tertre

In a pentagon, the sum of its interior angles measures 180 * 3 = 540 degrees.

Let angle M = angle T = angle H = y.

Thus, the remaining angles measures 540-3y

Let angle A = x  and angle S = 180 - x

x + (180-x)=540-3y

Solving for y, we get 3y=360

y= 120 degrees. Angle H measures 120 degrees.

Recognize that 0.001 is $10^{-3}$.

$\sqrt{10^{76}}$=$10^{38}$.

Thus, $10^n=10^{-5}*10^{38}=10^{33}.$

n = 33.

180-162=18 degrees-(measure of each exterior angle).

360 / y =number of sides the polygon has and 360 / 18 = 20 sides. The polygon has twenty(20) sides.

It's better to understand how to find the area of regular polygons: 1/2 * a * p, where a stands for the apothem and p stands for the perimeter of the polygon...

Mark the center and create a triangle joining two of the vertices. From the center of the polygon, drop a perpendicular line(this is the apothem !)

The central angle is 360 / number of sides, so 360/12=30.

Since the perpendicular line cuts the angle of 30 degrees in half, we have two fifteen(15) degree angles..

By the Law of Sines, we have $\frac{sin 15}{4.5}=\frac{sin 75}{y}$. Solving for $y$, gives the apothem, which is approximately 16.794 centimeters.

The perimeter of the polygon is 9 * 12 =108 centimeters.

Thus, the answer is $\frac{1}{2}*16.794*108\approx906.9$ centimeters squared.

The function is in the form: ax+b

2a+b=6

4a+b=14

2a=8

a=4 and  b=-2

(8)(4)-2=30.

No problem.......!  I also often feel confused about whether to use the which one....

Alice, Bob, Carol:

3 ways to choose the person for the first job, then two ways, and finally one way.

3 * 2 * 1 = 6 ways.

Is it P(5,3)=60 ways.

Hint: Try to use the formula 180*(n-2) / n to find the measure of one angle of the octagon. Then, go from there.

It's better to draw the diagram first!

-tertre