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(x^2 + 8x) / (3x^2 + 3x)  -  (x^2 + 2x - 6) / (3x^2 + 3x)
[(x^2 + 8x) - (x^2 + 2x - 6)] / (3x^2 + 3x)
[x^2 + 8x - x^2 - 2x + 6] / (3x^2 + 3x)
[6x + 6] / (3x^2 + 3x) 
6(x + 1) / 3x(x + 1)
6 / 3x =2 / x

10 weeks x 24 hours per week x $12 per hour =$2,880 Kelsey's gross income for her summer job.

Of all the numbers between 10,000 and 99,999 =90,000 numbers, there are 300 2s in every 1,000 numbers. From this 300 will subtract repeats of which there are 10 per 1,000, namely:22, 122, 222, 322, 422, 522, 622, 722, 822, 922. That leaves us with 300 - 10 =290 numbers with 2s in them. So, 290 x 90,000/1,000 =26,100 

   In the 4th position, we have 1,000 2s x 9 =9,000 2s. Such as:12,000, 22,000, 32,000, 42,000, 52,000, 62,000, 72,000, 82,000, 92,000.

  In the 5th position, we have 10,000 2s, namely:20,000 to 29,999. So, in total, we have:
26,100 + 9,000 + 10,000 =45,100 numbers with 2s between 10,000 and 99,999. This is in accord with the following computer count of ALL digits between 10,000 and 99,999, which adds 900 repeated(or 10 x 90,000/1,000) 2s to the count:

(0=36 000, 1=46 000, 2=46 000, 3=46 000, 4=46 000, 5=46 000, 6=46 000, 7=46 000, 8=46 000, 9=46 000)
The above applies exactly the same to 3s =45,100.

I was wondering, why wouldnt it be x+200 and instead of  x+20? for the final amount?

Thank You!

No prob  !!!

After reviewing your explanation I see where I made my mistake it would be the last answer, thank you for explaining it to me! I appreciate your help.

Rearrange as 

sqrt  ( 2x  - 4)  = x - 6      (1)   square both sides

2x - 4  =  x^2 - 12x + 36      simplify

x^2 - 14x + 40    =  0

(x - 10)  (x - 4)    =  0

So  possible values of x =   4    or    10

  10 is good

    4 is extraneous   .... the left side  of (1) can only be 0 or positive....but 4 makes the right side negative

  [ Last answer ]

Yep....replace "row"  with "n"

Example

-2x^3

When x  is a large negagtive......y is positive

When x is a large positive.....y is negative

So

"Up" at the left end   and "Down" at the right end

So.....the third answer

Thank you, I appreciate the help

Thnksomuch

Seats  in row  N  =

12  + 4 ( N - 1)

Note ...for example.... that on  row 2  we have 

 12 + 4 (2 - 1)  = 

12 + 4(2 - 1)  = 

12 + 4(1)  =

16 seats

Original ratio of saved to total money per paycheck  = 20 / 200    (10 %)

Final ratio of saved to total money per paycheck  = [ x + 20 ] / [ x + 200 ]

Final amt saved per paycheck =   x + 20

2.  The triangles are not congruent.......no angles match

1.  angle T  =  180  - 60 - 80  =  40

     angle  E  =  180 - 60 - 40  = 80

So  

angle T  = angle D

angle S  = angle E

angle R  = angle F

And RS   =  FE   =  4

So segment DF  is congruent to segment RT

So.....

yes, by ASA, FD

would i replace row with n?

\(\dfrac{4x^2-4}{x^2+4x+3} = \dfrac{4(x^2-1)}{(x+3)(x+1)}=\dfrac{4(x+1)(x-1)}{(x+3)(x+1)}\)

True

True

This is a bit tricky.  Clearly there are two terms in both the numerator and denominator as written but we should cancel out the (x+1) term in both the numerator and denominator and obtain

\(\dfrac{4(x-1)}{x+3}\)

This has only a single term in both the numerator and denominator.

The answer your teacher wants to see depends on them.

2.) Solve the equation [x] / [x-2] = [4] / [x^2-8x+12]  - [1] / [x-6]

x / [ x - 2]   = 4 / [ ( x -6 ) ( x - 2) ]  - 1/ (x - 6)

Multiply through by  (x - 6) ( x - 2)

x ( x - 6)   =  4  - ( x - 2 )   simpify

x^2 - 6x  = 4 - x + 2

x^2 - 6x = 6 - x

x^2 - 5x - 6  =  0     factor

( x - 6) ( x + 1)  =  0      set both factors to 0   and solve for x and we have that

x = 6     or  x  =  -1

The first solution  makes a denominator  =  0....so it is extraneous

So.....

c.) 6 is an extraneous solution because it creates a 0 in the denominator

d.) there is one acceptable solution to the equation

\(nseats(row) = 12 + 4(row-1)\)

1.) It takes max three times as long as Felix to complete the same job. When the men work together, they can complete the job in 9 hours. how many hours are required for max to do the job alone?

Let  the portion of the job that Felix can complete in one hour  =  1/x

Let the portion of the job that Max can complete in one hour  =  1 / [3x]

So.....  rate * time  =  potion of job done....so

Portion that Felix can do in 9 hours  + portion that Max can do in 9 hrs  =  1 job done

(1/x) (9)  +  ( 1 / [3x] )  (9)  =  1

9/x  +  3/x  =  1

12/x  =  1

x = 12  means that Felix can complete the whole job in 12 hours working alone

So..Max can complete the job  in 3(12)  =  36 hours working alone

Correct answer B

and  \(f(x)=3x^2\)

Hope it helps! 

\(\frac{x}{x−1} − \frac{1}{ x−2} = \frac{2x−5 }{ x^2−3x+2}\) ,\(x≠1,x≠2\) <=> \((x-2)\frac{x}{x−1(x-2)} − (x-1)\frac{1}{(x-1) x−2} = \frac{2x−5 }{ x^2−3x+2}\)<=>\(x^2-3x+1=2x-5\) <=> \(x^2-5x+6=0\) <=>\((x-3)(x-2)=0\)  

BUT  \(x≠2\) SO 

\(x=3\) 

So correct answer is B

Hope it helps! 

b)  total distance of felicias training run

  first two hours  x  = 2....so we have

[ 13 + 6(2 - 2)  ]  / 2  =  13 / 2  =  distance / rate  =  = 6.5  mph ⇒  "c"

distance covered in 4 hrs  =

[13 + 6( 4 - 2) ]  =  13 + 6(2)  =  13 + 12  =  25 miles

But  she ran  13 miles the first two hours

So....she must run 12 miles the last two hours   ⇒   "c"