CPhill

Here's the graph.........https://www.desmos.com/calculator/yzc7qojt7f

There is a vertcal asymptote at x = 0

(3/8)a=9      multiply both sides by  8/3

a = 9(8/3)   = 72/3  = 24

1.07^x=2   take the log of each side

log 1.07^x = log 2     and we can write

x log 1.07  = log 2    divide both sides by log 1.07

x = log 2 / log 1.07 = about 10.2448

21 / .30  =  21 X 100/ 30  =  2100 / 30   = 70 members in all

Proof

49  remembered   = 70% of 70

21 forgot = 30% of 70

13M + 30  = 134    subtract 30 from both sides

13M = 104      divide both sides by 13

M = 8   months

Cost per lb. =   $3.80 / 5   = .76

Can you take it from there????

Nice, Melody.....

ST can also be found, thusly :

AD = 6/tan(30) = 6sqrt(3)

And, using similar triangles, we have

DS / AD  ≈ AD / [DS + ST]

DS^2 + DS*ST   = AD^2

ST  = [ AD^2 - DS^2] /  DS

ST = [ 108 - 36] / 6  =  [ 72 / 6] = 12

And the area is :

[DS + ST + TC] * AD =

[6 + 12 + 3] * 6/tan (30) =  126/tan(30) =  126*sqrt(3)  units^2

1/3x =x-8  subtract x from both sides

-(2/3)x = -8    multiply both sides by -3/2

x = 12

-8/3x-y>=-9y+4     rearrange as

8y >= (8/3)x + 4      divide both sides by 8

y>= (1/3)x + (1/2)  

Here's the graph of this inequality :  https://www.desmos.com/calculator/ckh9w7myiu

-2(4+3^0)^2  =

-2 (4 + 1)^2 =

-2(5)^2  =

-2*25 =

-50