Agear in a watch turns clockwise, in 1° sections, a total of 300 times. how many degrees has the gear turned?

300°

Step-by-step explanation:

This may seem really strange and counterintuitive to you, but when you turn 1° 300 times, you have turned 300°.

If you don't want to add it up ...

1° + 1° + 1° ... + 1° . . . . . 300 times

you can use multiplication. It was invented as a shortcut to repeated addition:

1° × 300 = 300°

  x = 4 ± (1/7)√721

Step-by-step explanation:

7x – 9 = 7x^2 – 49

-9 = 7x^2 -56x . . . . . . . . subtract 7x

-9 = 7(x^2 -8x) . . . . . . . . factor out leading coefficient

-9 +7(16) = 7(x^2 -8x +16) . . . . . add the square of (-8/2) inside parentheses

103 = 7(x -4)^2 . . . . . collect terms, write as a square

103/7 = (x -4)^2 . . . . divide by the leading coefficient

±√(103/7) = x -4 . . . . . take the square root

x = 4 ± (1/7)√721 . . . . add 4, rationalize the denominator

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You "complete the square" by making sure the constant in the quadratic is the square of half the x-term coefficient. If changes are made on one side of the equation, the same changes need to be made on the other side of the equation. Here, we added 7(16) to complete the square.