Let U = {1, 2, 3, 4, 5, 6, 7}, A= {1, 3, 4, 6}, and B= {3, 5, 6}. Find the set A’ U B’
Art [367]
Answer:
Step-by-step explanation:
A'={2,5,7}
B'={1,2,4,7}
A'UB'={1,2,4,5,7}
Answer:
6
Step-by-step explanation:
The trick here is to know PEMDAS.
PEMDAS stands for: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
This is the order in which you should simplify a problem.
Parentheses:
(5 + 1)^2 - (11 + 32) + 4
(6)^2 - (43) + 4
Exponents:
(6)^2 - (43) + 4
36 - 34 + 4
We have no multiplication or division, so we can skip those steps.
Addition:
36 - 34 + 4
40 - 34
Subtraction:
40 - 34
6
So 6 is our answer.
For a regular tessellation, the shapes can be duplicated infinitely to fill a plane such that there is no gap. The only shapes that can form regular tessellations are equilateral traingle(all sides are equal. This means that it can be turned to any side and it would remain the same), square and regular hexagon. Looking at the given options, we have
Shape Tessellate?
Octagon No
Hexagon Yes
Pentagon No
Square Yes
Triangle No(unless it is specified that it is an equilateral triangle)
Answer: 6.82
Step-by-step explanation:
So we know the Law of Sines which is that Sin A/a = Sin B/b = Sin C/c. The Sin on top of the fraction is the angle, and the letter on the bottom is the side opposite from that angle.
Our first step is going to be finding the last angle. We have 2 angles already, but one that's missing. We know that all triangles' angles add up to 180, so we can add 68+40=108. Then do 180-108 to get 72. Now we know the third and final angle.
Ok so back to Law of Sines. Now we can plug into that equation. We only need Sin A/a = Sin B/b (It doesn't matter what order you put them in). And remember the lowercase letter at the bottom represents the OPPOSITE side from one of the angles. Since the problem wants the side opposite Sin 68, let's set up a proportion.

Set up we have what we know. We know one side, and opposite that is the angle we already solved for. Now we can cross multiply and end up with:

Since we want to isolate x, we can divide each side by Sin 72.
x= 7(Sin 68)/Sin 72
So now let's put it into the calculator:
7(Sin 68)=6.2853
Now let's divide 6.2853/Sin 72
And you should be left with 6.82 if you round it!