ElectricPavlov

f = fancy                  total cost  28 f

(7-f) = p = plain       total cost of plains 15 (7-f)      summed, the costs are 131

28f      +     15 (7-f)      = 131      solve for f, the number of fancy shirts..... then plains  =     7-f

Amplitude 4

   4 cos x

Shifted down 4

   4 cos x       - 4

Shifted pi/4  right

  4 cos(x- pi/4)   - 4

-5e-x+17=7    subtract 17 from both sides then divide by -5 to get

e^-x = 2           can you get it from here.....take the ln (natural logarithm) of both sides.....

Here is one way that doesn't use  logs

8^5x  =  (2^3)^5x   =   2^15x

16^*(3x+4) = (2^4)^(3x+4) = 2^(12x+16)

now equate the exponents

15x   = 12x + 16

3x = 16

x = 16/3

This makes no sense.....'A' working alone can create FOUR widgets in 12 hours......why would adding B slow it down?

Is it supposed to be  1/2 hour instead of 12 hours??????

number of pants sold per week = x        given

price of pants =27-(x/300)^2                   given

Revenue per week is the number of pants sold  *   the price

R(x)    =      x    *   [ 27-(x/300)^2 ]          domain  can be anything fro no pants sold ( 0 )    to infinty

Here is a graph......just look at the right hand side.....

https://www.desmos.com/calculator/tfzma6zdto

Start with 600       orange are  25%    .25 * 600=150  orange 

sell 30% of 150       .3 x 150 = 45 sold        105 remain

sell 20% of 105 =   .20 x 105 = 21 sold

you can add them ! 

I  think you are asking  two numbers thad add to 13    and their difference is 7

x+y =13

x-y =7       add the two equations together

2x = 20

x=10          since x+y = 13     y = 3

use the web2.0     or your own calculator      1.24^(1/10)     = 1.24^(.1) = 1.02174417

Distance formula

sqrt ( (a-4)^2  + (21-7)^2  )   =  10 sqrt 2

sqrt ( (a^2-8a+16) + 196 ) = 10 sqrt 2

          a^2-8a+16 +196     = 200

          a^2-8a + 12            =0                      either factor (in your head ) or use quadratic formula to find the TWO values of 'a'