All Answers 355956 Answers

We can place the box in the coordinate space, and solve the planes of the faces.  This gives us a volume of 32.

The polynomial is f(x) = 16x^3 - 61x^2 + 29x + 46, and the sum of the coefficients is 16 + (-61) + 29 = -16.

x= 3

y= -7

z= 2

9^-6

cancel out the exponents, we get 9^-6

1/9^6

(1/9)^6

I'm not that good at math... I might not be correct.

We only want one decimal place

So...   4.8

9x - 7y  = - 63

To get the slope, isolate y

-7y  =  - 9x  -  63       divide both sides by -7

y  =  (9/7)x + 9        the slope is 9/7

y intercept.....let x  =  0

9(0)  - 7y  =  - 63

-7y  = - 63       divide both sides by -7

y  = 9

x intercept.....let y  = 0

9x - 7(0)  =  -63

9x  = -63    divide both sides by 9

x  =  -7

See the graph here :   https://www.desmos.com/calculator/rj05khxcvb

36 = 2² * 3².

wait so its 4.8 or 4.86? or 4.858

Quick Question... Whoever downvoted TacoBell and My post...what is wrong with it!!

Nice solution!

Haven't seen one like this before....

Note that  4!   =  24

And 5!  =  120

So...we might guess that  x   falls between these two values

4.8! + 2(4.8)  =  95.198

4.9!  + 2(4.9)  = 111.04

Test some values  for  x   in  x! + 2x

x             result

4.81      96.66

4.85      102.77

4.86      104.36

It appears  that  4.8  is what we need

BTW....WolframAlpha  shows the result to be  x  ≈ 4.858

  Slope = 2.571/2.000 = 1.286

  x-intercept = 14/9 = 1.55556

  y-intercept = 14/-7 = 2/-1 = -2.00000

30.8333333

I have a different result.

The two trains meet after 125 minutes the first starts or at 2:05 pm

A 3-digit number is peachy if it has a 3 in the middle, or it both starts and ends in a 3.

There are 9*1*10 for the first one

There is 10 of the second type, but because we already counted 333 in the first case, so we don't have to count it again 

Without the overcounting, we get 9 new peachy numbers in the second case.

Therefore, there are \(90 + 9 = \boxed{99}\) peachy three-digit numbers.

A:B           A:B:C

3:7           3:7:4 =14

A:C            A:ALL SUITCASES

3:4             3:14

Call the  mass of  A  = M

Then the mass of  B  =  (7/3)M

And the  mass of C  =  (4/3)M

So     the total mass of all 3  =  M ( 1 + 7/3 + 4/3)  =  M ( 14/3)

So....the ratio  is

   M

________   =      3 /14   =    3 :  14

(14/3)M

o _ O xD

:D AoPS?