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There are two ways: as 1/15 + 1/15 and 1/20 + 1/12.

2. 

Since f(x) is divisible by x^3, f(x) is of the form ax^5 + bx^4 + cx^3.

You then want ax^5 + bx^4 + cx^3 + 2 to be divisible by (x + 1)^3.  Using long division, you get the equations

-10a  + 6b - 3c = 0

4a - 3b + 2c = 0

-a + b - c + 2 = 0

==> a = 6, b = 16, c = 12

So f(x) = 6x^5 + 16x^4 + 12x^3.

X = (2,-4), so the sum of the coordinates is 2 + (-4) = -2.

In triangle ABC, angle bisectors AD and BE meet at a point I. Prove that angle DIB = 90 - angle BCA/2.

I'm purposely using a right-angled triangle because it gives me a better overall picture. 

Angle ADB = 180º - (90º + 30º) = 60º

Angle  DIB = 90º ∠BCA /2               ∠DIB = 90º - 30º/2 = 75º

Look at a triangle BID                       ∠DIB = 180º - (45º + 60º) = 75º  

( This is one way to prove it...This may not be the answer they're looking for.)

This is easy!  Just use Cauchy-Schwarz.

VERY similar:

https://web2.0calc.com/questions/please-answer-this_7

q/p = 4/3.

The probability is 3/32.

(a + (2n + 1)d)^2 - (a + (2n)d)^2 + ... + (a + d)^2 - a^2 = (a + (2n + 1) d + (a + 2nd + ... + a + d) + a = n(3a + (n + 2)d).

The Euclidean algorithm gives the solution (x,y) = (-30,133).  You can check that 164(-30) + 37(133) = 1.

oh, I never thought of doing it like that! thanks!

big prism   

one rectangle top is     6x 6

one rectangle front is   6 x 8

one rectangle back is   6 x 10

TWO triangular sides are      two   x   1/2  6 * 8      add all of these together ......

10)    from 10 :15   to  1:45    is      3 1/2 hours

        3 1/2 hr  x 700 km/hr = 2450 km

         compass bearing to airport is 330       30 west of north

9)    322 degrees from the ship forms   322-270 = 52 degree angle (at the boat 'tail' )

               tan 52 = opp/adj

               tan 52 = 18.5 / d

                   d = 18.5 / tan 52 = ~~14.5 km

      14.5 km /  48 km/hr = .301 hr      = 18 min

If h is degree 5 or less    the terms from adding it all have exponents 5 or less

f(x) is multiplied by a polynomial of degree 2

    the right side has a term of degree 6      so f(x) must be of degree 4

           example    x^2  * f(x)

                             x^2 * x^4   = x^6

Law of sines

7/sin90 = TU/sin40

TU = 7 sin40 = ~4.5 cm

I don't quite understand why Cphill chose to rearrange the equation like that though. 

360 total shares

A = 35 dolar share quant                             value =  35A

B = 45 dollar share quant   = 360-A             value = 45(360-A)       

     the values summed = 15000

35A     +   45(360-A) = 15000     Solve for A         then  B = 360-A

Well...thanx!   That makes my answer a lot more confident !     ~EP

Let x =  sqrt 9 sqrt27 sqrt128.......

square it      square it     square it again

and you have     x⁸ =    612220032 sqrt 9 sqrt27sqrt128.....    the red part is 'x'   

(61222032 is 9⁴27²128)

                           x⁸  =61222032 x

                           x^7 = 612220032

                            x = 18                          ????

Important: The Median Theorem states that the medians of a triangle intersect at a point called the centroid that is two-thirds of the distance from the vertices to the midpoint of the opposite sides.

ST² - TN² = SN²                

SX / NX = 2 / 1

SX = 2/3 * SN  

First find  SN length     pythag theorem    4^4  + SN^2 = 22^2      SN = 21.6333   or 2 sqrt117

UM goes up  sqrt117  units  (Pythag theorem again with a line dropped from M)    for a horizontal distance of 6 units

sqrt117/6 = NX/4       yields NX = 2/3 sqrt 117         sooooo   SX =  2 sqrt 117  -  2/3 sqrt 117 =  4/3 sqrt(117)  units    (I think ! )

Not positive about this answer !

To be honest with you, geometry is not my game, so I will not try. (I am willing to, but it may be wrong anyways.) Instead of having a sloppy answer by me, check out this answer by CPhill, since this problem has been posted before. 

CPhill answered very well, and it was quite easy to follow along : https://web2.0calc.com/questions/help-quick-plz_2