Ray QM is the angle bisector of angle NQR. If angle PQN = 7x + 15 and angle NQM = 4x, what is the value of x?
1 answer:
Answer:
x = 2.7
Step-by-step explanation:
From the question given above, the following data were obtained:
QM = angle bisector of angle PQR
Angle PQN = 7x + 15
Angle NQM = 4x
x =?
Since QM is the angular bisector, it means that it bisect PQR into two equal angle i.e 45° each.
See attachment for diagram.
Thus, we can obtain the value of x as follow:
7x + 15 + 4x + 45= 90° (angle in a right angle triangle)
7x + 4x + 15 + 45= 90
11x + 60 = 90
Collect like terms
11x = 90 – 60
11x = 30
Divide both side by 11
x = 30/11
x = 2.7
Therefore, the value of x is 2.7
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Answer:
20 masks and 100 ventilators
Step-by-step explanation:
I assume the problem ask to maximize the profit of the company.
Let's define the following variables
v: ventilator
m: mask
Restictions:
m + v ≤ 120
10 ≤ m ≤ 50
40 ≤ v ≤ 100
Profit function:
P = 10*m + 65*v
The system of restrictions can be seen in the figure attached. The five points marked are the vertices of the feasible region (the solution is one of these points). Replacing them in the profit function:
point Profit function:
(10, 100) 10*10 + 65*100 = 6600
(20, 100) 10*20 + 65*100 = 6700
(50, 70) 10*50 + 65*70 = 5050
(50, 40) 10*50 + 65*40 = 3100
(10, 40) 10*10 + 65*40 = 2700
Then, the profit maximization is obtained when 20 masks and 100 ventilators are produced.
