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Snezhnost [94]
2 years ago
6

In exercises 13 and 14, find the distance between the two points.

Mathematics
1 answer:
Scorpion4ik [409]2 years ago
4 0

The distances between the two points are:

  1. A(x, y) = (- 1, 1), B(x, y) = (3, - 5): d = 2√13
  2. C(x, y) = (2, 4), D(x, y) = (5, - 4): d = √73

<h3>What is the straight line distance between two distinct points on a Cartesian plane?</h3>

Herein we find two cases of two distinct points on a Cartesian plane and we must calculate the length of the line segment generated by each pair of points. This can be done by using Pythagorean theorem:

d = √[(Δx)² + (Δy)²]         (1)

Where:

  • Δx - Change between the two points in the x direction.
  • Δy - Change between the two points in the y direction.

Now we proceed to calculate the straight line distance between each pair of points:

Case 1

d = √[[3 - (-1)]² + (- 5 - 1)²]

d = 2√13

Case 2

d = √[(5 - 2)² + (- 4 - 4)²]

d = √73

The distances between the two points are:

  1. A(x, y) = (- 1, 1), B(x, y) = (3, - 5): d = 2√13
  2. C(x, y) = (2, 4), D(x, y) = (5, - 4): d = √73

To learn more on distances between two points: brainly.com/question/12661159

#SPJ1

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Answer:

4/23

Step-by-step explanation:

Probability of choosing a red marble = # of red marbles / total # of marbles

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So the # of red marbles = 4

And the total # of marbles = 4 + 19

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Recall that probability of choosing a red marble is equal to # of red marbles / total # of marbles

Hence, the probability of choosing a red marble is 4/23

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Solve the equation: -8(2a-1)=36
SashulF [63]

The solution to the given equation is \frac{-7}{4}.

<h3>What is an expression?</h3>

Expression is a finite combination of symbols that is well-formed according to rules that depend on the context. An expression is a combination of numbers, variables, or a combination of numbers and variables, and symbols and it is connected by the sign of equal.

We have,

Expression -8(2a - 1) = 36

So,

Now,

To get the solution to this expression,

i.e.

-8(2a - 1) = 36

Rewrite it as,

i.e.

Opening Brackets,

We get,

-16a + 8 = 36

Now,

Taking variable terms on one side and other terms on another side,

We get,

-16a = 36 - 8

On solving we get,

-16a = 28

i.e.

a = \frac{-28}{16} = \frac{-7}{4}

So,

The solution to the given equation is \frac{-7}{4}.

Hence, we can say that the solution to the given equation is \frac{-7}{4}.

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check by plugging into both equations

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