CPhill

Thks, EP......I never remember this method, but it's a good one....!!!

42 + 2n  ≥ 80

And

2n ≥ 80 - 42

2n ≥ 38

n ≥ 38 / 2

n ≥ 19

9.5 for children   +  9.5 for adults  =

9.5c + 9.5a  =

9.5 ( c + a)

We don't need to worry about the "5"  part, yet

1)  Take 228  and subtract  the non-repeating part of the decimal  =  228- 22 = 206....this is our numerator

2) In the denominator, write the same number  of 9's as the repeating part  of the decimal= 9

    And write the same  number of 0's as the non-repeating part  of the decimal = 00

So  .228 (8 repeating)  =   206 / 900 =   103 / 450

So we have

5 + 103 / 450   =  2343 / 450

Thx, Mari  !!!

\( x=\frac{a+b\sqrt{c}}{d} if 5x/6 +1= 3/x - 1\)

5x / 6  + 1 = 3/x  -1        multiply through by the common  denominator of 6x

5x^2 + 6x  = 18 - 6x     rearrange as

5x^2 +12x - 18  =  0

Using the Q Formula  we have x = 

-12 +  sqrt  [ 12^2 - 4 (5)(-18) ]                   -12 +  sqrt  [ 144 + 360]            -12  +  sqrt [ 504]

_________________________=              ____________________ =     ________________ =

          2 (5)                                                                10                                      10 

-12  +    6 sqrt  [  14  ]               -6   + 3sqrt [14 ]

_________________   =      __________________

              10                                          5

acd / b   =  (-6) (14) (5)  /  3  =        -140

Factor as   ( x -3) (x + 2)

                 ____________

                  ( x - 5) ( x + 2)

The function is not continuous at x values that make the denominator = 0   ⇒ x= 5  and x = -2

We have a removable discontinuity  at    x + 2 = 0  ⇒     x =  -2

The function is not continuous when an x makes the denominator  = 0.....so.....

x^2 - 16   = 0

(x + 4) ( x - 4)  = 0

Setting each factor to 0  and solving for x  produces   x = -4  and  x = 4

Factor the   numerator  as  ( x + 4) ( x + 7)

We are left with

(x + 4) ( x + 7)             ( x + 7)

___________  =        _______       

(x + 4) ( x - 4)              ( x  - 4)

The discontinuity is  removable  at  ( x + 4)  = 0    ⇒  x = - 4

f(0) =   7

f(1)  = 16

7 ≤ k ≤ 16

Factor  the numerator as   (5x + 6) ( - x + 2)

Factor the denominator as  ( 3x + 5) ( -x + 2)

We are left with

(5x + 6)  /( 3x + 5)

The value of C  that makes this  continuous at x = 2   is     ( 5 (2) + 6)  / (3(2) + 5) =   16 / 11