A directed segment ST¯¯¯¯¯ is partitioned from S (−5,0) to T in a 32 ratio at point M (10, 15). What are the coordinates of point T? (20, 25) (15, 20) (7, 3) (5, 15

Answers

Answer 1

Answer:

[tex]T = (20,25)[/tex]

Step-by-step explanation:

Given

[tex]S = (-5,0)[/tex]

[tex]M = (10,15)[/tex]

[tex]Ratio = 3:2[/tex]

Required

Determine the coordinate of T

Line division by ratio is calculated using:

[tex]M(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]

Where:

[tex](x_1,y_1) = (-5,0)[/tex]

[tex](x,y) = (10,15)[/tex]

[tex]m:n = 3:2[/tex]

So, we have:

[tex](10,15) = (\frac{3 * x_2 + 2 * -5}{3+2},\frac{3 * y_2 + 2 * 0}{3+2})[/tex]

[tex](10,15) = (\frac{3x_2 -10}{5},\frac{3y_2}{5})[/tex]

Multiply through by 5

[tex]5 * (10,15) = (\frac{3x_2 -10}{5},\frac{3y_2}{5}) * 5[/tex]

[tex](50,75) = (3x_2 -10,3y_2)[/tex]

By comparison:

[tex]3x_2 - 10 = 50[/tex]

[tex]3y_2 = 75[/tex]

[tex]3x_2 - 10 = 50[/tex]

[tex]3x_2 = 50 + 10[/tex]

[tex]3x_2 = 60[/tex]  --- Divide through by 3

[tex]x_2 = 20[/tex]

[tex]3y_2 = 75[/tex]

[tex]y_2 =75/3[/tex] --- Divide through by 3

[tex]y_2 =25[/tex]

Hence:

The coordinates of T is

[tex]T = (20,25)[/tex]


Related Questions

Given f(x) = 5x + 1, find f(-3).
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Answer:

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Pure acid is to be added to a 10% acid solution to obtain 99L of a 20% acid solution. which amounts of each should be used ?

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Answer:

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y = amount of 10% acid solution (acid + water)

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Step-by-step explanation:

A serving of rice is 2/5 of a cup. How many servings are there in a 1 3/5-cup bag of rice?

Answers

3 i think i’m not sure tho if u add 2/5 until u get 1 3/5 that might help

Write each fraction as a percent. Use a model if needed. V-2
7/10

21/25

3/5

18/25​

Answers

7/10 = 70%
21/25 = 84%
3/5 = 60%
18/25 = 72%
7/10 is 70%
21/25 is 84%
3/5 is 60%
18/25 is 72%

Given z1 = StartRoot 2 EndRoot (cosine (StartFraction 3 pi Over 4 EndFraction) + I sine (StartFraction 3 pi Over 4 EndFraction) ) and z 2 = (Cosine (StartFraction pi Over 2 EndFraction) + I sine (StartFraction Pi Over 2 EndFraction) ) , what is the value of z1 – z2?

cos(0) + isin(0)
cos(0) – isin(0)
cos(Pi) + isin(Pi)
cos(Pi) – isin(Pi)

Answers

Answer: C. cos(Pi) + isin(Pi)

Step-by-step explanation:

The value of subtraction of two given complex numbers z₁ and z₂ is cos(π) + isin(π).

What are complex numbers?

A complex number is an element of a number system that includes real numbers and a specific element labeled i sometimes known as the imaginary unit, and which obeys the equation i² = 1. Furthermore, every complex number can be written as a + bi, where a and b are both real values.

How to solve this problem?

We know that cos(π - x) = - cosx, sin(π - x) = sinx, cos(π/4) = 1/√2 = sin(π/4), cos(π/2) = 0, sin(π/2) = 1, cos(π) = - 1, sin(π) = 0.

Given that z₁ = √2[cos(3π/4) + isin(3π/4)] = √2[cos(π - π/4) + sin(π - π/4)] = √2[- cos(π/4) + sin(π/4)] = √2[- 1/√2 + 1/√2] = √2[0] = 0

and z₂ = cos(π/2) + isin(π/2) = 0 + i × 1 = 1

Now, z₁ - z₂ = 0 - 1 = - 1 = - 1 + i × 0 = cos(π) + isin(π)

Therefore, the value of subtraction of two given complex numbers z₁ and z₂ is cos(π) + isin(π).

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Question 5
Here are four cards.
4 5 0.
Use each card once to make the largest number that is less than 10
Here are four cards.
4 5 0 .
Use each card once to make the largest number that is less than 10​

Answers

Answer:

9 by adding all the three cards

Compare: -7 -4


PLEASE HELP ME!

Answers

-11? What do u mean compare

Write the rational number as a decimal -4 2/3

Answers

Answer:

- 4.(6)

Step-by-step explanation:

Hi there !

- 4  2/3 =

= - 4  6/9

= - 4.(6)

Good luck !

divide 25.84 divide by 4

Answers

i believe it is 6.46

Answer:

25.84 divide by 4 Is 6.46.

Analyzing a Linear Function Expressed in Different Ways Choose the true statements. A linear function is expressed by a graph of a line that crosses both axes at the origin. An equation is written in slope-intercept form to express the same function as shown in the graph. From just this information, what statements can be made? A) The slope of the equation must be positive. B)The y-intercept of the equation is zero. C) It is possible that the line on the graph is horizontal. D) The slope of the equation must be negative.​

Answers

Answer: The answer is option B and option C.

Answer:

B and C

Step-by-step explanation:

Siobhan earned $45 babysitting on Friday. On Saturday, she babysat for 5 hours at $4 per hour. On Sunday she bought a DVD for $32. How
much money did she have left after buying the DVD?

Answers

$30

Work: 45+20=65

          65-35=30

4 tens + 14 ones = 5 tens + ___ ones

Answers

Answer:

4 becuase 40+14 = 54 so 50+4= 54 too

Step-by-step explanation:

HOPE THIS  HELPS :)

A researcher is exploring the notion that there is an economy of scale in raising children. While having one child might add to a family's financial stress, the second or third one might not be as "expensive" since they would already be sharing one roof, could share clothing, etc. The researcher has access to a large community of parents where 15% have one child under 18 in their home, 65% of parents have two children, and 20% of parents have three or more children. Rounded to the nearest whole number, the probability that any given family who is selected has two or more children at home is ________ %?

Answers

Answer:

The probability that any given family who is selected has two or more children at home is 85%.

Step-by-step explanation:

The information provided is as follows:

Number of Children        Probability

             1                            0.15

             2                            0.65

          > 3                            0.20

Compute the probability that any given family who is selected has two or more children at home as follows:

P (At least 2 Children) = P (2 children) + P (More than 3 children)

                                   = 0.65 + 0.20

                                   = 0.85

Thus, the probability that any given family who is selected has two or more children at home is 85%.

Susan's grandpa was fibbing again: "your grandma and I, together, we are over 150

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Answers

answer: 71 + 68 = 139
Answer:71.68

Easy as pie.

Just add em.

Making it.

71

+68

------

139

Meaning both of em are 139 years.

This also means they are not over 150.

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Answers

Answer: 3/4 divided by 1/2 is 1.5

Find three nonzero vectors a, b, and c such that a × b = a × c != 0 but b != c.

Answers

9514 1404 393

Answer:

  a = {1, 2, 3}, b = (2, 4, 7}, c = (-3/14, -3/7, 5/14}

Step-by-step explanation:

For the above vectors, ...

  a × b = a × c = (2, -1, 0)

__

Here, c is found to be a scaled version of (a×(a×b)).

Giving out brainlst to whoever can answer this

Answers

100 - 5d + 10d = 130

5 x 20 = 100
5 x -d = -5d

A fast-food restaurant has a cost of production C(x)=12x+114 and a revenue function R(x)=6x. When does the company start to turn a profit?

Answers

Step-by-step explanation:

Given data

C(x)=12x+114

R(x)=6x.

The company will start to run on profit just when revenue equals the production cost, that is

C(x)=R(x)

equating the two expressions we have

12x+114=6x

solving for x we have

12x-6x+114=0

6x+114=0

6x=-114

x=-114/6

x=-19

Hence the company will start to run on proft when they start to produce above 19 items

Profit is the difference between the revenue and cost functions

A production greater than 19 will turn a profit

From the question, we have:

[tex]\mathbf{R(x) = 6x}[/tex]

[tex]\mathbf{C(x) = 12x + 114}[/tex]

So, the profit function is:

[tex]\mathbf{P(x) = R(x) - C(x)}[/tex]

Substitute known values

[tex]\mathbf{P(x) = 6x - 12x - 114}\\[/tex]

[tex]\mathbf{P(x) = - 6x - 114}[/tex]

Equate to 0

[tex]\mathbf{- 6x - 114 = 0}[/tex]

Collect like terms

[tex]\mathbf{- 6x= 114}[/tex]

Divide both sides by -6

[tex]\mathbf{x= -19}[/tex]

The above equation means that: A production greater than 19 will turn a profit

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How do you find what p is?

Answers

Answer:

p > -3

Step-by-step explanation:

This is an alternating p-series.  It is absolutely convergent if│an│converges.  1 / nᵖ⁺³ converges if the exponent is greater than 1.

p + 3 > 1

p > -2

The series is conditionally convergent if │an│diverges.  1 / nᵖ⁺³ diverges if the exponent is greater than 0 and less than or equal to 1.

0 < p + 3 ≤ 1

-3 < p ≤ -2

Combining these two, we get p > -3.

7 – 0.2n = -0.8n + 10
What value of n makes this equation true?
Please helpp

Answers

The answer to the equation is [tex]n=5[/tex]

First, you must add 0.8n on both sides.

[tex]0.6n+7=10[/tex]

Then, subtract 7 from both sides.

[tex]0.6n=3[/tex]

Finally, divide both sides by 0.6

[tex]n=5[/tex]


$11000 is compounded semiannually at a rate of 8% for 19 years. What is the total amount in the compound interest account?

Answers

Answer:

all really all you have to do is do 8 divided by 19 and then whatever that number that you get from that attractive from your highest number that you have in your question which is 11000

What is 715 divided by 25 and what is 514 divided by 28?

Plsss help I really need it for my HW

Answers

Answer:

715 divided by 25 is 28.6, while 514 divided by 28 is 18.35. Hope this helps!

Step-by-step explanation:

20 points & will give brainliest

Find the distance between (5,8) and (3,-1)

Answers

Answer:

root 85

decimal 9.21

slope 9/2

Step-by-step explanation:

didnt know which one you wanted fully

Where is the vertex of f(x) = -2x - 3| +6.4?

Answers

(-2x-19.2) I think that is the answer :(

When Alexander moved into a new house, he planted two trees in his backyard. At

the time of planting, Tree A was 36 inches tall and Tree B was 21 inches tall. Each

year thereafter, Tree A grew by 6 inches per year and Tree B grew by 9 inches per

year. Let A represent the height of Tree At years after being planted and let B

represent the height of Tree Bt years after being planted. Write an equation for each

situation, in terms of t, and determine which tree is taller after 3 years.

Answers

Answer:

The equations for each situation are

A = 36 + 6t

B = 21 + 9t

After 3 years, Tree A is taller.

Step-by-step explanation:

From the question,

Tree A was 36 inches tall and Tree B was 21 inches tall at the time of planting; and

Tree A grew by 6 inches per year and Tree B grew by 9 inches per  year after planting.

For Tree A,

Given a period of t years after planting, the height would have increased by 6t

A = 36 + 6t

For Tree B,

Given a period of t years after planting, the height would have increased by 9t

B = 21 + 9t

To determine, which tree is taller after 3 years,

t = 3

For Tree A

A = 36 + 6t

A = 36 + 6(3)

A = 36 + 18

A = 54 inches

For Tree B

B = 21 + 9t

B = 21 + 9(3)

B = 21 + 27

B = 48 inches

Hence, After 3 years, Tree A is taller.

Jesse is driving to a town that is 210 miles away with a speed of 60 miles per hour. If he makes no stops, how long will the trip take?

Answers

Answer: The trip should take 3.5 hours.

Step-by-step explanation: To find the time, divide the distance by the rate. In this case, 210/60 = 3.5.

Answer:

3.5 hours or specifically, 3 hours and 30 minutes

Step-by-step explanation:

We know that the car can be driven 60 miles per hour. The goal is 210 miles. If you divide 210 miles by 60, the result is 3.5. The whole number 3 in 3.5 will represent the hours taken which means 3 hours. The 0.5 will also represent the minutes. 0.5 = 1/2, 1/2 of an hour = 30 minutes.

6. The store paid $2.50 for a book and sold it for $5.25. What is the profit as a percent?

Answers

7.75 I hope this helps

The base of a triangle is 12 inches greater than the height. If the area is 80 square inches, find the length of the base
PLEASE HELP

Answers

Answer:

Step-by-step explanation:

Because the area of a triangle you have to divide by 2 and then you get the area right so we multiply 80 x 2 = 160 is the area of the square which you divide by 2 but we are not going to do that. now we have to get 2 lengths with 12 difference so we have to just do trial and error method.

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Answers

24/18 in decimal form is 0.778

Answer:

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Step-by-step explanation:

the 7 is repeating so you can put a dash above the second 7

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Answers

Answer: -2/6 or -1/3
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