CPhill

XY  = 28

Y = 196

So

X (196)   =  28     divide both sides by 196

X  = 28 / 196   =  1 / 7

The number of distinguishable "words"  that can be made is

5!  /  2!   =    120  / 2   =  60

1  is in the domain of both functions....so....subbing any number in the domain into both fumctions should make them equal

So

[ 2 (1) - 8 ] / [ 1^2 - 6 - 8 ]   =  ???     2 / [ 1 - 6]

[ - 5 ] / [ - 13 ]  =  ???  2 / -5

5/13  =  ???  - 2/5

Not true...so......these functions are not equal

If the combination  can't start with  0

1 / [ 9 * 10^4 ]   =   1 / 90000

If  it can start with 0

1 / 10^5     =   1 / 100,000

(a)    P(jack and then red) 
 There are 4 jacks  and  26  reds

The probability =   4/52 * 26/52  =  1/13 * 1/2  =  1 / 26

(b)    P(red and then diamond) 

We have  26 reds  and 13 diamonds

Probability =  26/52 * 13/52  =  1/2 * 1/4  =  1 / 8

(c)    P(three and then face card) 

The are 4 threes  and 12 face cards

The probability  =   4/52 * 12/52  =   1/13 * 3/ 13  =   3 / 169 

(d)    P(ace of hearts and then eight) 

We have 1 ace of hearts and 4 eights

The probability  =    1/52 * 4/52   =  1/52 * 1/13   =  1 / 676

If B'  were (-2, -2)...... A'B'C'  would be  ABC  translated down 5  units...but since  B' = (-2,- 6) 

There is no sequence of rigid motions that maps  ABC to A'B'C'    [ last answer ]

√ [3x+1 ]   - x + 3 = 0     rearrange  as

√[3x+1]   =  x - 3       square both sides

3x + 1  =  x^2 - 6x + 9      subtract 3x , 1 from both sides and we get

x^2 - 9x + 8  =  0    factor

(x - 8) ( x - 1)  = 0      set each factor to 0  and solve for x and we get

x = 8    and   x  = 1

Check that the first answer makes the original equation true, but not the second

So....  "D"  is correct

1 / [ x - 1 ]  + 2 /x  =  x / [ x - 1]

get a common denominator  on both sides

[ x + 2 ( x - 1) ] / [ x (x - 1)]   =  x^2 / [ x (x - 1} ]

[3x - 2 ]  / [ x^2 - x ]   =  x^2 / [ x^2 - x ]

Solve for the numerators

3x - 2  = x^2     rearrange as

x^2 - 3x + 2  =  0     factor

(x - 2) ( x - 1)  =  0      set each factor to 0 and solve for x and we get the possible solutions

x  = 2    or x =1

Reject the second because it makes an original denominator  = 0  [ extraneous solution ]

"C"  is correct

The denominator cannot  = 0

So...set the denominator  = 0  to find the x values that are excluded from the domain

So we have

x^2 + 2x  - 3   =  0      factor

(x + 3) ( x - 1)  =  0

Set  each factor to 0 and solve for x  and we get that

x = -3     and  x  = 1

And these are the two values excluded from the domain

[ Second and third answers  ]

a.     4  of 10 are experienced  ....so.....4 / 10

b.    Final ratio of experienced to total players  =  [ x + 4 ]  / [ x + 10 ]

c.      Final ratio of experienced to total players =  x + 10