geno3141

Since  2² = 4  and  3² = 9, the √8 lies between 2 and 3.

3x³ - 12x² + 27x

=  3x(x² - 4x + 9)

Any further factoring would require radicals.

sin(45)  =  √2/2

30/sin(45)  =  30/(√2/2)  =  60/√2  =  30√2

sqrt( 30√2 )²  =  30√2

30√2 - 30²  =  30√2 - 900

The answer is not exactly 0, but it is so small that the calculator can no longer print it.

For example by the time it calculates 0.4444444 ^ 300, the answer has more than 100 zeros right after the decimal point. The calculator isn't programmed to have numbers that small, even when written in scientific notation. Instead, it rounds off the answer, as best it can, to zero.

-5*(-6) -3*(-5-3*(-4)+6)

[-5*(-6)] - [3*(-5 - 3(-4) + 6)]                              

[30] - [3*(-5 - 3(-4) + 6)]              (Multiplied -5 x -6.)

[30] - [3*(-5 - [3*(-4)] + 6)]          (Work from the innermost set of parentheses.)

[30] - [3*(-5 + 12 + 6)]                 (Multiplied 3 x -4)

[30] - [3*(13)]                              (Combined -5 + 12 + 6)

30 - 39                                         (MUltiplied 3 x 13)

= -9

Let  P  =  number of dozen peanut butter cookies sold.

Let  C  =  number of dozens chocolate chip cookies sold.

Number equation:  P  =  85 + C

Value equation:     6.50P + 9.00C  =  4055.50

Substituting the first equation into the second:

                           6.50(85 + C) + 9.00C  =  4055.50

                           552.50 + 6.50C + 9.00C  =  4055.50

                           552.50 + 15.50C  =  4055.50

                                         15.50C  =  3503.00

                                                 C  =  226

                                                 P = 85 + 226  =  311

Let  P  stand for the amount of money made on selling paperback books.

Let  H  stand for the amount of money made on selling hardcover books.

Then:  P + H  =  124,300

But, since they make four times on paperback books as on hardcover books:  P  =  4H

         4H + H = 124,300

               5H  =  124,300

                 H  =  24,860

    P  =  4H  =  4(24,860)  =  99,440

Key words:  "times"  <--->  x

"divided by"  <--->  /       (or  ÷)

5 times G divided by R

5 x G / R

To emphasize in what order they should be done:

(5 x G) / R 

It was a surprise that when any circumference of a circle is divided by its diameter, the answer was always the same; the number we know know as Π. This was known many years BCE; but, it wasn't named then.

No one created pi; it's just there when calculating using our base 10 number system.

The first person to use the symbol Π for this number was William Jones in the eary 1700's. It became popular when Leonhard Euler, in the mid 1700's began to use it. (Euler was one of the greatest mathematicians of all times; and probably wrote more articles and books on mathematics than anyone else; so, when he began to use it, it came into standard use.)

-5t² + 20t + 50

-5(t² - 4t - 10)

This cannot be factored any farther using whole numbers.

By completing the square, you can get:  -5(t - 2 + √14)(t - 2 - √14).  (Don't wory about this answer, unless you have been doing advanced algebra.)