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kicyunya [14]
3 years ago
13

Given the points A(0, 0), B(e, f), C(0, e) and D(f, 0), determine if line segments AB and CD are parallel, perpendicular or neit

her.
Mathematics
1 answer:
Virty [35]3 years ago
5 0

Answer:

Perpendicular

Step-by-step explanation:

Calculate the slopes m of the segments using the slope formula.

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

Parallel lines have equal slopes

The product of the slopes of perpendicular lines equals - 1

(x₁, y₁ ) = A(0, 0) and (x₂, y₂ ) = B(e, f)

m_{AB} = \frac{f-0}{e-0} = \frac{f}{e}

Repeat with (x₁, y₁ ) = C(0, e) and (x₂, y₂ ) = D(f, 0)

m_{CD} = \frac{0-e}{f-0} = - \frac{e}{f}

Thus AB and CD are perpendicular since \frac{f}{e} × - \frac{e}{f} = - 1

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The frequency distribution representing the number of frequent flier miles accumulated by employees at Brumley Statistical Consu
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Answer:

a. How many employees accumulated less than 3,000 miles?

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So the number of employees accumulated less than 3,000 miles is 5.

d. Based on the cumulative frequency polygon, about 75% of the employees accumulated how many miles or less?

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Step-by-step explanation:

The given frequency distribution representing the number of frequent flier miles accumulated by the employees in a company.                        

Frequent Flier Miles (000) Frequency

0                     up to 3 5

3                      up to 6 12

6                      up to 9 23

9                     up to 12 8

12                   up to 15 2

Total                       50

a. How many employees accumulated less than 3,000 miles?

The number of employees accumulated less than 3,000 miles= 5

So the number of employees accumulated less than 3,000 miles is 5.

b. Convert the frequency distribution to a cumulative frequency distribution.

We make the cumulative frequency distribution from the frequency distribution by adding up a frequency and all other frequencies below it.                

Frequent Flier Miles Frequency Cumulative frequency

0 up to 3                                5 5

3 up to 6                                      12 17

6 up to 9                                      23 40

9 up to 12                               8 48

12 up to 15                               2 50

Total 50

d. Based on the cumulative frequency polygon, about 75% of the employees accumulated how many miles or less?

8.5 thousands of miles, found by starting at 75 percent on the vertical axis on the right, over to the polygon and then down to the horizontal axis.

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