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(4  + 1)(8 + 1)(2 + 1)(2 + 1) = 5 * 9 * 3 * 3 = 45 * 9 = 405

you can simplyfy this into 4^2 * 81^2 * 5^2 * 7^2

so you can have 2, 4, 8, 16, 9, 6, 3, 81, 25, 5, 15, 49, 7, and 45 just to name a few.  Try to find out more by multypliying some of the numbers.

The VERTICAL line (via pythag theorem)  =   sqrt (5^2 - 1^2 ) = sqrt 24

then use pythag theorem on the larger triangle

(sqrt24)^2 + 5^2 = ?²

     24 + 25    = ?²

           49 = ?²         then ? = 7 units

12 m x 250 m = 3000 m²

3000 m^2  / ( .3048 m/ft  * .3048 m/ft) = 32291.73 ft²

32291.73 ft²  /  200 ft² / gal = .........    gallons     ( round UP to whole gallons)

We will asume you want a straight line distance from E to A

she needs to throw it UP 8 ft to reach the height of A    and horizontally 15 feet

using pythagorean theorem     d^2 = 8^2 + 15^2          d = 17 ft

y^2 +(- B-C) y + BC = 6y^2 -y-15

A = 6   

- B-C = -1                       (    and  BC = -15  )

  B+C = 1

then A + B+ C = 6 +1 = 7

By the Pythagorean Theorem, the question mark is sqrt(39 + 25) = sqrt(64) = 8.

There are four ordered pairs (m,n).

Divisors of 30

1   2    3   5    6   10    15   30      Reds are prime nos.

When x = 0 the equation becomes

1 + 0 + 1 + 0 = 2

  as x increases toward infinity , so does the value of the function

so range   [2, + inf)

Binomial Coefficient

The sum formula : n(n + 1)/2

n(n + 1)/2 = 325, so n(n + 1) = 650, so n = 25 

Edit: hope that helped

x = 369       100(369) mod 997 = 11

admission and 9     minus    admission and 4      will give you the cost of 5 samples

   11.75                       -           6.75                      =  $ 5    for five samples   <===== each sample costs $ 1

so for admission + 4 samples

  6.75 = admission + 4

2.75 = admission

y = $ 2.75 + $1 (x)

y =  $ 2.75 + $ x

y = 2.75 + x             would be the cost   2.75 to get in....then $1 for each sample

Answer 17

\((a + b)^{-1}(a^{-1} + b^{-1}) \equiv (a + b)^{-1}(a + b)(ab)^{-1}\equiv(ab)^{-1}\equiv2\pmod{n}\)

\(\quad \dfrac1{\sqrt2 +\sqrt5+\sqrt7}\\ =\dfrac{\sqrt2-\sqrt5+\sqrt7}{(\sqrt2+\sqrt7)^2-\sqrt5^2}\\ =\dfrac{\sqrt2-\sqrt5+\sqrt7}{4+2\sqrt{14}}\\ =\dfrac{(\sqrt2-\sqrt5+\sqrt7)(2-\sqrt{14})}{(4+2\sqrt{14})(2-\sqrt{14})}\\ =\dfrac{\sqrt{70}-2\sqrt5-5\sqrt2}{2(2^2 - \sqrt{14}^2)}\\ = \dfrac{2\sqrt5 + 5\sqrt 2 - \sqrt{70}}{20}\)

Nice answer! 

Well for this one you would need to first do 8.90 * 7 then 7.20 * 1

So, 8.90 * 7 = 62.30

then, 7.20 * 1 which of course is 7.20

Then you add the two together,

So, 62.30 + 7.20 = 69.50 

Hope that helps.

A square sheet of paper ABCD is folded such that B falls on the midpoint M of CD. In what ratio does the crease divide BC?

Here's another way of looking at it:

The volume of a conical frustum is 2401π cu. cm. If the radius of the lower base is 14 cm and the altitude is 21-cm.

Calculate the lateral area of the conical frustum. *

Actually it’s “Field’s Metal,” the metal alloy that melts at 144°F.

This is the principal alloy forming the composite medal known as the “Fields Metal,” which is analogous to the Ig Nobel Prize.

The Ig Nobel Prize is awarded to those who make trivial contributions in scientific research, especially if a significant amount of time and research funds are invested in the process.  

The Fields Metal is awarded to those who have advanced skills at stating the obvious and presenting fake math in the form of pseudo mathematical prestidigitation. One advanced method is to use one of the organic Houdini processing algorithms, where one or more mathematical theorems and the numerical data are fed to a bull. After the bull digests it and dumps the Pi, the prestidigitator reveals his true self as a mutant dung beetle –aka a bullshit bug, and presents the wondrous BS solution for all to admire.      

Our forum’s wunderkinder do not presently have these skills, but they have the talent to easily learn them. At present their skills allow them to make advanced trivial contributions to trivial math problems, skillfully stating the obvious and burying most of the actual process in bullshit.

If you mentor them Mr. BB, they will become the youngest winners of the Fields Metal in history. 

GA

Let the lower base  = R   and  the upper  base =  r

And we have that

V =  (pi/3) height  ( r^2   + Rr   + R^2)

2401 pi  = (pi/3)  21  *  ( r^2 + 14r + 14^2)

2401/7  =  r^2 + 14r + 196

343  = r^2  + 14r+ 196

r^2 + 14r   - 147 =   0

(r + 21) ( r - 7) = 0

r - 7 =  0    

r = 7(cm)   =  the  upper base

Lateral surface area =    pi *slant height  *  ( R + r)

slant height =   sqrt   [  (R-r)^2  + h^2  ]     =   sqrt  [ (14 - 7)^2 + 21^2 ]  =  sqrt [ 49 + 441] = sqrt [ 490] =

7sqrt (10)

Lateral surface area =    pi * 7sqrt (10)  *  ( 14 + 7)  =  147sqrt (10)  ≈  1460 cm^2