geno3141

Since I am one of the five friends, we each get 4/5ths of an apple.

If you are going to graph them, you can use the slope-intercept form above.

You can also just find the intercepts:

7x + 3y = 21

    when x = 0, y = 7     --->   (0,7)

    when y = 0, x = 3     --->   (3,0)

    plot these two points and draw the line that connects them

-7x + 3y = 21

   when x = 0, y = 7      --->  (0,7)

   when y = 0, x = -3     --->   (-3,0)

   plot these two points and draw the line that connects them

At what point do these two lines intersect?

If you can only use the whole numbers from 1 through 9 to solve that problem, you won't get an answer.

1/x² + 1/x + 1/x = 1

1/x² + 2/x = 1                         

1 + 2x =  x²                                (multiplying both sides by x²)

0 = x² - 2x - 1

x = 1 ± √2                                   (using quadratic formula)

The calculator at this site can give you the answer.

Since I'm driving the bus, I could look into the mirror, or look at my driver's license, or ask the person next ot me, ...

1 000 x 1 000 = 1 000 000

Place a zero in front of the decimal point, then the decimal point, then 29 zeros, then 7.

If you are supposed to change from standard form to y-form (which is slope-intercept form):

7x + 3y = 21

       3y = -7x + 21                 subtract 7x from both sides

         y = -(7/3)x + 3             divide by 3

-7x + 3y = 21

         3y = 7x + 21                add 7x to both sides

           y = (7/3)x + 7            divide by 3

But, I don't know what the instructions of the problem are. (And, I don't know why there is a comment about absolute value.)

Taking a shot into the dark:  no, they aren't perpendicular and no, they aren't parallel.

Can you post back with the rest of the instructions?

First, I am going to eliminate x:

Using the first two equations:

x - 3y + 6z = 21      --->  x -3                  --->     -3x + 9y - 18z = -63

3x + 2y - 5z = -30   --> leaving this alone  --->     3x + 2y - 5z = -30

               Adding down the columns          --->            11y - 23z = -93

Using the first and the third equations:

x - 3y + 6z = 21      --->  x -2                  --->   -2x + 6y - 12z = -42

2x - 5y + 2z = -6    --->  leaving this alone  --->  2x - 5y + 2z = -6

               Adding down the columns           --->           y - 10z = -48

We now have thse two equaitons:

 11y - 23z = -93

y - 10z = -48

Eliminating the y-term:

11y - 23z = -93    --->  leaving this alone  --->  11y - 23z = -93

-y - 10z = -48       -->  x  -11     --->               -11y +110z = +528

               Adding down the columns        --->                87z = 435            --->  z = 5

Substituting z = 5 back into y - 10z = -48   --->   y - 10(5) = -48               --->  y = 2

Substituting z = 5 and y = 2 back into x - 3y + 6z = 21  --->  x - 3(2) + 6(5) = 21   ---> x = -3

I hope that helps!

2*( (2 @ 6) @ -4 ) - 1

2 @ 6  =  (6 + 2)(6 - 2)  =  (8)(4)  =  32   because a ≤ 5 and b > 5

=  2*( 32 @ -4 ) - 1

32 @ -4  =  (32 + -4)((32 - -4)  =  (28)(36)  =  1008  because a > 5 and b ≤5

=  2*(1008) - 1

=  2016 - 1

=  2015