CPhill

In exponential form, this says

(1/3)^x = 9 

Note that 1/3  = 3^-1 and 9 = 3²   so we can write

(3^-1)^x  = 3²

3^-x = 3²    and, equating exponents, we have

-x  = 2     so   x = -2

So

log_1/3 9 = -2

I think this might be  [csc^2x secx] / [sec^2x+csc^2x ].....if so, convert to sines and  cosines

[ 1 / sin^2x * 1 / cosx ] / [ 1 / cos^2x  + 1 / sin^2x ]     simplify the denominator

[ 1 / sin^2x * 1 / cosx ] / [(sin^2x + cos^2x) / (cos^2x sin^2x) ] =

[ 1 /(sin^2x * cosx)] / [1 /( cos^2x * sin^2x) ] =

( cos^2x * sin^2x) ] / (sin^2x * cosx) =

cosx

Nice, saseflower.....!!!

Saseflower has almost gotten you home......the y intercept is at -4......this is the point (0, -4)....plot this point on the graph.....

Now...the slope is (1/3)......this means that y changes by 1 and x changes by 3. So, from (0, -4).....go up 1 unit on y and over 3 units on x.  You should be at the point (3, -3). Draw a line through these two points......there's your graph...!!!!

-3/10x - 2 < 2/5    multiply through by 10 to clear the fractions

-3x - 20 < 4           add 20 to both sides

-3x < 24              divide by -3 (and remember to  "reverse" the inequality sign)

x > -8

and this 

4 + 14b ≥ 13(b + 4)   simplify

4 + 14b  ≥ 13b + 52    subtract 13b, 4 from each side

b  ≥ 48

Let N be the total number of $3 bags sold....then, 307 - N  must be the number of $1 bags sold...so we have....price times units sold = revenue (total sales)

3(N) + 1(307-N) = 515  simplify

3N + 307 - N = 515

2N + 307 = 515   subtract 307 from both sides

2N = 208   divide by 2 on both sides

N = 104     and that's the number of $3 bags sold

So 307 - 104 = 203  = the number of $1 bags sold

Thanks, geno.....yours "works," too!!!

I'm not that great.....more just lucky.....!!!!