CPhill

Thanks, MG......you are entirely correct......!!!

16^(1.5)   =  16^(3/2)   =   [16^(1/2)]^3  =  [ √16 ]^3  =  4^3  =   64

I have to agree, Melody......I see how  this works, but I don't understand the rationale for wanting to do it.....!!!

-58 - (-49)  = -9     is the difference in these terms which seems to imply that  -9/3 = -3 is the common difference between terms

So......

-58  = a₁ + d(n - 1)              

-58   = a₁ - 3(25 - 1)

-58  = a₁ - 72    add 72 to both sides

14  = a₁

125km / 3600 sec = x / 0.8 sec     cross-multiply

(0.8 sec)(125 km) = (3600 sec)x        divide both sides by 3600 sec

(0.8)(125 km)/ 3600  = x = .02777 km = 27.77 m

A = (1/2)bh   ...  so.....

36 + 5/6 =  (1/2)(6 + 1/2) h       and 36 + 5/6 =  221/6   and 6 + 1/2  =  13/2   ...so.....

221/6  = (1/2)(13/2) h

221/6  = (13/4) h     multiply both sides by 4/13

(221/6)(4/13)  = h

(221/13)(4/6)  = h

(221/13)(2/3)  = 442 / 39  = 34/3 ft  = h = (11 + 1/3) ft

If 4 assistants take 60 minutes to do the job, then one assistant would take four times as long = 240 min

So 25 assistants could do the job in 1/25 of the time.......so ......  240* 1/25 = 9.6 minutes

2 - 12/(4 - x)  = (2x + 4) / (x^2 - 16)   we can rewrite this as

2 + 12/(x - 4)   = 2(x + 2)/ [(x - 4) (x + 4) ]        multiply through by [(x - 4) (x + 4) ]

2 [(x - 4) (x + 4) ] + 12(x + 4)  = 2(x + 2)        divide thrrough by 2

[(x - 4) (x + 4)] + 6(x + 4)  = x + 2    simplify

x^2 - 16 + 6x + 24  =  x + 2   

x^2 + 6x + 8   = x + 2

x^2 + 5x + 6    =  0      factor

(x + 3) (x + 2)  = 0      and setting each factor to 0 we have x = -2   or  x = -3 

{There are no extraneous solutions }

Thanks for that great answer, Mathcad.......here's a graph of the given line......