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3 years ago

What is the slope of a line that is perpendicular to the

Mathematics

1 answer:

alexgriva [62]3 years ago

5 0

Answer:

The slope of a line that is perpendicular to the line

shown in the graph is = 4

Hence, option 'd' is true.

Step-by-step explanation:

From the line equation, let us take two points

(0, 2)

(4, 1)

Finding the slope between two points

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(0,\:2\right),\:\left(x_2,\:y_2\right)=\left(4,\:1\right)$

$m=\frac{1-2}{4-0}$

$m=-\frac{1}{4}$

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so

The slope of the perpendicular line will be:

$-\frac{1}{-\frac{1}{4}}=4$

Thus, the slope of a line that is perpendicular to the line

shown in the graph is = 4

Hence, option 'd' is true.

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3 years ago

If 8 identical blackboards are to be divided among 4 schools,how many divisions are possible? How many, if each school mustrecei

MAXImum [283]

Answer:

There are 165 ways to distribute the blackboards between the schools. If at least 1 blackboard goes to each school, then we only have 35 ways.

Step-by-step explanation:

Essentially, this is a problem of balls and sticks. The 8 identical blackboards can be represented as 8 balls, and you assign them to each school by using 3 sticks. Basically each school receives an amount of blackboards equivalent to the amount of balls between 2 sticks: The first school gets all the balls before the first stick, the second school gets all the balls between stick 1 and stick 2, the third school gets the balls between sticks 2 and 3 and the last school gets all remaining balls.

The problem reduces to take 11 consecutive spots which we will use to localize the balls and the sticks and select 3 places to put the sticks. The amount of ways to do this is ${11 \choose 3} = 165 .$ As a result, we have 165 ways to distribute the blackboards.

If each school needs at least 1 blackboard you can give 1 blackbooard to each of them first and distribute the remaining 4 the same way we did before. This time there will be 4 balls and 3 sticks, so we have to put 3 sticks in 7 spaces (if a school takes what it is between 2 sticks that doesnt have balls between, then that school only gets the first blackboard we assigned to it previously). The amount of ways to localize the sticks is ${7 \choose 3} = 35$ . Thus, there are only 35 ways to distribute the blackboards in this case.

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3 years ago