ElectricPavlov

6/11 = .545454......      even numbered decimal places are represented by the numeral '4'

20 000 ( 1-.12)³ = $ __________

(a²+2)(a² - 5)

x^2 - 15 < 12x + 7x - 3

x^2 - 19x -12 < 0             Use quadratic formula    x = 19/2 +- sqrt(409)/2

                                             or  b =19    a = 0  (as largest and smallest integers)     b-a then becomes 19

I think this is how to do this one:

log_b (x^2) = 10

2 log_b (x) = 10

log_b (x) = 5

Now use the log base-change rule for the second part   ( to change to base 'b' )

    = log_b (1/x) / log_b ( b^1/3) 

    = log_b (x^-1) / ( 1/3 log_b (b) )              remember   log_b (b) = 1

   = (-1) log_b (x) / (1/3)

   = -3 log_b(x)   = - 3 ( 5) = -15  

Everywhere the red line below crosses the graph is where f(c) = -1    ( this is the same as y = -1)        How many do you see?

Here is a Venn diagram to get you started:

355 = n^2/5 + 175

n^2/5  = 180

n  = 434691.61  in   = 36224  feet ....   a very LARGE window !    ( are you sure you copied the equation correctly?)

Perhaps you meant    n² / 5   +  175     then n = 30 inches     =   2.5 feet

log x - log y = 3

log (x/y) = 3

x/y = 10³ = 1000

From BB:

a = (b+c)/3     and   a = 5b - c       <======equate

 5b-c = (b+c)/3

   re-arrange to    16b - 4c = 0         sub in  c = 80 + b

                             16 b - 4(80+b) = 0            results in    b = 32      then   c = 112      then a = 48      summed = 192