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If you factor  a² + 2a + 1, you get (a+1)(a+1).

Now the problem is:  (a+1) / [ (a+1)(a+1) ].

Cancel the (a + 1) in the numerator with one of the (a + 1)'s in the denominator, you have;

  1 / (a + 1)

If something is reduced by 12%, it must only be worth 88% of what it once was.

So, let P be the original price.

And we have...

88% of P  = 132.88      ....or, mathematically.......

.88 * P = 132.88           divide both sides by .88

P = £ 151

multiply 12x132.88 divide it 100 = 15.94

then just add 132.88 + 15.94 = 148.82 (original price)

Relax, rosala...it was just a joke........9 + 10 still = 19 !!!!  (I hope !!!)

OK....since each nalil is 1+ 3/4 in long = 1.75 in......then the total length of 240 of them must be....

240 x 1.75 in = 420 in = 35 ft.

CPhill , i dont understand , how can it be 18, have you any proof , i mean like any site showing the proof?

Sorry....geno and rosala.......I guess you haven't seen the latest release from the World Historical Academy of Arts and Technological Sciences of the Upper Peninsula ....otherwise known as (WHAAT'S UP???)

After rigorous proof and peer review, the esteemed gentlemen of the College of Mathematics at this venerated institution have concluded that the sum of 9 + 10 fails to follow established laws of sums and differences. In fact....it is the only sum known to do so. It has been found that this sum only equals 18 - not 19 - as previously suppposed!!!!

Therefore.......the WebCalc2.0 calculator will be reprogrammed to conform to this finding.......

Also, Dear Questioner......previous responses of "19" to your query are now amended and edited to "18"

Your Humble Servant,

CPhill

CPhill , your always the first one to post a comment on my laughs!thats really nice of you!i'd give  a point for it!

and yes , History does interest me a lot!and i guess thats a nice option , be a professor!sounds interesting!

Thanks for the informative "tour" of Delhi, rosala......you should be a history/cultural studies professor......!!!!!!

Use a calculator to find invSin(0.8752).  Usually, you'll need to use the (2nd) key or the (shift) key.

Similarly, you can find invCos and invTan.

Thank you CPhill! I think I understand now.

Heres the answer to your question Sir.Anonymous!(lol, sounds too formally funny hun?)

Geno's answer is good....let me see if I can break it down more for you....

Let the first integer = x

Then, the next odd integer is just two more = x + 2

And the 3rd odd integer is just two more than the second = (x + 2) + 2 = x + 4

Now...let's look at what's said (in pieces)

"The sum of the first and the third" is just x  + (x + 4)   = 2x + 4

So....."Four times the sum of the first and the third" is just  4(2x + 4)     =  (A)

And "The product of 3 and the second number means to multiply the second number by 3 =  3(x + 2)  = (B)

Now....here's the tricky part.....

We're told that (A) is 5 more than (B)...this must mean that, if I subtracted 5 from (A), I'd end up with (B) !!

Therefore......(A) - 5 = (B)

And, substituting in for (A) and (B),we have

4(2x + 4) - 5 = 3(x + 2)

Simplify both sides

8x + 16 - 5 = 3x + 6

8x + 11 = 3x + 6

Subtract 6 and 8x from both sides

5 = -5x

Divide both sides by -5

-1 = x

That's the first integer

And the second is just  x + 2 = -1 + 2 = 1

And the third is just x + 4 = -1 + 4 = 3

And that's it !!!

12^3  =  12 x 12 x 12  =  1728

It also equals (3·4)^12  =  3^12 · 4^12

Plus a lot of other expressions; just what are you looking for?

We need to find the proportionality constant, here.     

So we have

y = kx     

And we/re told that

10 = k500  

Divide both sides by 500

k = (1/50)

So the relationship is given by

y = (1/50) x

Thanks for your help but I am still totally lost on this one.

Anonymous , posting this question again  n again wont change the answer!it will reamin 19 till the end of this Earth so the answer is 19 , once again!

It's still 19.

I'm picturing something that looks like a Rubik's cube, but each side is  4 x 4.

The top side is  4 x 4             (so 16 cubes); 

the bottom side is also 4 x 4  (so another 16 cubes)

the front side is  4 x 4  but  we already have cubes on the top and on the bottom,                                                                                       so all we need are another  8 cubes

same for the back side           (so another  8  cubes).

for the left side, we have its top row, its bottom row, its left column and its right column, 

                                            so all we need are  4  more cubes

same for the right side          (so another 4  cubes )

For a total of 56 cubes.

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

Another way to look at this (perhaps easier) is to find the total number of cubes necessary if it were hollow:        4 x 4 x 4  =  64

And then subtract out the inside; which is a  2 x 2 x 2  cube  =  8 

For a total of  64 - 8  =  56  cubes

4×4×4=64 cc

If  x  is the smallest odd integer, then  x + 2  will be the next larger odd integer, and  x + 4  will be the largest of the three odd integers.

4[ (x) + (x + 4) ] = 5 + 3(x + 2)

4( 2x + 4 )  =  5 + 3x + 6

8x + 16  =  3x + 11

5x  =  -5

So the smallest integer is  -1.

Use this to find the other two.

If we call the numbers  x  and  y:

                                               x + y  = -5

                                               x - y  =  13

Add down the columns to get:  2x      =  8,  which means that  x  =  4.  

Then, using the equation  x + y  =  -5     --->     4 + y  =  -5     --->     y  =  -9  

-2 - 37    is    -2 + -37    which equals  -39

To remove a  log  use the  (2nd) log  feature of your calculator or use  10^x.

if  log K = 18  then  k = 10^18 

Prime numbers are:  2, 3, 5, 7, 11, ...

Start with 2:  900 ÷ 2  =  450

                    450 ÷ 2  =  225

                    225 ÷ 2  =  a fraction; so, don't count this

Next, try 3:  225 ÷ 3  =  75

                     75 ÷ 3  =  25

                     25 ÷ 3  =  a fraction; so, don't count this

Next, try 5:    25 ÷ 5  =  5

                      5 ÷ 5  =  1  We're done!

The prime factors are 2, 3, and 5.

The prime fractorization is:  2² · 3² · 5²   (the prime factors with the number of times each one is used)