CubeyThePenguin

complement = the angle that added with the original angle forms a right angle

Let the angle measure be x.

x = 2(90 - x)

x = 180 - 2x

3x = 180

x = 60 degrees.

We are basically finding the number of arrangements of the sequence {122333}, which is \(\frac{6!}{2! \cdot3!} = \boxed{60}.\)

The separations between numbers on a clock are 30 degrees each. (360 degrees in a circle, 12 hours)

At 5 o'clock, the hour hand is at 150 degrees and the minute hand is at 0 degrees. This makes an angle of 150 degrees.

If we define the smallest integer to be \(x\), then

\(x + (x+5) + (x+7) = 42.\)

\(3x + 12 = 42\)

The integers are x, x + 5, x + 7, or 10, 15, 17.

Logarhythm's answer is correct.

\(\frac{y-2}{y^2 - 9} - \frac{y-7}{y^2 + 4y - 21}\)

\(\frac{y-2}{(y+3)(y-3)} - \frac{y-7}{(y+7)(y-3)}\)

\(\frac{(y+7)(y-2) - (y+3)(y-7)}{(y+3)(y-3)(y+7)}\)

\(\frac{(y^2 + 5y - 14) - (y^2 - 4y - 21)}{(y+3)(y-3)(y+7)}\)

\(\frac{y+7}{(y+3)(y-3)(y+7)}\)

\(\boxed{\frac{1}{(y+3)(y-3)}}\)

\(\frac{2}{1+2\sqrt{3}} \cdot \frac{1-2\sqrt{3}}{1-2\sqrt{3}}+ \frac{3}{2-\sqrt{3}} \cdot \frac{2+\sqrt{3}}{2+\sqrt{3}}\)

\(\frac{2 - 4\sqrt{3}}{13} + \frac{6 + 3\sqrt{3}}{1}\)

\(\frac{(2 - 4\sqrt{3} )+ 13(6 + 3\sqrt{3})}{13}\)

\(\frac{80 +35\sqrt{3}}{13}\)

Use the order of operations:

PEMDAS

P - Parentheses

E - Exponents

M - Multiplication

D - Division

A - Addition

S - Subtraction

2(5 + 8/4 * 3) - 7

2(5 + 2 * 3) - 7

2(5 + 6) - 7

2(11) - 7

22 - 7

15

Let z^2 = a, so we are solving:

a^2 - 4a + 4 = 0

(a - 2)^2 = 0

a = 2

z^2 = 2

\(\boxed{z = \pm \sqrt{2}}\)

We are given two angles of an isosceles triangle (because all sides of a rhombus are equal).

So, (2x-1) + (2x-1) + (4x+28) = 180.

Solve for x.