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mylen [45]
3 years ago
12

Write a complete two-column proof for the following information. Hint: Use the Angle Addition Theorem and the fact that a line i

s made up of two opposite rays.
Given: m∠1 = 62° and lines t and l intersect

Prove: m∠4 = 62°

Mathematics
1 answer:
DaniilM [7]3 years ago
3 0

Given

m∠1 = 62°

lines t and l intersect

Prove: m∠4 = 62°

To proof

Angle addition property

Two angles side by side with their vertices together creates a new angle whose measure equals the sum of the measures of the two original angles.

As shown in the diagram

m ∠1 + m∠ 2 = 180 °

( by linear pair property )

Given:

m∠1 = 62°

Put in the above equation

we get

m∠ 2 = 180° -62°

m ∠2= 118°

Also

m∠ 2 + m∠4 = 180°

( By linear pair property )

m∠4 = 180° - 118°

m ∠4 = 62°

Hence proved




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A large city has a population of 8,000,000 and an area of 20.5 square miles. what is the city's approximate population density?
gayaneshka [121]

Answer: Approximately 390,244 people per square mile

Work Shown:

Density = population/area

Density = (8 million people)/(20.5 square miles)

Density = 390,243.9024 approximately

This rounds to 390,244 since we're talking about the number of people.

3 0
2 years ago
0.6 of the Chang family expenses are for internet service what fraction of the family's expenses is for internet service put the
sattari [20]
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4 0
3 years ago
Two trains leave stations 360 miles apart at the same time and travel toward each other. One train travels at 70 miles per hour
cricket20 [7]
S=d/t     ⇒d=s*t
s=speed
d=distance
t=time

The first train :
d=x

x=70 miles/h*t                             ⇒   x=70t  (1)

The second train
d=360 miles - x

360 miles - x=80 miles/h*t          ⇒360-x=80t   ⇒ x=360-80t   (2)

therefore, with the equations (1) and (2) we have a systeme of equations:

x=70t
x=360-80t

we can solve this system of equations by equalization method.

70t=360-80t
70t+80t=360
150t=360
t=360/150=2.4     (≈2 hour  24 minutes)

Answer:  the first train meet with the second train in 2 hour 24 minutes. 


3 0
3 years ago
Read 2 more answers
2,8 -4,-4 what is the slope
emmasim [6.3K]

Answer:

For (2, 8) the slope is 2

For (-4, -4) the slope is -4

Step-by-step explanation:

The slope is the x axis which goes first

and the y intercept would be the y axis which goes second

Slope goes before the y intercept

for example: (8, 4) the slope is 8 the y intercept is 4

7 0
2 years ago
15,35,40 will it make a right triangle
KIM [24]

Answer:

NO.

Step-by-step explanation:

If it is a right triangle then by the Inverse of the Pythagoras Theorem:

40^2 = 35^2 + 15^2

Testing:

40^2 = 1600

35^2 + 15^2 = 1225 + 225 = 1450

So the answer is NO>

6 0
3 years ago
Read 2 more answers
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