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OleMash [197]
2 years ago
5

What is the rate of change between the points 6,45 and 9,67.5

Mathematics
1 answer:
pochemuha2 years ago
5 0

Answer:

7.5

Step-by-step explanation:

the slope m is a measure of the rate of change

Calculate m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = (6, 45 ) and (x₂, y₂ ) = (9, 67.5 )

m = \frac{67.5-45}{9-6} = \frac{22.5}{3} = 7.5 ← rate of change

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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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