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1 year ago

Show that (0, 0) is equidistant from (1, 2), (-1, -2) and (2, 1).

Mathematics

1 answer:

Len [333]1 year ago

3 0

Step-by-step explanation:

1) if (0;0) if point A, (1;2) is point B; (-1;-2) is C, (2;1) is D, then

2) the vector AB is (1;2); vector AC is (-1;-2) and vector AD is (2;1), then

3) the length of AB, AC and AD are:

$|AB|=\sqrt{1^2+2^2}=\sqrt{5};$

$|AC|=\sqrt{(-1)^2+(-2)^2}=\sqrt{5};$

$|AD|=\sqrt{2^2+1^2}=\sqrt{5}.$

4) if the lengths above are equal, then it means that (0, 0) is equidistant from (1, 2), (-1, -2) and (2, 1).

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2 years ago

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IRINA_888 [86]

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0.0025 = 0.25% probability that both are defective

Step-by-step explanation:

For each item, there are only two possible outcomes. Either they are defective, or they are not. Items are independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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And p is the probability of X happening.

5 percent of these are defective.

This means that $p = 0.05$

If two items are randomly selected as they come off the production line, what is the probability that both are defective

This is P(X = 2) when n = 2. So

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2 years ago

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3 years ago

Which statements about this system of equations are true? Check all that apply. - x + 6y = 16 8x - 6y = -2 The x-variable will b

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Answer:

The true statements are:

The y-variable will be eliminated when adding the system of equations

There is only one solution to the system of equations is

Step-by-step explanation:

* Lets explain how to solve the problem

- We use the elimination method to solve the system of the

linear equation

- The solution is one of three cases

# Exactly one solution ⇒ the 2 lines which represented the equations

intersect each other at one point

# No solution ⇒ the 2 lines which represented the equations are

parallel to each other

# Infinite solutions ⇒ the two lines are coincide

- In the system of the linear equations of the problem we have two

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∵ The y's in the two equations have the same coefficients and

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∴ We add the equations to eliminate y

∴ (-x + 8x) + (6y - 6y) = 16 + -2

∴ 7x = 14 ⇒ divide both sides by 7

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∴ 6y = 18 ⇒ divide both sides by 6

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∴ The solution of the system of the equations is (2 , 3) ⇒ only one

solution

- Lets check the statements to find the true statements

# The x-variable will be eliminated when adding the system of

equations is not true

# The y-variable will be eliminated when adding the system of

equations is true

# The sum of the system of equations is - x + 6y is not true

# There is only one solution to the system of equations is true

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2 years ago

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Show that (0, 0) is equidistant from (1, 2), (-1, -2) and (2, 1).​

Show that (0, 0) is equidistant from (1, 2), (-1, -2) and (2, 1).