Draw and classify the polygon with the given vertices. Find the perimeter and the area of the polygon. M(-2,5), N(3,-2), P(-2,-2
)
2 answers:
Answer:
- see below for a drawing
- right triangle
- perimeter = 20.6 units
- area = 17.5 units²
Step-by-step explanation:
A graph shows the figure to be a right triangle with a base of 5 units and a height of 7 units. Its hypotenuse will be given by the Pythagorean theorem:
MN² = MP² +PN²
MN² = 7² +5² = 74
MN = √74 ≈ 8.60
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The perimeter is the sum of the side lengths:
Perimeter = MN +MP +PN = 8.60 +7 +5
Perimeter = 20.60 . . . . units
__
The area is given by the area formula:
Area = 1/2bh = 1/2·5·7 = 35/2
Area = 17.5 . . . . square units
The polygon is a right triangle with a perimeter of 20.60 units and an area of 17.5 square units
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Answer:
The speed in of the plane is 115.47 m/sec
Step-by-step explanation:
Given:
Height at which the plane is flying = 6000 m
Angle of elevation at the radar base = 30 Degrees
Angle of elevation at the radar base after one minute = 60 Degrees
To Find:
The Speed of the plane in meter per second = ?
Solution:
Let us use the tangent of the angle to find the distance (d) to a point directly below plane:
<u>when the angle is 30 degrees</u>
d1 = 10392.3 meters
<u>when the angle is 60 degrees</u>
d2 = 3464.1 meters
<u>distance travelled by aircraft in 1 min is </u>
=>d1 - d2
=>0392.3 - 3464.1
= 6928.2 m/min
<u>Now converting to m/sec</u>
=>
=>115.47 m/sec
Answer:
For this case we want to test if life expectancy in country 1 is more than 10 years lower than in country 2, (alternatibe hypothesis), so then the system of hypothesis are:
Null hypothesis:
Alternative hypothesis:
Or equivalently:
Null hypothesis:
Alternative hypothesis:
Step-by-step explanation:
Previous concepts
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
Solution to the problem
For this case we want to test if life expectancy in country 1 is more than 10 years lower than in country 2, (alternatibe hypothesis), so then the system of hypothesis are:
Null hypothesis:
Alternative hypothesis:
Or equivalently:
Null hypothesis:
Alternative hypothesis: