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3 years ago

Find the equation in standard form of the line passing through the points (2,-3) and (4,2)

Mathematics

1 answer:

mario62 [17]3 years ago

8 0

The line passes through (2,-3) and (4,2).

Calculate the slope of the line.
m = (2+3)/(4-2) = 5/2

The equation of the line is therefore
$\frac{y-2}{x-4} = \frac{5}{2}$

Cross multiply.
2(y-2) = 5(x-4)
2y - 4 = 5x - 20
2y = 5x - 16
Rewrite as
5x - 2y = 16

Answer: C. 5x - 2y = 16

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Consider two people being randomly selected. (For simplicity, ignore leap years.)

inna [77]

Answer:

$(a) = \frac{144}{133225} \\\\(b) = \frac{1}{365}$

Step-by-step explanation:

Part (a) the probability that two people have a birthday on the 9th of any month.

Neglecting leap year, there are 365 days in a year.

There are 12 possible 9th in months that make a year calendar.

If two people have birthday on 9th; P(1st person) and P(2nd person).

$=\frac{12}{365} X\frac{12}{365} = \frac{144}{133225}$

Part (b) the probability that two people have a birthday on the same day of the same month

P(2 people selected have birthday on the same day of same month) + P(2 people selected not having birthday on same day of same month) = 1

P(2 people selected not having birthday on same day of same month):

$= \frac{365}{365} X \frac{364}{365} =\frac{364}{365}$

P(2 people selected have birthday on the same day of same month) $= 1-\frac{364}{365} \\\\= \frac{1}{365}$

7 0

3 years ago

Dina and Masha start cycling on a 20 km bike path at the same time. When Dina reaches the end of the path, Masha still has 4 km

sammy [17]

Answer:

0.5 hour

Step-by-step explanation:

Given

Speed of Dina = 10 km/h

Distance = 20 km

So the time Dina taken to complete the track is:

$Speed=\frac{distance}{time}\\10=\frac{20}{time}\\time=\frac{20}{10}\\ time=2\ hours$

The time taken by Dina is 2 hours. As masha started with dina but she was 4 km of the path left to cycle,

her distance covered in 2 hours was:

$Distance\ covered\ by\ Masha\ in\ 2\ hours=20-4\\=16 km$

So we know the time and distance:

Now,

$Speed\ of\ Masha=\frac{distance}{time}\\ =\frac{16}{2}\\ =8\ kilometer\ per\ hour$

We have to calculate the time that will be needed by MAsha to complete the track:

As we know the speed and remaining distance

$Speed=\frac{distance}{time}\\8=\frac{4}{time}\\ time=\frac{4}{8}\\time=0.5\ hours$

Masha needs 0.5 hour to complete the track ..

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Answer:rental cost for movie $5.50 rental cost for video game $5.00

Step-by-step explanation:

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Svetlanka [38]

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3 years ago

If x = 10, which lines are parallel? Check all that apply.

mart [117]

Answer:

c is parallel to d

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the degrees need to be equal in order for them to not intersect at any point, if you set x = 10 as given.

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