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Then why does it not have the off-topic marking????

Are you sure this is off topic...

Travis?

?

And also, Happy B-day

I almost posted happy d-day... :( whoops

thank you sorry your a db is it genetic by birth or what

yes it is off topic

Please tell me this is off topic.

Please Travis?

I'm only a regular sorry Guest but I have diabetes so I'd have to pass on the cake but thanks anyway.  Happy Birthday.

.

No problemo amego

Travisio

Triple click on the blank line to reveal some hidden text

Ok Thank you Travisio

Sorry, M-G.....saw that a little too late

its even numbers

Never mind !    I see it says 'even' numbers    !!!!!!

There are 968 such numbers that begin with:

10048  10066  10084  10138  10156  10174  10192  10228  .............etc.

Note: If you want them all listed, just let us know.

Thank you! This should've been easy, I will have to remember about isosceles triangles and Pythagorean theorem.

You are welcome..... I hope you understand the solution!   ~EP

There are 22 "a_n" that are divisible by 9:

a_8, 9, 17, 18, 26, 27, 35, 36, 44, 45, 53, 54, 62, 63, 71, 72, 80, 81, 89, 90, 98, 99.

Let \(a_n\) be the number obtained by writing the integers 1 to n from left to right. Therefore, \(a_4\) = 1234 and \(a_{12}\) = 123456789101112. For 1 ≤ n ≤ 100, how many \(a_n\) are divisible by 9?

Hello xXxTenTacion!

\(checksum\\ \sum^i_{i=1}(n_i)=(1+i)\cdot \frac{i}{2}\)

1  1

12  3

123  6 

1234  10

12345  15

123456  21

1234567  28

                  36  45  55  66  78  91  105  121 ... 5050

12345...100  5050

Sorry. I have to give up.

3)

-3 + 4i           [ 1 - 2i ]          -3 + 4i +6i - 8i^2          -3 + 10i - 8(-1)          5 + 10i

_______                       =   ______________  =   _____________  =    ______  =

1  + 2i           [ 1 -2i ]           1 -  4i^2                        1 - 4(-1)                        5

1 + 2i

BTW ....William Sydney Porter  ....better known as  .....  "O Henry "

Thank you!!!

Price of phone = 450 - 5x      where x = number of $5 decreases in price

    income from number of phones sold will be   500(450-5x)  + 10x (450-5x)

                                                                                 225000 - 2500x + 4500x - 50 x^2

                                                                                 - 50 x^2  + 2000x + 225000     = revenue

          Max occurs at - b/2a  =  -2000/(2*-50) = 20 reductions of $5

                  $350 price results in maximum revenue of $ 245000

2)    sumfor(n, 1, 44, 2*n^2) + 27*45 = 59,955

1.

2log ( a - 2b)  = log a + log  b

log(a - 2b)^2  = ;og (ab)      which implies that

(a - 2b)^2  = ab

a^2 - 4ab  + 4b^2  =  ab

a^2 - 5ab + 4b^2  =  0    factor

(a - 4b)  ( a - b)  = 0

So...either   a - 4b  = 0  ⇒   a = 4b   ⇒  a / b   = 4    (1)

or

a - b  =  0   ⇒  a  = b

If a is positive.....the original log on the left hand side is undefined

If a is negative......log a is undefined..so...

a / b   = 4

2(x - 4)^2  + 8   =

2 (x^2 - 8x + 16) + 8  =

2x^2 - 16x + 32 + 8  =

2x^2 - 16x  + 40    so........a = 2, b = -16 and c  =  40

So....3ax^2 +3bx + c   =   3(2)x^2 + 3(-16)x  + 40  =  6x^2  - 48x + 40

Factor out the 6  and we have

6 ( x^2  - 8x   +  40/6 )      T

Take 1/2 of - 8  = - 4.....square this = 16 and add and subtract within the parentheses

6 ( x^2  - 8x  + 16  + 40/6 - 16)    factor the first three terms  and simplify the rest

6 [ (x - 4)^2 +  20/3  -48/3 ]

6 [ ( x - 4)^2  - 28/3 ]

6 ( x - 4)^2  - 56

So h = 4

The guest's answer is correct, Manuel.....

Because it appears that  (0,0)  is on the graph, the numerator has the form Dx^2

Because we have vertical asymptotes  at x  = -2  and x = 3.....the denominator has the form

A (x + 2) (x - 3)

And the line y = 0.4 = 2/5  is an asymptote  for x > 4......so  we might guess that the ratio of D/ A  = 2/5

So....it appears that we have

                          2x^2                    2x^2                          2x^2

f(x)  =    ______________ =     ______________ =    _________________ 

              5 ( x + 2) (x - 3)           5 (x^2 - x - 6)             5x^2 - 5x - 30

So A + B + C  =   5 - 5 - 30   =    -30

Note that when  x < -6, the graph  will cross the asymptote of y = 2/5

Here's a graph :  https://www.desmos.com/calculator/7i9wnrvuuc