An exterior angle of a triangle is equal to the sum of the opposite interior
angles
4x - 20 = 2x - 4 + 52
4x - 2x = 20 - 4 + 52
2x = 68
x = 68/2
x = 34
Answer:
a) The value of 
is 81.30.
b) The value of is 81.
Step-by-step explanation:
a) The value of is the ratio of the mass of the Earth to the mass of the Moon. That is:
The value of is 81.30.
b) If is a integer, then the result must have only two significant figures. Given the result, we must approximate to the closest integer. That is:
The value of is 81.
Pick’s Theorem is used to find the areas of figures on lattices easily. The formula is:
A = (B)/2 + I - 1, where B is the number of points on the border of the shape, and I is the number of points inside the shape.
Here, there are 8 points on the outside of the shape, and there are 12 points inside the shape. So, we do:
8/2 + 12 - 1 = 4 + 12 - 1 = 15 units squared.
We can check by finding the areas of the non-shaded region and subtracting that area from the whole rectangle area of 4 * 10 = 40:
4 * 1 + (3 * 1)/2 + 1 * 9 + (3 * 1)/2 + (9 * 2)/2 = 25
40 - 25 = 15, so we’re right!
The answer is 15 units squared, or choice (B).
