geno3141

Assuming that you want to factor:  5n³ -40n² + 4n - 32

Split this into two groups, the first two and the last two:

                                                  [ 5n³ - 40n² ] + [ 4n - 32 ]

Factor 5n² out of the first two and factor 4 out of the last two:

                                                   [ 5n²(n - 8) ] + [ 4(n - 8) ]

                                                       5n²(n - 8)  +  4(n - 8)

Factor (n - 8) out of the two parts:

                                                           (n - 8)(5n² +  4)

Since 5n² +  4 cannot be factored any furher, we are done.

Replace x = 6 and y with -2:

    -2   ?=?   (1/2)·(6) - 5

                         3 - 5

                          -2

The left side does equal the right side, so it is a solution.

All points in Quadrant I have the form  (+, +).

All points in Quadrant II have the form (-, +).

All points in Quadrant III have the form (-, -).     <---(-2, -5)

All points in Quadrant IV have the form (+, -).

7n - (9n + 1) > 5

Distributive the negative sign:

7x - 9n - 1 > 5

Simplify:

    - 2n - 1 > 5

Add  1  to both sides:

         -2n > 6

Divide both sides by -2 (whenever you multipy or divide an inequality by a negative number, you must change the direction of the inequality sign; you don't change the direction if you multiply or divide by a positive number):

           N < -3

If Saturn is 1.43 x 10^12 km from the sun and earth is 1.5 x 10^8 km from the sun, to find the distance between them subtract:  

       1.43 x 10^12  -  1.5 x 10^8

Get the same exponent on 10:

       1.43 x 10^12  =  1.43 x 10^4 x 10^8  =  1.43 x 10000 x 10^8  =  14300 x 10^8

      14300 x 10^8 - 1.5 x 10^8  =  14298.5 x 10^8  

But, we can't be that precise, so rounding it, we have: 14300 x 10^8  =  1.43 x 10^12

A rather surprising answer, but Saturn is 10000 times farther away from the sun as we are!

Slope-intercept form:  y  =  m·x + b

where  m  is the slope and  b  is the y-intercept.

Use the distributive property to reduce  7(3x + 6)  to get  21x + 42.

Use the distributive property to reduce  5(4x - 3)  to get  20x - 15.

7(3x + 6) - 2  =  6 + 5(4x - 3)

 21x + 42 - 2  =  6 + 20x - 15

Simplify each side:

     21x + 40  =  20x - 9

Subtract  20x  from both sides:

         x + 40  =  -9

Subtract  40  from both sides:

       x  =  -49

( -10 ± √212 ) / 8

=  (-10 ± √4√53 ) / 8

=  (-10 ± 2√53 ) / 8

Now, this fraction can be reduced by cancelling only if you cancel out of the -10, the 2, and the 8; you can cancel 2 out of each: (when you cancel 2 out of 2, it becomes 1, but you need not write it in this case)

=  (-5 ± √53 ) / 4

Remember: when cancelling, you MUST cancel the same number out of ALL THREE!

I'm assuming that you mean  0.12 1122 111222 ...

This pattern does not repeat, because each block of digits gets longer; for a pattern to repeat, the same block of digits (such as 1234) must continue to repeat, in the original fashion, from there forever; for example:

198.72736 1234 1234 1234 1234...

Look at both the numerator and the denominator. If you can find a number that divides evenly into both, divide that number out of both the numerator and the denominator.

You now have a reduced fraction. Now, go back and do the previous step again and again, until you can't do it anymore.

For example:    210 / 378

Since they are both even, 2 will divide into both the numerator and the denominator; after dividing each by 2:

  =    105 / 189

They aren't even, so 2 won't work again, try 3:

  =    35 / 63

If you try 3 again, it won't work (35 isn't divisible by 3); 5 won't work (63 isn't divisible by 5), but 7 will:

  =  5 / 9.

No more numbers work; you're done!