OM , ON and OP are the angle bisectors of ∠AOB, ∠BOC, and ∠COD respectively. ∠AOD and ∠BOE are straight angles.
1 answer:
Find m∠BOC, if m∠MOP = 110°.
Answer:
m∠BOC= 40 degrees
Step-by-step explanation:
A diagram has been drawn and attached below.
- OM bisects AOB into angles x and x respectively
- ON bisects ∠BOC into angles y and y respectively
- OP bisects ∠COD into angles z and z respectively.
Since ∠AOD is a straight line
x+x+y+y+z+z=180 degrees
We are given that:
m∠MOP = 110°.
From the diagram
∠MOP=x+2y+z
Therefore:
x+2y+z=110°.
Solving simultaneously by subtraction
x+2y+z=110°.
We obtain:
x+z=70°
Since we are required to find ∠BOC
∠BOC=2y
Therefore from x+2y+z=110° (since x+z=70°)
70+2y=110
2y=110-70
2y=40
Therefore:
m∠BOC= 40 degrees
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the cost of labour per hour is $7.20
the cost of raw materials per pound is $11.60
Explanation:For product one:
time = 5 hours of labour
let the cost labour per hour = x
Amount = 3 pounds of raw amterials
let the cost of one pound raw material = y
Cost to produce each product = $70.8
The equation:
time (cost per hour) + amount (cost of one pound of raw material) = Cost to produce each product
5(x) + 3(y) = 70.80
For product 2:
time = 3.5 hours of labour
let the cost of labour per hour = x
Amount = 13 pounds of raw amterials
let the cost of one pound raw material = y
Cost to produce each product = $176.00
The equation:
time (cost per hour) + amount (cost of one pound of raw material) = Cost to produce each product
3.5(x) + 13(y) = 176
combining both equations:
5x + 3y = 70.8 ...(1)
3.5x + 13y = 176 ....(2)
Using elimination method:
To eliminate y, we will multiply equation (1) by 13 and equation (2) by 3 so that both coefficient of y become the same
65x + 39y = 920.4 ...(*1)
10.5x + 39y = 528 ...(2*)
subtract equation (2*) from (1*):
65x - 10.5x + 39y - 39y = 920.4 - 528
54.5x + 0 = 392.4
54.5x = 392.4
divide both sides by 54.5:
x = 392.4/54.5
x = 7.2
substitute for x in any of the equations
Using equation 1: 5x + 3y = 70.8
Hence, the cost of labour per hour is $7.20 and the cost of raw materials per pound is $11.60