CPhill

Hey, Hayley  !!!

-25+[7-(-2-3)]+(1-3)^4  =

-25 + [  7 - (-5) ] + (-2)^4  =

-25 +  [ 12 ] + 16  =

-25  +  28  =

3

a₁  =   3

a_n  =   a_n-1 * (1/6)

Thanks, X²

Here's another way to do this

Irma  paints   1/9  of a room in one hour

Paulo  paints  1/8  of a room in one hour

So.....Rate  * Time  =  Total Job Finished

(1/9)x + (1/8)x   =  1

(9  + 8) x

________      =  1        cross-multiply

    72

17x  =  72       divide both sides by 17

x  =  72/17  ≈  4.24  hrs

Notice something else, NSS....  if we add  1/8  and 1/9   and then take the reciprocal of that answer, we will get the total time  !!!!

Thanks, Coop!!!!!....here's one more way to determine this :

If direct  we have that

y  =  ax     so

2  = a(5)

a  = 2/5

So......looking at  x  =  10

y  = (2/5)* 10   =   4

But y  should   =  1

So....not direct

If inverse, we have that

y  =  a/x

2  =  a/ 5

10  = a

So.....looking at x  = 10, we have that

y  =  10  / 10   =    1

Which is exactly what we require......so.......inverse

d^2 - 7d + 12               d^2 + 5d + 6

___________     +     ______________

d^2  - d  - 6                  d^2 - 2d  -  15

(d - 4) ( d - 3)            (d + 3) (d + 2)

___________   +     ____________

(d - 3) (d + 2)           (d - 5) (d + 3)

( d - 4)               ( d + 2)

______     +       _____

( d + 2)              (d - 5 )

(d - 4) (d - 5)  + (d + 2)(d + 2)

________________________

  (d + 2)  ( d - 5)

d^2 - 9d + 20  + d^2 + 4d + 4

_______________________

 (d + 2) (d - 5)

   2d^2  - 5d + 24

______________

   (d + 2) (d - 5)

n^2 + 3n + 2                 2n

___________   -    __________

n^2  + 6n + 8            n  +  4

(n + 2) ( n + 1)             2n (n + 2)

____________  -      ____________

(n + 4) ( n + 2)           (n + 4) ( n + 2)

( n + 2) ( n + 1)  - 2n ( n + 2)

________________________

  (n + 4)  ( n + 2)

n^2 + 3n + 2  - 2n^2 - 4n

____________________

  (n + 4) ( n + 2)

-n^2 - n + 2

____________

(n + 4) ( n + 2)

- ( n^2 + n - 2)

____________

(n + 4) ( n + 2)

- (n + 2) (n - 1)

____________

( n + 4) ( n + 2)

- (n - 1)

____________

(n + 4) 

    (1 - n)

____________

   ( n + 4)

Here's a "formula"  that can be used to find a new point :

New Point '   =  [ Old Point  - Dilation Center ] *Scale Factor  + Dilation Center

Note that   (a , b)  - (c, d)  =  (a - c, b - d)

(a, b) + (c , d)  =  ( a + c, b + d)     and

(a, b) * S  =  (Sa, Sb)

So.....to transform (0, - 4)   as follows

New Point'  =    [  ( 0 - 4) - ( 2, - 7) ] * 3  +  ( 2, -7)  =

[ ( -2, 3) ] * 3  + (2, -7)  =

(- 6, 9)  + ( 2, - 7)   =

(-4, 2)

You can compute the other points yourself

Note that we can write

    1

 ______    -   3            as

 2x - 10

    1

_______     -  3     =

2 ( x - 5)

 1             1

___  *   ________    -  3

 2          (x - 5)

This  graph  shifts  the parent graph to  the right by 5 units, down by 3 units,  and vertically "compresses"  the parent by a factor of (1/2)

Very nice, Coop  !!!

.45 D   =  135        divide both sides by  .45

135 / .45   =   D   =    300 miles