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saw5 [17]
3 years ago
5

OM , ON and OP are the angle bisectors of ∠AOB, ∠BOC, and ∠COD respectively. ∠AOD and ∠BOE are straight angles.

Mathematics
1 answer:
Orlov [11]3 years ago
3 0

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

2x+2y+2z=180^\circ

We are given that:

m∠MOP = 110°.

From the diagram

∠MOP=x+2y+z

Therefore:

x+2y+z=110°.

Solving simultaneously by subtraction

2x+2y+2z=180^\circ

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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Question 2 -of 15 Step 1 of 1No Time LimitA company manufactures two products. One requires 5 hours of labor, 3 poundsof raw mat
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the cost of labour per hour is $7.20

the cost of raw materials per pound is $11.60

Explanation:

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time = 5 hours of labour

let the cost labour per hour = x

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time (cost per hour) + amount (cost of one pound of raw material) = Cost to produce each product

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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

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combining both equations:

5x + 3y = 70.8 ...(1)

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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

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subtract equation (2*) from (1*):

65x - 10.5x + 39y - 39y = 920.4 - 528

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divide both sides by 54.5:

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substitute for x in any of the equations

Using equation 1: 5x + 3y = 70.8

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