Answer:
a) A triangle which the angles ratio is 1 : 2 : 3 is a 30º - 60º - 90º right triangle.
b) The shortest side is opposite to the shortest angle. So, we can calculate it using sin 30º.



The value of
is 
Explanation:
The function
is given by

The function
is given by

To determine the value of
, let us first substitute the value of
.
Thus, we get,

Now, substituting for
in the function
, we get,

Simplifying, the expression, we get,

Multiplying the term within the bracket, we have,

Thus, the value of
is 
Hence, the value of
represents the total amount of money that Barrett earns for working x hours.
Answer:
Please check the explanation.
Step-by-step explanation:
The midpoint (a, b) of line joining points (x₁, y₁) and (x₂, y₂)
a = x₁ + x₂ / 2
b = y₁ + y₂ / 2
Given that the midpoint of AB is (4, -3).
i.e. (a, b) = (4, -3)
Given that A has coordinate (1, 5).
i.e. (x₁, y₁) = (1, 5)
We have to determine the coordinates of B.
i.e. (x₂, y₂) = B
Thus,
4 = (1 + x₂)/2
(1 + x₂) = 4 × 2
1 + x₂ = 8
x₂ = 7
and
-3 = (5 + y₂)/2
(5 + y₂) = -3 × 2
5 + y₂ = -6
y₂ = -11
so (x₂, y₂) = (7, -3) = B
Thus, the coordinates of B = (x₂, y₂) = (7, -3)
Therefore,
x₂ + y₂ = 7 + (-3)
= 7 - 3
= 4
Hence, the value of x₂ + y₂ = 4