geno3141

Factor out the common term: 2^2013:

Since:  2^2014 = 2·2^2013

So:  2^2014 - 2^2013

  =   2·2^2013 - 2^2013

  =  2^2013·( 2 - 1 )

  =  2^2013·(1)

  =  2^2013

If you want to find the value of log(to the base 16) 19, use the change-of-base formula:

log(to the base 16) 19  = log(19) / log(16) = 1.06198...

You could also use natural logs and have  ln(19) / ln(16) = 1.06198...

I would disagree that 0^0 = 1.

I believe that it is an indeterminate expression; which means that it can have any value, depending upon how it was created.

I do fully agree that a^0 = 1, whenever a ≠ 0.

Yes, the quotient is 84 and the remainder is 8.

If you use a calculator to divide 764 by 9 and get an answer like 84.8888888889 (the number in front of the decimal point, the 84, give you the quotient) and you want to find the remainder, do this:

first, subtract the number in fromt of the decimal point; subtract the 84, and you will have .8888888889 on your calculator;

then mulitply this long decimal by your original divisor (the 9); now, the answer on your calculator will be the remainder.

Example:  find the quotient and remainder of 86 divided by 7.

Divide 86 by 7:  12.28571429      --->  the quotient is 12

Subtract the 12:  .2857142857

Multiply by 7:  2                           --->  the remainder is 2

This is not an equation; to have an equation, you have to have an equal sign and something on the other side.

"at least" becomes "≥".

"fewer than" means subtract, so "9 fewer than" becomes "- 9".

y represents the pages read on Saturday.

x represents the pages read on Friday.

y  ≥  4x - 9

Draw the line y = 4x -9 and shade the region above the line to show "at least".

Points that you can use:  x = 0 and y = -9                  x = 4 and y = 7.

Do you have to be more careful than this? Because, x can't be negative and y can't be negative (you can't read a negative number of pages); do you have to worry about this?

Since there is no x-term on the right side of the function, any value of x can be used to make f(x) = 12/16.

In fact, there is no way to make f(x) have any value but 12/16.

For instance:  f(0) = 12/16, and f(1) = 12/16, and f(2.75) = 12/16, etc., for all values of x.

Let w represent the number of weeks; then:  100 + 50w ≥ 375

"sin" is an abbreviation for "sine"

In a right triangle, the sin of an angle is the ratio of the side opposite that angle to the hypotenuse.

a is the coefficient of the t-term on the left side:  a = 1

b is the number on the left side:  b = -4

c is the coefficient of the t-term on the right side:  c = 4

d is the number on the right side:  d = -21