Answer:

Step-by-step explanation:
Given

Required
Use the expression to prove a trigonometry identity
The given expression is not complete until it is written as:

Going by the Pythagoras theorem, we can assume the following.
- a = Opposite
- b = Adjacent
- r = Hypothenuse
So, we have:


Having said that:
The expression can be further simplified as:

Substitute values for sin and cos
becomes

Answer:
The total number of students in a survey is 300.
Let the number of junior male(JM) be x and the number of senior males(SM) be y.
Let the number of junior female(JF) be p and the number of senior males(SF) be q.
It is given that there are 160 males, 80 junior females, 130 seniors.
Since number of males are 160. So the number of females are,

Since number of junior females is 80.

Since number of seniors are 130.

Since number of males is 160.

Therefore, the table and venn diagram is shown below.
You need to show us the circle in order to let us answer the question.
Answer:
2x + 3y ≥ 5
Step-by-step explanation:
See the graph attached.
The bold straight line passes through the points (1,1) and (4,-1).
Therefore, the equation of the straight line will be
⇒ 3(y + 1) = - 2(x - 4)
⇒ 3y + 3 = - 2x + 8
⇒ 2x + 3y = 5 ............. (1)
Now, the shaded region i.e. the solution to the inequality does not include the origin(0,0).
So, putting x = 0 and y = 0 in the equation (1) we get, 0 < 5
Therefore, the inequality equation is 2x + 3y ≥ 5 (Answer)