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asambeis [7]
3 years ago
5

Line m passes through the points (5, 1) and (8, 6) while line n passes through the points (-4, 3) and (-1, 8). Which statement a

ccurately describes the relationship between the two lines? A. Lines m and n have the same slope so they are perpendicular. B. Lines m and n have opposite reciprocal slopes so they are perpendicular. C. Lines m and n have opposite reciprocal slopes so they are parallel. D. Lines m and n have the same slope so they are parallel.
Mathematics
1 answer:
Anna [14]3 years ago
8 0
Find the equations of the lines...

First find the slope...(y2-y1)/(x2-x1)=m

m=(6-1)/(8-5)=5/3 and it passes through (5,1) so

y=mx+b becomes:

y=5x/3+b and using (5,1)

1=5(5)/3+b

1=25/3+b

3/3-25/3=b

b=-22/3 so 

y1=(5x-22)/3

.... now y2...

m=(8-3)/(-1--4)=5/3 (note it has the same slope as y1...

y=5x/3+b and using the point (-1,8)

8=5(-1)/3+b

8=-5/3+b

24/3+5/3=b

b=29/3, now note that the y-intercept is different...

y2=(5x+29)/3

Since these lines have the same slope but different y-intercepts, they are parallel to each other. (and will never intersect.)
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Step-by-step explanation:

<u>Entiendo que de los 120 tripulantes, sobrevivió el 30%. Y de los sobrevivientes, 25% son casados.</u>

<u></u>

Primero, debemos calcular la cantidad de sobrevivientes:

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2 years ago
Uma rede de supermercados fornece a seus clientes um cartão de crédito cuja identificação é formada por 3 letras distintas (dent
Vitek1552 [10]

Answer:

The correct option is (A) 33,600.

Step-by-step explanation:

The question is:

A supermarket chain provides its customers with a credit card whose identification is formed by 3 different letters (among 26), followed by 4 different digits. A given city will receive cards with L as the third letter, the last number is zero and the penultimate is 1. The total number of distinct cards offered by such supermarket chain for that city is A) 33600 B) 37800 C) 43200 D ) 58500 E) 67600

Solution:

The general format of the credit cards provided by a supermarket chain is as follows:

<u>X</u> <u>X</u> <u>X</u> <u>#</u> <u>#</u> <u>#</u> <u>#</u>

Here, <em>X</em> represents letters and # represents numbers.

All the three letters have to different and all the four numbers have to different, i.e. no repetition allowed.

It is provided that a given city will receive cards with L as the third letter, the last number is zero and the penultimate is 1.

Then the general format of this cities credit cards is as follows:

<u>X</u> <u>X</u> <u>L</u> <u>#</u> <u>#</u> <u>1</u> <u>0</u>

Now there are two spaces left for letters and 2 for numbers.

As there are no repetition allowed the two letter spaces can be filled by:

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And the number of ways to select two numbers when there is no repetition allowed is:

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Compute the total number credit cards available at the supermarket as follows:

Total number credit cards = 600 × 56 = 33600

Thus, the total number of distinct cards offered by such supermarket chain for that city is 33,600.

The correct option is (A).

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2 years ago
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