geno3141

(4x² - 16x + 7) / (x² - 4x + 4)  >  3

Multiply both sides by  x² - 4x + 4:

4x² - 16x + 7  >  3(x² - 4x + 4)

4x² - 16x + 7  >  3x² - 12x + 12

Subtract  3x² - 6x + 12 from both sides:

x² - 4x - 5  >  0

(x - 5)(x + 1) > 0

Either  both x - 5 and x + 1 are positive   or  both x - 5 and x + 1 are negative.

If  x - 5 > 0  and  x + 1 > 0   --->   x > 5  and  x > -1   --->   x > 5

If  x - 5 < 0  and  x + 1 < 0   --->   x < 5  and  x < -1   --->   x < -1

Answer:  x < -1  or  x > 5

-3 x 3 + 4

=  -9 + 4

=  -5

press (2nd)

press (atan)                          <--- "atan" = "arc tan" = "inv tan"

enter the number 

press (=)

When graphed, 5.25 is the slope of the line, representing the cost of manufacturing each radio.

Also, when graphed, 125 represents the y-intercept, which is the start-up cost.

"!" means "factorial" and it's a fast way to indicate multiplication:

0!  =  1                     (a special case)

1!  =  1                     (a special case)      also:  1!  =  1 x 1!

2!  =  2 x 1  =  2                                   also:  2!  =  2 x 1!

3!  =  3 x 2 x 1  =  6                              also:  3!  =  3 x 2!

4!  =  4 x 3 x 2 x 1  =  24                       also:  4!  =  4 x 3!

5!  =  5 x 4 x 3 x 2 x 1  =  120                also:  5!  =  5 x 4!

etc. 

Another way to define !:  0! = 1  and, if n is a whole number > 0:  n! = n x (n - 1)!

2p - 10 - 4p - 7

=  2p - 4p  - 10 - 7

=  -2p  - 17

happy 7 is correct.

If you need to show some work:   14/x² - 9 + 6/x - 3  =  8/x + 3

Multiply each term by x² to get rid of denominators:

                (x²)(14/x²) - (x²)(9) + (x²)(6/x) - (x²)(3)  =  (x²)(8/x) + (x²)(3)

                                               14 - 9x² + 6x - 3x²  =  8x + 3x²

                                                      14 - 12x² + 6x  =  8x + 3x²

                                                       14 - 15x² - 2x  =  0 

                                                      -15x² - 2x + 14  =  0

                                                       15x² + 2x - 14  =  0

Using the quadratic equation:  x  =  [ -b ± √(b² -4ac) ] / (2a)

                             a = 15     b = 2     c = -14

                                            x  =  [ -2 ± √(2² -4·15·-14) ] / (2·15)

                                            x  =  [ -2 ± √(4 + 840) ] / (30)

                                            x  =  [ -2 ± √(844) ] / (30)

                                            x  =  [ -2 ± √4√211 ] / 30

                                            x  =  [ -2 ± 2√211 ] / 30

                                            x  =  [ -1 ± √211 ] / 15

Drawing the number 41:  If she uses only the numbers from 1 through 40, can she draw the number 41?

Is the chance of drawing a number between 1 and 16 the same as drawing a number between 17 and 40 ?  --- How many numbers are from 1 through 16, how many numbers are there from 17 through 40, are there the same number of numbers in both cases?

Is the chance of drawing an even number the same as the chance of drawing an odd number?  -- How many even numbers are in the range of 1 through 40? How many odd numbers are in the range of 1 through 40? Are there the same number of numbers in both cases?

Drawing a multiple of 10: which are 10, 20, 30, and 40. Is the chance of drawing a multiple of 10 the same as the chance of drawing a number (from 1 through 40) which is not a multiple of 10?

(2x² + 63y²)(2x² - 63y²)

Using FOIL  (First, Outside, Inside, Last):

(2x²)(2x²)  +  (2x²)(-63y²)  +  (63y²)(2x²)  + (63y²)(-63y²)

=  4x⁴  -  126x²y  +  126x²y²  -  3969y4

=  4x⁴  -  3969y4

2x - 7  =  19

      2x  =  26                     (add 7 to both sides)

       x  =  13                      (divide both sides by 2)