A line passes through the points (4, 19) and (9, 24). Write A linear function in the form Y equals MX plus be for this line.

Mathematics

1 answer:

avanturin [10]3 years ago

3 0

Answer:

y = x + 15

Step-by-step explanation:

okay so you're gonna use the y2-y1/x2-x1 formula to find the slope (m)

24 - 19/9 - 4 = 5/5 = 1

so that is your slope (m)

and now if you follow your slope then you should get your y-intercept (b)

4 - 1 = 3 19 - 1 = 18

(3, 18)

3 - 1 = 2 18 - 1 = 17

(2, 17)

2 - 1 = 1 17 - 1 = 16

(1, 16)

1 - 1 = 0 16 - 1 = 15

(0, 15)

so thats your y-intercept (b)

and the equation will look like:

y = mx + b y = x + 15 or y = 1x + 15 (but the 1 isn't necessary)

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Let n be a positive integer and define [n] to be the set of the first n positive integers. That is, [n] = {1, 2, 3, . . . , n}.

yaroslaw [1]

Answer: There are $2^{n-1}$ ways of doing this

Hi!

To solve this problem we can think in term of binary numbers. Let's start with an example:

n=5, A = {1, 2 ,3}, B = {4,5}

We can think of A as 11100, number 1 meaning "this element is in A" and number 0 meaning "this element is not in A"

And we can think of B as 00011.

Thinking like this, the empty set is 00000, and [n] =11111 (this is the case A=empty set, B=[n])

This representation is a 5 digit binary number. There are $2^5$ of these numbers. Each one of this is a possible selection of A and B. But there are repetitions: 11100 is the same selection as 00011. So we have to divide by two. The total number of ways of selecting A and B is the $2^{5-1} = 2^4$ .