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abcd =2,996

[2 * 2996 + 1000] =6,992 =dcba

can u show me how u got this answer

Did you forget the 2nd step for the number of cups of yellow paint?

[4.5 / 8 ] * 12 =6.75 cups of yellow paint.

5.25 red + 6.75 yellow =12 cups of orange paint.

Observation: What's the minimal polynomial of \(x\)?

\(2x = 1 + \sqrt 3\\ 2x - 1 = \sqrt 3\\ (2x - 1)^2 = 3\\ 4x^2 - 4x - 2 = 0\\ 2x^2 - 2x - 1 = 0\)

Having that in mind:

\(\quad 4x^3 + 2x^2 - 8x + 7\\ = 4x^3 - 4x^2 - 2x + 6x^2 - 6x + 7\\ =2x(2x^2 - 2x - 1) + 3(2x^2 - 2x - 1) + 10\\ = 2x(0) + 3(0) + 10\\ = \boxed{10}\)

3c + 5 - 4c =   (3c-4c) +5 = - c+5       or       5-c

Let \(t = x - \dfrac1x\).

\(t^2 + 2 = x^2 + \dfrac1{x^2} = 171\)

\(t^2 = 169\)

\(t = \pm 13\)

\(x - \dfrac1x = \pm13\)

Therefore there are two possible values.

a+b has to equal t

a*b  has to equal - 9   

-9 1

9 -1

3 -3

-3 3       two of these are repeats      so    9 , -1   and  3,  -3      these add together  to make t =  8  or 0     summed = 8

(5x^2 +3x^2)   + (-2x + x)  +  ( -4)

8x²  - x - 4

the amount of space to be divided equally    =  3 3/4 - 2 1/2  =  1 1/4 inches

1 1/4  / 2  =   5/8  inch on each side of the label to the edge  

vertex   -2, -3

Vertex form of parabola:    y = a (x-h)² + k

y = a  (x+2 )^2   - 3      Now look at x = -4   the function needs to be = -1

      x^2+4x+4    - 3 = -1

      a(16 -  16 + 4) - 3 = -1

          4a = 2

             a = 1/2

y = 1/2 (x+2)² -3

Ratio of red to yellow    3.5 : 4.5       3.5  out of 8 are red    or   3.5/8

3.5/8  * 12 cups = 5 . 25 cups    or    5 1/4 cups red

Both of these are incorrect

6 x 6 x 6 = 216 possible rolls

'5' rolls

113

131

311

221

212

122       6 out of  216      (I think)

Sorry..... I misread (actually didn't read the whole Q)...

23 people must shake hands with AT LEAST 2 other people

23 x 2 = 46 handshakes    ....but each involves TWO people    sooooo   46/2 = 23 handshakes

Formula for distance from a point to a line :

3x+4y-5 = 0   (your line)       point (0, 0 )  means  x₁=0   y₁=0

a = 3   b = 4   c = -5

d=|ax1+by1+c| / sqrt(a2+b2)                    thry this ....let us know what you find !

I tried putting your answer in to the system but it said that the answer is incorrect.

23 people must shake hands with 22 other people  

   this would be 23 x 22 = 506 handshakes BUT two people are involved with each handshake

     so   506 /2 = 253 handshakes

Your welcome

Thanks so much!

So a circle has 360 degrees and each of them is that percent of 360 and we have:

Romance:  43.2 degrees

Comedy:  54 degrees

Science Fiction:  100.8 degrees

Adventure:  144 degrees

Other:  18 dgerees

Correct-o-mundo !

These questions are st up like this:

1/x + 1/y = 1/ t         t = 2 hours

1/5  + 1/y = 1/2        solve for y...the time for y alone

just to double check is x=11, -3

if it is do i add them?