All categories

2 years ago

Find the midpoint M of the line segment joining the points C = (-1, -1) and D = (5, -5).

Mathematics

1 answer:

Nadusha1986 [10]2 years ago

7 0

Answer:

The midpoint between the joining points C and D is (2, -3)

Step-by-step explanation:

How to find a midpoint

1: Label the coordinates(x₁,y₁) and (x₂,y₂).

2: Input the values into the formula.

3: Add the values in the parentheses and divide each result by 2.

4: The new values form the new coordinates of the midpoint.

Suppose we have a line segment and want to cut that section into two equal parts. To do so, we need to know the center. We can achieve this by finding the midpoint. You could measure with a ruler or just use a formula involving the coordinates of each endpoint of the segment. The midpoint is simply the average of each coordinate of the section, forming a new coordinate point. We shall illustrate this below.

Midpoint formula

If we have coordinates (x₁,y₁) and (x₂,y₂), then the midpoint of these coordinates is determined by (x₁ + x₂)/2, (y₁ + y₂)/2. This forms a new coordinate you can call (x₃,y₃). It is possible to divide a line segment into any given ratio, not just 1:1.

You might be interested in

What would 3y plus y be???????

NARA [144]

3y + y = 4y

3y = y + y + y

y + y + y + y = 4y

hope this helps

3 0

3 years ago

Read 2 more answers

The expression represents the cost of Janelle’s cell phone bill, where m represents the number of minutes of use.0.05m + 12

Sergio039 [100]

<u>The question is </u>

What is the constant in the expression?

we know that

$c=0.05m+12$

where

c---------> the cost of Janelle’s cell phone bill

m-------> represents the number of minutes of use

$0.05$ -------> represent the cost per minute (slope of the linear equation)

$12$ -------> represent the constant in the expression

therefore

<u>the answer is</u>

The constant is 12

4 0

3 years ago

Read 2 more answers

-5x + 8y = -21<br> 3x - 4y = 15

fomenos

The value of x and y in the equation -5x + 8y = -21 and 3x - 4y = 15 are 9 and 4 respectively.

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

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

The equation is given as:

-5x + 8y = -21

3x - 4y = 15

Multiply equation i by 3

Multiply equation ii by 5

-15x + 24y = -63

15x - 20y = 75

Add both equations

4y = 12

Divide

y = 12/4

y = 3

From 3x - 4y = 15

3x - 4(3) = 15

3x - 12 = 15

Collect like terms

3x = 12 + 15

3x = 27

Divide

x = 27/3

x = 9

Therefore, x = 9 and y = 4.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

6 0

1 year ago

The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.08

kvv77 [185]

Answer:

a) 44.93% probability that there are no surface flaws in an auto's interior

b) 0.03% probability that none of the 10 cars has any surface flaws

c) 0.44% probability that at most 1 car has any surface flaws

Step-by-step explanation:

To solve this question, we need to understand the Poisson and the binomial probability distributions.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

Binomial 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.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Poisson distribution with a mean of 0.08 flaws per square foot of plastic panel. Assume an automobile interior contains 10 square feet of plastic panel.

So $\mu = 10*0.08 = 0.8$

(a) What is the probability that there are no surface flaws in an auto's interior?

Single car, so Poisson distribution. This is P(X = 0).

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-0.8}*(0.8)^{0}}{(0)!} = 0.4493$

44.93% probability that there are no surface flaws in an auto's interior

(b) If 10 cars are sold to a rental company, what is the probability that none of the 10 cars has any surface flaws?

For each car, there is a $p = 0.4493$ probability of having no surface flaws. 10 cars, so n = 10. This is P(X = 10), binomial, since there are multiple cars and each of them has the same probability of not having a surface defect.

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

$P(X = 10) = C_{10,10}.(0.4493)^{10}.(0.5507)^{0} = 0.0003$

0.03% probability that none of the 10 cars has any surface flaws

(c) If 10 cars are sold to a rental company, what is the probability that at most 1 car has any surface flaws?

At least 9 cars without surface flaws. So

$P(X \geq 9) = P(X = 9) + P(X = 10)$

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

$P(X = 9) = C_{10,9}.(0.4493)^{9}.(0.5507)^{1} = 0.0041$

$P(X = 10) = C_{10,10}.(0.4493)^{10}.(0.5507)^{0} = 0.0003$

$P(X \geq 9) = P(X = 9) + P(X = 10) = 0.0041 + 0.0003 = 0.0044$

0.44% probability that at most 1 car has any surface flaws

5 0

3 years ago

The slope of a line is 2. The y-intercept of the line is –6. Which statements accurately describe how to graph the function?

Butoxors [25]

Answer:

The correct answer is the first one of your list of options:

"<em>Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points</em>."

Step-by-step explanation:

Since the y-intercept is -6, then the point (0, -6) is a point on the line.That is x = 0 and y = -6. From there you move according to the slope value "2 = 2/1" which means two units of rise when the run is one.

Then, from (0, -6) move up 2 units and then right one unit. The new point should also be a point on the line. Join the two points with a line to graph the function.

4 0

4 years ago

Find the midpoint M of the line segment joining the points C = (-1, -1) and D = (5, -5). ​

Find the midpoint M of the line segment joining the points C = (-1, -1) and D = (5, -5).