On a coordinate plane, a line segment has endpoints P(6,2) and Q(3. 8). 9. Point M lies on PQ and divides the segment so that the ratio of PM-MQ is 2-3. What are the coordinates of point M?​

Answers

Answer 1

The coordinates of point M are:

Coordinates of M = (4.5 + sqrt(34)/5, 5)
Coordinates of M = (5.86, 5)

To find the coordinates of point M, we first need to find the coordinates of the midpoint of segment PQ.

The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is ((x1 + x2)/2, (y1 + y2)/2).

Using this formula, we can find the midpoint of PQ as follows:

Midpoint = ((6 + 3)/2, (2 + 8)/2)
Midpoint = (4.5, 5)

Now we can use the fact that PM/MQ = 2/3 to find the coordinates of point M.

Let's start by finding the distance between P and the midpoint:

Distance between P and midpoint = sqrt((4.5 - 6)^2 + (5 - 2)^2)
Distance between P and midpoint = sqrt(4.25)

Since PM/MQ = 2/3, we know that PM is 2/5 of the total distance between P and Q, and MQ is 3/5 of the total distance.

Let's call the total distance between P and Q "d". Then we have:

PM = (2/5)d
MQ = (3/5)d

We can use these expressions to find the distance between M and the midpoint:

Distance between M and midpoint = PM - MQ
Distance between M and midpoint = (2/5)d - (3/5)d
Distance between M and midpoint = -(1/5)d

Finally, we can use the distance formula to find the coordinates of point M:

Coordinates of M = (4.5, 5) + (Distance between M and midpoint in the x direction, Distance between M and midpoint in the y direction)

In other words, the x-coordinate of M is 4.5 plus the distance between M and the midpoint in the x direction, and the y-coordinate of M is 5 plus the distance between M and the midpoint in the y direction.

We already know that the distance between M and the midpoint in the y direction is 0 (since M lies on the same horizontal line as the midpoint), so we only need to find the distance between M and the midpoint in the x direction:

Distance between M and midpoint in the x direction = sqrt((1/5)d^2)

Since d is just the distance between P and Q, we can find it using the distance formula:

d = sqrt((6 - 3)^2 + (2 - 8)^2)
d = sqrt(34)

So we have:

Distance between M and midpoint in the x direction = sqrt((1/5)(sqrt(34))^2)
Distance between M and midpoint in the x direction = sqrt(34)/5

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Related Questions

3) What is the third term of the recursive sequence: a(1) = 3
a(n) = 2 · a(n-1)
(A) 6 [B] 10 [C] 12 [D] 53​

Answers

Answer:a

Step-by-step explanation:I too, the test

I took the test already trust me

What is the percent of 40 of 230

Answers

Answer:

17.39

Step-by-step explanation:

40:230*100 =

( 40*100):230 =

4000:230 = 17.39

Answer:

20 % would be ur answer to ur question

Please help! Correct answer only!

Chef Cline's fridge is filled with 10 milk cartons, 5 of which contain lactaid milk. Before she begins to bake, she examines the cartons' expiration dates.
If Chef Cline checks the expiration dates on 4 randomly selected cartons, what is the probability that exactly 2 of the chosen milk cartons contain lactaid milk?
Write your answer as a decimal rounded to four decimal places.

Please help! Correct answer only!Chef Cline's fridge is filled with 10 milk cartons, 5 of which contain

Answers

Answer:

Probability ≈ 0.4762

Step-by-step explanation:

See explanation below;

\(Total Number of Outcomes - 10C4,\\10 ! / 4! * ( 10 - 4 ),\\10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1 * 6 * 5 * 4 * 3 * 2 * 1,\\\\Total Outcomes = 210,\\\\Number of Outcomes - 5C2 * 5C2,\\5C2 = 5 * 4 * 3 * 2 * 1 / 2 * 1 * ( 3 * 2 * 1 ),\\\\Number of Outcomes - ( 10 )^2 = 100,\\\\Conclusion; Probability = 100 / 210 = 0.4762\)

Solution; Probability ≈ 0.4762

what is the quotient of 30 and the sum of 5 and 7.

Answers

Answer:

2  1/2

Step-by-step explanation:

30/ (5+7)

solve using system of operations

PEMDAS

Parenthesis

Exponent

Multiplication/Division

Addition/Subtraction

30/(5+7)

parenthesis first so

5+7 = 12

30/12

then division

30/12= 2  6/12

6/12 can be simplified by 6 so

6/6 = 1 and 12/6 = 2

So your answer would be 2  1/2

The quotient of 30 and the sum of 5 and 7 is 2.5

Expressions and equations

From the question we are to write the information as an expression:

The sum of 5 and 7 is given as 5+7 = 12

The quotient of 30 and the sum of 5 and 7 is expressed as \(\frac{30}{5+7}\)

Simplify the result

\(\frac{30}{5+7} =\frac{30}{12} = 2.5\)

Hence  the quotient of 30 and the sum of 5 and 7 is 2.5

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find the value of x. Part 1c​

find the value of x. Part 1c

Answers

Answer:

x=11

Step-by-step explanation:

Please see attached image.

find the value of x. Part 1c

Answer: x = 11

Step-by-step explanation:

a) bottom triangle, bottom right angle: Using Linear Pair Postulate, 180° - 114° = 66°

b) bottom triangle, top angle: Congruent sides implies congruent angles = 66°

c) bottom triangle, bottom left angle: Using the Triangle Sum Theorem, 66° + 66° + y = 180° --> y = 48°

d) top triangle, bottom angle: Using Complimentary Angles Theorem, 90° - 48° = 42°

Congruent sides implies congruent angles:

42° = ∠2

42 = 2x + 20

22 = 2x

11 = x

find the value of x. Part 1c

If the given ΔXYZ is rotated by 180 degrees around point X in a clockwise direction, what are the new coordinates of the Y and Z vertices? Select the two correct answers.

If the given XYZ is rotated by 180 degrees around point X in a clockwise direction, what are the new

Answers

Answer:

Options C and D

Step-by-step explanation:

From the graph attached,

Coordinates of the vertices,

X → (0, 0)

Y → (-1, -2)

Z → (0, -2)

Rule for the rotation of a  point (h, k) by 180° about the origin is given by,

(h, k) → (-h, -k)

By this rule,

Coordinates of the image points will be,

X(0, 0) → X'(0, 0)

Y(-1, -2) → Y'(1, 2)

Z(0, -2) → Z'(0, 2)

Therefore, Option (C) and Option (D) are the correct options.

Answer

C/D

Step-by-step explanation:

A map has a scale factor of 1:25 000

What real distance is represented by a distance of 6.8 cm on the map?

Answers

12.1 cm jsijdgsjdbdnjdgakjehdhjdjrjrgskhs

30. the intelligence quotient (iq) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. what is the probability we could select a sample of 50 adults and find that the mean of this sample is between 98 and 103. * a. 0.3264 b. 0.9428 c. 0.4702 d. 0.7471

Answers

The probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 is approx b). 0.9428.

The intelligence quotient (IQ) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. The standard deviation of the mean of a sample of 50 adults can be calculated as the population standard deviation divided by the square root of the sample size, or 15/√50 = 1.58.

Using a standard normal distribution table, the probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 can be calculated as the area under the standard normal curve between the z-scores corresponding to 98 and 103. These z-scores can be calculated using the formula z = (x - mean) / standard deviation, where x is the value of interest and mean is the population mean. The z-score for 98 is (98 - 100) / 1.58 = -1.27, and the z-score for 103 is (103 - 100) / 1.58 = 2.53.

The area under the standard normal curve between -1.27 and 2.53 can be found using a standard normal distribution table or a calculator with normal distribution functions. The probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 is approximately 0.9228, which is closest to the answer choice b. 0.9428.

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pls help me in this question

pls help me in this question

Answers

Im so sorry that people these days are racist towards black people i just wish that people could protest not riot people are dying and and suffering i cant  believe that is alright not all white people are racist  and i just want peace in this world people losing there homes their cars their money i will not stand up for the rioting or the violince but i will not stand for racisim either srew every racist b**ch out there. please give me feedback i want to know your point of view

What is 13200 as a ratio?

Answers

Answer:

13200n: 4 is 600

Step-by-step explanation:

if U= {1,2,3,4,5,6}, A ={1,2,3,}
B={2,3,5},and C ={4,5,6}
find (AUB)'n c

Answers

Answer:   {4, 6}

======================================================

Explanation:

A = {1,2,3}

B = {2,3,5}

A u B = {1,2,3,5}

The set A u B consists of anything in either set A or set B. This is a set union.

The complement of this is the complete opposite. So we only consider the items 4 & 6

(A u B)' = {4,6}

Note that sets AuB and (AuB)' can be unioned together to end up with the universal set U. Be sure not to mix up the universal set notation U with the union symbol 'u'

The last step is to see what sets (AuB)' and set C have in common. That would be 4 and 6 since both values are found in both sets

Therefore, (A u B)' n C = {4, 6}

The n refers to the intersection symbol.

2a) Determine the unknown angle x.

2a) Determine the unknown angle x.

Answers

The unknown angle x in the triangle is 80 degrees

How to determine the unknown angle x.

From the question, we have the following parameters that can be used in our computation:

The triangle

The unknown angle x is calculated using the sum of angles in a triangle theorem

So, we have

x + 60 + 40 = 180

Evaluate the like terms

x + 100 = 180

So, we have

x = 80

Hence, the unknown angle x is 80 degrees

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Mai got a prepaid debit card with $20 on it. For her first purchase with the
card, she bought some bulk ribbon at a craft store. The price of the
ribbon was 11 cents per yard. If after that purchase there was $17.14 left
on the card, how many yards of ribbon did Mai buy?

Answers

Answer:

26 yards of ribbon

                               

State whether the standardized test statistic t indicates that you should reject the null hypothesis. Explain.
​(a) t=2.126
​(b) t=0
​(c) t=1.966
​(d) t= -2.055
(a) For t=2.126​, should you reject or fail to reject the null​ hypothesis?
A. Reject H0​, because t>2.047.
B. Fail to reject H0​, because t<2.047.
C. Fail to reject H0​, because t>2.047.
D. Reject H0​, because t<2.047.
Part 2
​(b) For t=0​, should you reject or fail to reject the null​ hypothesis?
A. Reject H0​, because t<2.047.
B. Reject H0​, because t>2.047.
C. Fail to reject H0​, because t>2.047.
D. Fail to reject H0​, because t<2.047.
(c) Forvt=1.966​, should you reject or fail to reject the null​ hypothesis?
A. Reject H0​, because t>2.047.
B. Fail to reject H0​, because t>2.047.
C. Fail to reject H0​, because t<2.047.
D. Reject H0​, because t<2.047. Part 4 ​(d) For t=−2.055​, should you reject or fail to reject the null​ hypothesis?
A. Reject H0​, because t>2.047.
B. Fail to reject H0​, because t<2.047.
C. Fail to reject H0​, because t>2.047.
D. Reject H0​, becauset<2.047.

Answers

The standardized test statistic t indicates that you should reject the null hypothesis are as follows:

(a) For t=2.126, we should Reject H0, because t>2.047. This is option A

(b) For t=0, it Fail to reject H0, because t<2.047. This is option D

(c) For t=1.966, it Fail to reject H0, because t<2.047. This is option C

(d) For t=−2.055, we should Reject H0, because t<2.047. This is option D

The value of the standardized test statistic t indicates whether you should reject or fail to reject the null hypothesis. The critical value of t is determined by the significance level of the test and the degrees of freedom.

If the absolute value of the calculated t statistic is greater than the critical value, the null hypothesis should be rejected, indicating that the result is statistically significant.

If the absolute value of the calculated t statistic is less than or equal to the critical value, the null hypothesis should be failed to be rejected, indicating that the result is not statistically significant.

Hence, the answer of the questions are A, D, C and D respectively.

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Which of the following explains the relationship between angles B and C?

Answers

Considering that the angles are opposite by the same vertex, the relationship between angles B and C is given by:

Vertical Angles.

What is the relationship between angles B and C?

Researching this problem on the internet, it is found that there is a vertex, and angles are diagonal, also called opposite by the same vertex. These angles are also called vertical angles, hence this is what describes the relationship between these angles.

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Write the coordinates of each image. Use the graph to help you out. ​

Answers

where’s the image love?

Pt. 1 write a congruence statement for the above triangles.

Pt. 1 write a congruence statement for the above triangles.

Answers

The congruence statement for the triangles is SSS

How to determine the congruence statement

From the question, we have the following parameters that can be used in our computation:

The triangles

On the triangles, we can see that

The corresponding sides have the same mark i.e. I, II and III

This means that The corresponding sides are equal

So, the triangles are congruent by SSS

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a census is a regularly-occurring and official count of a particular population. census data available at the united states census bureau website are an example of:private informationpublic beha

Answers

Census data available at the United States Census Bureau website is an example of public information.

Census data is collected by the government and is intended to provide statistical information about a population. It is considered public information because it is made available to the general public for research, analysis, and decision-making purposes.

The United States Census Bureau collects and publishes census data to ensure transparency and accessibility to a wide range of users, including policymakers, researchers, businesses, and the general public.

This data helps inform various aspects of society, such as planning public services, determining representation, and studying demographic trends. It is important to note that while individual responses to the census are confidential and protected by law, aggregated census data is made public to benefit society as a whole.

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The sum of half of a number and 49is 2 whole 1/4 of the number. find the number

Answers

Answer:

-93.5

Step-by-step explanation:

let the number be y

1/2 × y + 49 =2 1/4

y/2 +49 =9/4

y/2 =9/4-49

y/2 = 9-196/4

y/2 = -187/4

cross multiply

4y = -374

y = -93.5

Answer:

28

Step-by-step explanation:

Let the number is x

Half of a number = (1/2) x2 whole 1/4 of the number = (2 1/4) x = (9/4) x

The sum:

(1/2) x + 49 = (9/4) x(9/4)x - (1/2)x = 49(9/4 - 1/2)x = 49(7/4)x = 49x = 49 : 7/4x = 49 * 4/7x = 7 * 4x = 28

20 Points- Which of the following is true for f of x equals the quotient of the quantity x squared plus 9 and the quantity x minus 3?
There is a removable discontinuity at x = 3.
There is a non-removable discontinuity at x = 3.
The function is continuous for all real numbers.

Answers

Answer:

There is a non-removable discontinuity at x = 3

Step-by-step explanation:

We are  given that

\(f(x)=\frac{x^2+9}{x-3}\)

We have to find true statement about given function.

\(\lim_{x\rightarrow 3}f(x)=\lim_{x\rightarrow 3}\frac{x^2+9}{x-3}\)

=\(\infty\)

It is not removable discontinuity.

x-3=0

x=3

The function f(x) is not define at x=3. Therefore, the function f(x) is continuous for all real numbers except x=3.

Therefore, x=3 is non- removable discontinuity of function f(x).

Hence, option B is correct.

Certify Completion Icon Tries remaining: 3 A high school has 52 players on the football team. The summary of the players' weights is given in the box plot. What is the median weight of the players?

Answers

Certify Completion Icon Tries remaining: 3 A high school has 52 players on the football team. The summary of the players' weights is given in the box plot. The median weight of the players on the football team is 160 pounds.

The box plot shows that the median weight of the players is the middle value of the distribution. In this case, the median weight is halfway between the 26th and 27th players, which is 160 pounds.

The box plot also shows that the minimum weight of the players is 150 pounds and the maximum weight is 212 pounds. The interquartile range, which is the range of the middle 50% of the data, is 20 pounds.

In conclusion, the median weight of the players on the football team is 160 pounds. This means that half of the players on the team weigh more than 160 pounds and half of the players weigh less than 160 pounds.

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Solve for x 33 = 34x+2

Answers

Answer:

31/34

Step-by-step explanation:

33 = 34x +2

31=34X

31/34 = x

X=0.91




33=34x+2
-2. -2
31 = 34x
—- ——
31. 34
X=0.91

Answer this question for me ASAP

Answer this question for me ASAP

Answers

Answer:

Option A: (It's just that the y-intercept and slope are in different spots.)

Line in (y=mx+b) form is y = 2x + 4

Slooe is 2

y-intercept is 4

Step-by-step explanation:

Slope-intercept form is written as y=mx+b, where m is slope and b is y-intercept.

By looking at the graph, we can already tell that the y-intercept is positive 4, since the line crosses the y-axis at that point.

Now use rise/run to find slope. (Remember that rise is movement up or down, and run is movement left or right.) With this in mind, the slope is 4/2, and if we simplify it, it's 2/1 (or basically just 2). Because we go upwards 4 units and to the right 2 units.

Hope this helps :)

Preform the following operations with fractions.
-11/5+4/6

Answers

(-11/5)(6/6) + (4/6) (5/5)
-66/30 + 20/30
-46/30
23/15

which factor has the greatest influence on the number of daylight hours that a particular earth surface location receives

Answers

Our amount of daylight hours depends on our latitude and how Earth orbits the sun.

Our location and the Earth's orbit around the sun both affect how many hours of daylight we receive. The axis of rotation of the Earth is inclined with respect to its orbital plane and always faces the North Star.

Every day of the year, there are precisely twelve hours of daylight and twelve hours of darkness where the equator is. Although not by much, atmospheric refraction causes sunrise to occur a bit earlier and dusk to occur a little later.

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What is the solution to the equation 3x + 2(x - 9) = 8x + X- 14?
O-8
-1
O1
O8

What is the solution to the equation 3x + 2(x - 9) = 8x + X- 14?O-8-1O1O8

Answers

Answer is B -1
Hope it helps

Answer:

-1

Step-by-step explanation:

Simplify both sides: 3x + (2(x) + 2(-9)) = 8x + x -14

Add/Combine like terms: 3x+2x= (5x-18) = (9x-14)

New Equation: 5x-18 = 9x-14

add 14 to both sides: 5x-4 = 9x

Subtract 5x from both sides: -4 = 4x

Divide both sides by 4 to get: -1 = x

Answer: x = -1

Jamie purchased a baseball card at a garage sale for $6 and marked it up 75% before reselling it to a baseball card dealer. How much did he charge the baseball card dealer?​

Answers

Answer:

$10.5

Step-by-step explanation:

Cp = $6

Mark up  percentage = 75%

Mark up  price = 75/ 100 x 6  = $4.5

SP= $6+  $4.5  = $10.5

I Hope Im right!!!

$10.5 is the answer but make sure u check to

12. DIG DEEPER The sum of a three-digit
number and a one-digit number is 731.
The product of the numbers is 2,908,
What are the numbers?

Answers

The three digit number is 727 while the one digit number is 4

Given data

The sum of a three-digit number and a one-digit number is 731.

The product of the numbers is 2,908

How to solve for the numbers

let three digit number be x, y, and z

let the one digit be w

The sum

xyz + w =731

xyz * w = 2,908

making xyz the subject of formula

xyz = 731 - w

plugging in xyz into xyz * w = 2,908

( 731 - w ) * w = 2908

731w - w^2 = 2908

w^2 - 731w + 2908 = 0

solving the quadratic equation gives

w = 727 or 4

since w is a one digit number then w = 4

plugging in w = 4 into xyz + w =731 we have

xyz + w =731

xyz + 4 =731

xyz =731 - 4

xyz  = 727

Hence the three digit number is 727 while the one digit number is 4

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Please answer this function !!!

Please answer this function !!!

Answers

Answer:

f(6)=-114

Solution,

\(f(x) = - 4 {x}^{2} + 5x \\ f(6) = - 4 \times {6}^{2} + 5 \times 6 \\ \: \: \: \: \: \: = - 4 \times 36 + 30 \\ \: \: \: = - 144 + 30 \\ \: \: \: - 114\)

hope this helps.

Good luck on your assignment..

Answer:

-114

Step-by-step explanation:

To find f(6), you need to plug in the value in parentheses wherever there is an x in the equation.

f(x) = -4x + 5x

f(6) = -4(6) + 5(6)

f(6) = -4(36) + 30

f(6) = -144 + 30

f(6) = -114

The answer is -114.

help please...geometry....
Determine whether a translation maps
quadrilateral LMNP onto quadrilateral
L'M'N'P'. If so, find the translation vector.
If not, explain why.

help please...geometry....Determine whether a translation mapsquadrilateral LMNP onto quadrilateralL'M'N'P'.

Answers

The quadrilateral LMNP can be mapped onto the quadrilateral, L'M'N'P', by a translation of 4 units to the left and 3 units down

The translation vector is <-4, -3>

What is a translation vector?

A translation vector changes the location of an figure on the coordinate plane from one point to another.

The coordinates of the vertices of the quadrilateral LMNP are;

L(4, 2), M(4, -1), N(0, -1), and P(1, 4)

The coordinates of the vertices of the quadrilateral L'M'N'P' are;

L'(0, -1), M'(0, -4), N'(-4, -4), and P'(-3, 1)

The change in the coordinates from L to L' is; (0 - 4, -1 - 2) = (-4, -3)

The change in the coordinates from M to M' is; (0 - 4, -4 - (-1)) = (-4, -3)

The change in the coordinates from N to N' is; (-4 - 0), -4 - (-1)) = (-4, -3)

The change in the coordinates from P to P' is; (-3 - 1, 1 - 4) = (-4, -3)

Therefore;

A translation of 4 units to the left and 3 units down maps the quadrilateral LMNP to L'M'N'P'

The translation vector is therefore <-4, -3>

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