CPhill

Pretty easy

Let the hours of the second person  = H

So....we want to find where  their weekly pay is equal...so....

428  = 15 H     divide both sides  by  15

28.53  = H  ≈  28.5 hours

One way of doing this is to get the powers of 10 the same...the answer is usually easier to  see then

.176 x 10 ^18  =    1760 x 10^14   = A

22.13 x 10^16  =   2213 x 10^14   = B 

31.42 x 10^14 =    31.42  x 10^14  = C

125.5 x 10^15  =  1255 x 10^14     = D

Note that C isn't close to  anything...so we can eliminate that choice

Distance from A to B  =   [2213 - 1760 ] x 10 ^14  =  453 x 10^14

Distance  from  A to D  =  [ 1760 - 1255 ] =  505 x 10^14

Distance from  B to D  =  [2213  - 1255] x 10 ^14   = 958 x 10^14

Note that A and B  are the closest  !!!!

Yep...that is what makes this a little difficult...there  isn't a "cookbook"  method of doing these....

Don't worry...you will get the hang of it....!!!!!

Just practice a few...

f(x)  =        x + 2

           __________

           x^2 - 2x - 24

The domain will only be affected by the denominator....[the numerator has a domain of all real numbers]

So....when the denominator  = 0 , this function is undefined....so...let's find out what makes the denominator  = 0

x^2 - 2x  - 24  = 0    factor

(x - 6) ( x + 4)  =0     set both factors to 0 and solve for x and we  get  x = 6  and  x  = -4

Note...you have the right  answers, Mathtoo...we just need to take it a little further

We are saying that the domain is all real numers  EXCEPT   -4  and 6

So.....the solution is

(-infinity, -4 )  U ( - 4, 6)  U  ( 6 , infinity )

Do you see  ???

3)   0 =  -36x + 14y  + 8

      0 =  18y  - 9  - 27x

Rearrange these as

36x - 14y  = 8

27x  - 18 y   = -9

Divide the first equation through by 2  and the second one through  by 9

18x  -  7y   =  4

3x   -  2y   =  -1

I see that we  can  get  "-18x"  by multiplying the second equation by  -6  ...so we have

18x - 7y   =  4

-18x + 12y  = 6    add these

5y  = 10    divide by 5

y  = 2

Using   3x  - 2y  =  -1   to find x, we have

3x  - 2(2)  = -1

3x  - 4  =  -1

3x  = 3   divide by 3

x  = 1

So  (x,y)  = ( 1, 2)

You're not  "dumb"....it's just hard to  get the hang of this...

I'll do   2)  and  3).....maybe that will help some

2)  - 9x  - 14y   = -29

     10x + 7y  =   -2

Ok....do you see that we  can  eliminate y  by  multiplying the second equation by -2  ??...so we have

-9x - 14 y  =  -29

20x  + 14y  = -4     add these

11x  = -33   divide by 11

x  = -3

Using  10x + 7y   = -2 to find y, we have

10(-3) + 7y  = -2

-30  + 7y = -2    add 30  to both sides

7y  = 28   divide by 7

y  = 4

So...(x, y)  = ( -3, 4)

Thanks, Tertre  !!!!

Well, Guest.....maybe everyone isn't as brilliant as you are...besides....this elimnation stuff isn't that easy when you're new to  it....

4)  -20  + 10 x  = -10y   

      45  = 6x  - 27 y

Rearrange each as

10x  + 10y   = 20

6x  - 27 y  = 45

I see that I can divide the top equation  by 10  and the bottom by 3  to  get :

x + y  = 2

2x - 9y  = 15

I see that I can  eliminate  'x"  by multiplying the top equation by  -2

-2x - 2y  = -4

2x - 9y  = 15     add these

-11y = 11     

y = -1

And using any equation to find x, we  have

x + y  = 2

x + (-1)  = 2

x - 1  = 2

x  =3

So  (x,y)  =  (3 , -1)

Do these steps help  ???

Sorry.... typo...should be 29....