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The midpoint of a line segment is (−3,2). One endpoint of the line segment is (4,−7).What are the coordinates of the other endpoint of the line segment?

Answers

Answer 1

Answer:

The coordinates of the other endpoint of the line segment are $Y(x,y) = (-10, 11)$ .

Vectorially speaking, the midpoint of a line segment is determined by the following expression:

$M(x,y) = (1)/(2)\cdot X(x,y) + (1)/(2)\cdot Y(x,y)$ (1)

Where:

$M(x,y)$ - Midpoint.
$X(x,y)$ , $Y(x,y)$ - Endpoints of the line segment.

If we know that $M(x,y) = (-3, 2)$ and $X(x,y) = (4, -7)$ , then the coordinates of the other endpoint is:

$(1)/(2)\cdot Y(x,y) = M(x,y) -(1)/(2)\cdot X(x,y)$

$Y(x,y) = 2\cdot M(x,y) -X(x,y)$

$Y(x,y) = 2\cdot (-3,2)-(4,-7)$

$Y(x,y) = (-6, 4) - (4, -7)$

$Y(x,y) = (-10, 11)$

The coordinates of the other endpoint of the line segment are $Y(x,y) = (-10, 11)$ .

We kindly invite to check this question on midpoints: brainly.com/question/17506315

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If apple=5, orange=6 and strawberry=10 then banana=?

Answers

Answer:

Step-by-step explanation:

The number corresponds with how many letters there are in a word. In this case, banana has 6 letters.

Answer:

The answer is 6

Step-by-step explanation:

They are counting the nuber of letters in the word apple has 5, orange has 6, and strawberry has 10. Banana has 6 B-A-N-A-N-A.

According to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $1,999. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $574. (Round your z-score computation to 2 decimal places and final answers to 2 decimal places.) What percent of the adults spend more than $2,550 per year on reading and entertainment?

Answers

Answer:

The probability is $P(X > x ) = 0.19215$

Step-by-step explanation:

From the question we are told that

Th The population mean $\mu = \$ 1,999$

The standard deviation is $\sigma = \$ 574$

The values considered is $x = \$ 2,500$

Given that the distribution of the amounts spent follows the normal distribution then the percent of the adults spend more than $2,550 per year on reading and entertainment is mathematically represented as

$P(X > x ) = P(( X - \mu)/(\sigma ) > ( x - \mu)/(\sigma ) )$

Generally

$X - \mu}{\sigma } = Z (The \ standardized \ value \ of \ X )$

$P(X > x ) = P(Z > ( x - \mu)/(\sigma ) )$

substituting values

$P(X > 2500 ) = P(Z > ( 2500 - 1999)/(574 ) )$

$P(X > 2500 ) = P(Z >0.87 )$

From the normal distribution table the value of $P(Z >0.87 )$ is

$P(Z >0.87 ) = 0.19215$

Thus

$P(X > x ) = 0.19215$

Final answer:

We calculate the z-score for the amount $2,550 using the given mean and standard deviation. The z-table gives us the percentage of people who spend less than this, which we subtract from 1 to find the percentage who spend more. Approximately 16.85% of adults in the 25- to 34-year age group spend more than $2,550 on reading and entertainment each year.

Explanation:

To compute the percentage of adults spending more than $2,550 per year, we must first find the z-score associated with this value. The z-score is a measurement of how many standard deviations a particular data point is from the mean.

The formula for calculating the z-score is: Z = (X - μ) / σ.

Where:
- X is the value we are interested in.
- μ is the mean.
- σ is the standard deviation.

Using this formula, the z-score for $2,550 is:
Z = ($2,550 - $1,999) / $574 = 0.96.

Next, we need to use a z-table or a standard normal distribution table to find out the probability that lies below the calculated z-score. Looking this up on a z-table, we get a value of 0.8315, meaning that 83.15% of the population will spend $2,550 or less per year on reading and entertainment. Since we want to know the percentage spending more than $2,550, we subtract this value from 1: 1 - 0.8315 = 0.1685.

Therefore, based on the given mean and standard deviation, about 16.85% of adults in the 25- to 34-year age group spend more than $2,550 on reading and entertainment each year.

Learn more about Z-Score here:

brainly.com/question/31613365

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Match the operations with the order in which you should do them whensimplifying an exponential expression.

Answers

Answer:

It should go exponents, multiplication and division, then addition and subtraction

Step-by-step explanation:

By using PEMDAS, for order of operations, it's easier to remember which set comes first. (parentheses, exponents, multiplication, division, addition, subtraction)

Which expressions represent rational numbers? Check all that apply.

Answers

The answers are numbers two and four.

Answer:

Step-by-step explanation:

NVM ITS WRONG

Jan raised $120.75 at the car wash. If each wash costs $5.75, how many cars did she wash?

Answers

Answer:

She washed 21 cars

Step-by-step explanation:

Answer:

Jan washed 21 cars

Step-by-step explanation:

120.75 / (Divided) 5.75=21

If you were to times 5.75 by 21 you will get the amount she rasied at the car wash

Sandy wants to carpet the game room in her house. How many square feet of carpet will she need to complete her project if the diameter of the semicircle portion of her room is 12 ft and the base of the triangle is 5 ft? Carpet is only sold in whole number quantities.