geno3141

The hypotenuse is side c = 15.

The value of cos(A) is its adjacent length divided by the hypotenuse:  cos(A)  =  9/15  =  0.6000

the value of tan(A) is its opposite length divided by its adjacent length:  tan(A)  =  12/9  =  1.3333

Use the distributive property:

-3(1 - 2b) - 4b

-3(1) - (-3)(2b) - 4b

-3 + 6b - 4b

-3 + 2b

To rationalize the denominator, multiply the numerator and the denominator by √3:

Numerator:  (-1 + √3) x √3  =  -√3 + 3

Denominator:  √3 x √3  =  3

Answer:  ( -√3 + 3 ) / 3

You can enter the expression just as it is:  -0.518 - 184ln(1 - 0.2)

If you want to simplify it, simplify what's inside the parentheses first:   -0.518 - 184ln(0.8)

You then get an answer that rounds to 41.

When you had 3x + 3 - 2x² - 2x  =  6x - 9

   --->             - 2x² + x + 3  =  6x - 9

   --->                   - 2x² - 5x  + 12  =  0

it should be  -5x, not -7x ... 

Change 1% into a decimal:  15%  = 0.15

30 + ( 0.825 x 30 ) + 0.15 x 30 =

Enter this into a calculator ...

There are 60 minutes in a degree and 60 seconds in every minute.

If you take 0.3185 x 60  =  19.11 minutes  --->  19 minutes

.11 minutes x 60  =  6.6 seconds

0.3185  =  19 minutes and 6.6 seconds

For the top equation:  there is: (√2 - 1) / (√2 - 1)   --->  but this equals 1. So any finite exponent of 1 will work.

For the second equation:

2^(x - 2) - 4^x + 8^x  =  0

--->  2^(x - 2) - (2^2)^x + (2^3)^x  =  0

--->  2^(x - 2) - 2^(2x) + 2^(3x)  =  0     --->  x = -1     (I solved it by graphing; but it checks fairly easily.)

Write 19% as a decimal and interpret "of" as "times":

19% of 75  =  0.19 x 75  =  14.25

You can use these:

A ≥ 5000

C ≥ 195

D ≥ 700

x  =  3000A + 45C + 75D

y  =  1000A + 50C + 200D

However, the direct combination of these equations/inequalities won't give you the answer that you want.

The number of type x pills necessary:

   For vitamin A, you would need to take at least 2 type x pills (5000÷3000 = 1.67 --> 2 pills)

   For vitamin C, 195 ÷ 45  =  4.33 ---> 5 pills. 

   For vitamin D, 700 ÷ 75  =  9.33 ---> 10 pills.

You can make a similar analysis for type y pills.

Then, there is the possibility that you can take a combination of x and y pills.

This can get quite complicated.