

1+2+3+X   has to equal a factor of 64   (1,2,4,8,16,32,64)

1+2+3 =6     so x has to equal  2 10 26 or 58   I don't think 0 will fit the bill.....

y=amount of oz in can originally. 
x=number of oz of water every second comes out of the container. 
y-5x=58
y=5x+58

y-15x=28
5x+58-15x=28
-10x=28-58
-10x=-30
x=3
y=73

Hope this helps!

Sorry I'm saying this a little late, but thank you. This really helped, and now I understand the concept

If 20% off, then you pay only 80%.....right?

89 x .8 = $ 71.20   (as CCM found......and she/he INCLUDED UNITS!  Excellent!)

With dimensional analysis :

354 q   x   2.5 d/q  = 885 d    (see how the q's cancel out?....and you are left with d's ?)

52 q  x  do/4q = 13 do

35 q x  5 n/q =175  n

75 q x 25 p/q =1875 p

Using dimensional analysis makes large conversions or complex equations easier to visualize (and figure out how to solve) and find the resultant 'units'   ....... believe me, in engineering and physics and complex math there are some CRAZY big formulas and equations to calculate......and units ARE VERY IMPORTANT !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!    There have been rockets/satellites/shuttles fail due to incorrect units etc used in the calculations.  (My soapbox.....without units answers are only partially correct!   )

you are finding 20% percent of 89, so the expression would be 0.2 times 89

this would leave you with 17.80, which you subtract from 89. The result is

$71.20.

Let me know if you have any questions!

Never mind i got the answer

If you mean 

8x+16 = 4(2x+4) 

then the answer is all real numbers. 

Using the distributive property of multiplication, the 4 on the right hand side would be distributed evenly among the parenthesis. 4 times 2x is 8x. 4 times 4 is 16

you would be left with

8x+16=8x+16

4(2x+4) Using the distributive property 

=8x+16

what do you think??

8x+16=8x+16

Yes they are equivalent...

I think I can speak for tertre, too...we are glad to help   [ if we can  !!! ]

Thank you so much CPhill and Tertre. You guys are very good at math and have helped so many people including me and i want to thank you so much for that

Thanks, CPhill! 

Nice explanation, tertre...!!!

If you read CPhill's solution to the previous problem, it will make it easier to understand.

Again, factor the numerator and the denominator! This a key factor for solving these types of problems!

For the numerator, we have \(x^2+18x+81\), and that changes into \(\left(x+9\right)^2\) after factoring.

Now, for the denominator, we have \(\:x^2-81\), and that changes into \(\left(x+9\right)\left(x-9\right)\) after factoring.

So, we have \(\frac{\left(x+9\right)^2}{\left(x+9\right)\left(x-9\right)}\) and that yields our final answer as \(\boxed{\frac{x+9}{x-9}}\).

The scalle factor  of the larger triangle to the smaller  = 

sqrt  [ larger area / smaller area ] =    

sqrt  [ 150 / 6]  =

sqrt (25)   =  5

The legs of the smaller triangle are   3  and 4

The legs of the larger triangle are each  5 times as much =  15 and 20

So...the sum of the legs of the lager triangle   = 15 + 20   = 35 units

Hint: Right triangles, hypotenuse=5..Does that take you somwhere? You can use the Pythogorean Triplets to rememeber.

I don't know if this is a good way to do this, but...

First, you can factor the numerator, which is \(15x^2-8x-7\), to \(\left(x-1\right)\left(15x+7\right)\).

We can do the same thing with the denominator \(\:x^2-2x+1\), to \(\left(x-1\right)^2.\)

Now, we have \(\frac{\left(x-1\right)\left(15x+7\right)}{\left(x-1\right)^2}\). And, we can cancel \(x-1\), since that is our common factor. Thus, we are left with \(\boxed{\frac{15x+7}{x-1}}\).

If you need more explanation on the factoring, just tell me. Also, I think synthetic division works.

...."  What is the ratio of the area of △PQT to the area of △P  "

What  is the second triangle  ???

15x^2 - 8x - 7   factors as  (15x + 7) (x - 1)

x^2 - 2x + 1   factors as  ( x - 1) (x - 1)

So we have

[ (15x + 7) (x - 1) ] / [ ( x - 1) (x - 1)  ]      ...cancel the  x - 1  factors on top/bottom and we have

[15x + 7 ]  / [ x - 1 ]    =    tiles needed

I do not understand your question. Can you please be more specific

Not totally sure about this, NSS...but here is my  best shot....

APY  = (1 + r/n)^n - 1

APY for monthly compounding =  (1 + .055/12)^12  - 1  ≈  .05640  ≈  5.640%

APY  for quarterly compoundng   = ( 1 + .055/4)^4  - 1  ≈  .05614 ≈ 5.614%

[5.640 - 5.614 ] ≈  .026%

Interest  = Pricipal *rate * time

1242 * .0125 * 1 month   =  $15.53 ⇒ B

 The ratio  area of triangle  PQT   to the area of  triangle  P (what)    ????

Using the answer from 9, we have

Total payback / 24 months

[2741.04] / 24   =  $114.21

We don't need to do any math here, NSS....we can't pay back less than $2500....so "D"  must be correct