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Domain  ....we ask.........what values are  covered  by x  ???  this is    -3 ≤ x ≤ 3

Range  .....we ask.....what values are covered by y  ???   this is    1 ≤ y ≤ 4

What is the greatest integer value of x for which 6x^2 + x - 2 < 0?   

This will factor to ( 3x + 2 )( 2x – 1 )

So you get      3x = –2   therefore   x = –2/3 

and you get     2x = +1   therefore   x = +1/2 

_.

Thank you! This helped a lot!:D

Let's look at this from a slightly different perspective

Let the  interger  in   the exact  middle of the two integers   (their average) =  x   

Then the lesser  number =   (x - 9)

And  the greater =   (x + 9)

Note that there is a difference of 18 units  between the integers

Note  that  their product is  ( x - 9) ( x + 9)  =  x^2  - 81

This is an upward turning parabola.....we will have no max.....but we will have a minimum  (at the vertex )

The  vertex  is at   (0, -81)....so  this is the  minimum  =  -81

Then this  must  imply  that  x  = 0       because  0^2   - 81   =   -81

So

( x - 9)  =  -9   ⇒  the lesser integer

And

(x + 9)  =   9 ⇒  the greater integer

How about you? I'm curious :D

Correct-a-mucho, Chris! LOL

Let       B =  number of burgers

      B - 2  =  number of fries

           D  =  number of drinks.

B + (B - 2) + D  =  53

  B + B - 2 + D  =  53

            2B + D  =  55

   6·B + 3·(B - 2) + 2·D  =  204.00

         6B + 3B - 6 + 2D  =  204.00

                       9b + 2D  =  210.00

Combining these two equations:

     9B + 2D  =  210                                        --->      9B + 2D  =   210

     2B +   D  =    55     --->   (multiply by -2)   --->     -4B - 2D  =  -110

    (adding down the columns)                                   5B          =  100

                                                                                            B  =  20

Since  2B + D  =  55   --->   2(20) + D  =  55   --->              D  =  15

Since the number of burgers is 20, the number of fries is 18, and the number of drinks is 15.

Pretty  easy to  figure  if  we  just think about  it

%  of shaded region  =  

degrees  in central angle  /  total  degrees  in a circle  =

106  /360   =   .294  ≈  29.4%

Hehe thanks :D

Good job, geno!

I got most of it wrong anyway -_-

Good job, Chris :)

Solution:

The first 10 terms of an arithmetic sequence can be represented as, where is the first term and is the constant difference between each consecutive term. So, the sum of all of these terms will include and, which equals. As a result, the sum of all the terms is and the greatest number we can factor out is, where we end up with 5(2x+9c). or 5

@Fourth, it's okay! Anyone can post!