CPhill

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

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

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

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"

ab - 6a + 5b  =  373

We can write this as

ab - 6a + 5b  - 30  =  373 - 30

(a + 5 )  ( b - 6 )  =  373 - 30

(a + 5) (b - 6)  =  343

343  as a product of two factors  = 

1  * 343    or  343 * 1       

7 * 49    or   49 * 7

So....we have the following possibilities for a, b

a           b

338      7

2         55

44       13

So....   l a - b l    minimized  =  l 44 - 13 l  =  31

 B. The numerator has three terms 

 C. 6X -5 is a single factor in the denominator 

 E. The denominator has two terms

d. The denominator represents Nancy’s average speed if she averages 4 mph less than Sarah

  We are missing the squared power

2 [   1   3     0     -2     4  ]

            2   10    20   36

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       1   5   10    18    40

 [ First answer  ]

No triangle shows up  ???

Excellent,  Dimiristhym   !!!!