Endpoints of segment MN have coordinates (0, 0), (5, 1). The endpoints of segment AB have coordinates (1 1/22 , 2 1/4 ) and (−2 1/4 , k). What value of k makes these segments perpendicular?

Answers

Answer 1

Answer: [tex]k=18\dfrac{8}{11}[/tex].

Step-by-step explanation:

If a line passing through two points, then

[tex]Slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Endpoints of segment MN have coordinates (0, 0) and (5, 1).

Slope of MN [tex]=\dfrac{1-0}{5-0}=\dfrac{1}{5}[/tex]

The endpoints of segment AB have coordinates [tex]\left(1\dfrac{1}{22} , 2\dfrac{1}{4}\right)[/tex] and  [tex]\left(-2\dfrac{1}{4} , k\right)[/tex].

[tex]A=\left(1\dfrac{1}{22} , 2\dfrac{1}{4}\right)=\left(\dfrac{23}{22} ,\dfrac{9}{4}\right)[/tex]

[tex]B=\left(-2\dfrac{1}{4} , k\right)=\left(-\dfrac{9}{4} , k\right)[/tex].

Slope of AB [tex]=\dfrac{k-\frac{9}{4}}{-\frac{9}{4}-\dfrac{23}{22}}[/tex]

[tex]=\dfrac{\frac{4k-9}{4}}{\frac{-99-46}{44}}[/tex]

[tex]=\dfrac{4k-9}{4}\times \dfrac{44}{-145}[/tex]

[tex]=4k-9\times \dfrac{11}{-145}[/tex]

[tex]=\dfrac{44k-99}{-145}[/tex]

Product of slopes of two perpendicular segments is -1.

Slope of MN × Slope of AB = -1

[tex]\dfrac{1}{5}\times \dfrac{44k-99}{-145}=-1[/tex]

[tex]\dfrac{44k-99}{-725}=-1[/tex]

[tex]44k-99=725[/tex]

[tex]44k=725+99[/tex]

[tex]k=\dfrac{824}{44}[/tex]

[tex]k=\dfrac{206}{11}[/tex]

[tex]k=18\dfrac{8}{11}[/tex]

Therefore, the value of k is [tex]k=18\dfrac{8}{11}[/tex].

Answer 2

Answer:

k=21

Step-by-step explanation:

Find the slope of MN which is 1/5, (use the slope formula.)

Use the slope formula for AB using k as y_2

Substitute and you get k=21

21-2.25/-2.25-1.5=-5

The lines are perpendicular because the slopes are the negative reciprocal of one another.


Related Questions

The map shows a straight highway between two towns. Highway planners want to build two new rest stops between the towns so that two rest stops divided the highway into three equal parts. Find the coordinates of the points at which the rest stops should be built.

Answers

1,1 and -1,0 would be the answer

(-2, -1/3)   and   (1,  1 1/3) the coordinates of the points at which the rest stops should be built.

What is coordinates point?

A pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes.

According to the question,

In given figure,

x   from  -3   to  +3    

1/3   would be  -2    

2/3 would be   +1

y   from  -2  to  +3        

1/3  would be   -2 + 5/3 = -1/3      

2/3 would be  -2 + 10/3 = 1 1/3

The two coordinates

(-2, -1/3)   and   (1,  1 1/3)  

Hence ,  (-2, -1/3)   and  (1,  1 1/3)  the coordinates of the points at which the rest stops should be built.

To learn more about coordinate from here

https://brainly.in/question/19953416

#SPJ2

Sebastian plays a snare drum that has a radius of 3 inches. What is the drum's diameter? ______ inches

Answers

Answer:6

Step-by-step explanation:

d=2r

Gertrude has 71.502 ounces of butter. How many ounces of butter does she have, rounded to the nearest hundredth?​

Answers

Answer:

71.500

Step-by-step explanation:

502 is closer to 500 than 600.

Answer:

71.50

Step-by-step explanation:

This is because 2 is not up to 5, so it can't be turned into 1 and be added to 0.

3x-2=7????????????????



Answers

Answer:

x=3

Step-by-step explanation:

Step 1: Add two to 7 and inverse the minus 2

3x=7+2 3x=9

Step 2: Divide each number by 3.

3x/3=x and 9/3=3

so x=3

According to a newspaper report, A 63 year old man has rowed around the world without leaving his living room. He clocked up 24084 miles on a rowing machine that he recieved for his 50th birthday. Roughly how many miles per year has he rowed since he was given the machine?

A) 200
B) 500
C) 1000
D) 2000
E) 4000

(can i get it with the full working out please)​

Answers

So he has had the machine for 13 yrs
24084/13 is roughly 2000 so I would say D

The number of miles per year that he has rowed since he was given the machine will be Roughly 2000. Then the correct option is D.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A 63-year-old man has rowed around the world in his living room, according to a newspaper story. On a rowing machine that he received for his 50th birthday, he logged 24084 miles.

The number of miles per year is calculated as,

⇒ 24,084 / (63 - 50)

⇒ 24,084 / 13

⇒  1852.61 ≈ 2,000

The number of miles per year that he has rowed since he was given the machine will be Roughly 2000. Then the correct option is D.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

6*10^-2 is how many times as large as 2*10^-8

Answers

Answer:

3000000

Step-by-step explanation:

6×[tex]10^{-2}[/tex] = 6 × 1/(10)² = 6 × 1/100 = 6/1002×[tex]10^{-8}[/tex] = 2 × 1/[tex]10^{8}[/tex] = 2 × 1/100000000 = 2/100000000

Divide 6/100 and 2/100000000 to find how many times as large

The answer is 3000000

3000000 is the answer

Solve ax + bx = c for x
a,b,c represent nonzero constants

Answers

Answer:

x=(c/a+b)

Step-by-step explanation:

..........

Answer:

x = [tex]\frac{c}{a+b}[/tex]

Step-by-step explanation:

Given

ax + bx = c ← factor out x from each term on the left side

x(a + b) = c ← divide both sides by (a + b)

x = [tex]\frac{c}{a+b}[/tex]

what is 660 increased by 1 followed by a further one

Answers

The answer is 662

660+1+1= 662


find the missing angle

Answers

Answer:

I don’t have the answer but I recommend downloading socratic I use this app and it is so helpful

Step-by-step explanation:

It helps me with all my questions

(D2+6d+9)+(d3-6d+9) ​

Answers

You can’t add d2 or d3 so ignore it for now u will subtract -6d from +6d to get 0 then add 9+9
Answer:
d3+ d2 + 18

D3 has to be in front because it has a larger exponent

Evaluate each expression if a = 4, b = 6, and c = 2.

Answers

Answer:

26

Step-by-step explanation:

ab+c

plug in #s

4(6)+2

start to solve

24+2

26

Solve the equation |x + 6|= |x– 12|. Graph the solutions, if possible.

Answers

Answer:

x=3

Step-by-step explanation:

Answer:

Step-by-step explanation:

|x+6|=|x-12|

x+6=±(x-12)

when x+6=x-12

6=-12

which is impossible hence rejected.

x+6=-(x-12)

x+6=-x+12

x+x=12-6

2x=6

x=6/2=3

so x=3

hey mm, i’m lost idk what to do •__•

Answers

It’s A. If you need another explanation I would be happy to explain it again

how many numbers lie between squares of 12 and 13 ​

Answers

Answer:

therefore 25 numbers lie inbetween.

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

The baseball team is ordering hats for the upcoming season. The hat company
charges a certain amount per hat plus an initial fee of $55. There are 14 players on the
baseball team. If there are 14 players on the baseball team and the hat order comes to a
total of $363, how much does each hat cost?

Answers

Each hat cost at least $25.92

Solve for w.
4 = 0.25(w-4.3)

Answers

W=20.3

solve what's in the parenthesis, move the terms, calculate, then divide both sides.

Answer:

20.3

Step-by-step explanation:

I did it and it was right on khan

please answer asap please

Answers

Answer:

( 6,-1)

Step-by-step explanation:

Point B is at ( 0,3)

We are going down 4 units so subtract 4 from y

and going right 6 units so add 6 to x

(0+6 , 3-4)

( 6,-1) is the location of B'

Answer:

B- its going 4 down from positive 3 which will make it -1 and 6 over from 0 which makes it 6 and that gives you the answer of (-1,6)

simplify the expression -4(x - 5)

Answers

Answer:

-4x+20

Step-by-step explanation:

[tex]-4(x - 5)\\\\=-4x-4(-5)\\\\=-4x+20[/tex]

Can someone help mewith this

Answers

Answer:

(x+3)(x-3)  *  2  

4 (x-3)          (x+3)

= 1/2

Answer:

1/2

Step-by-step explanation:

[tex]\frac{(x-3) * (x+3) }{2(2x-6)}[/tex] × [tex]\frac{2}{x+3}[/tex]

[tex]\frac{(x-3)*1}{2(x-3)}[/tex]

[tex]\frac{1}{2}[/tex]

1. Draw diagrams illustrating the relationship between the following sets of real numbers: (a) rational and irrational numbers (b) rational numbers and integers (c) irrational numbers and whole numbers (d) integers and whole numbers

Answers

Answer:

umm there is no answer u have to make a diagram of the rational and irratinal or the area of numbers its not a letter u have to make a diagram

Step-by-step explanation:

Please answer step by step 3(2y-7)=

Answers

Answer:

Step-by-step explanation:

3(2y-7)=

Distribute

3 * 2y - 3 *7

6y - 21

Step-by-step explanation:

3(2y-7) = 6y-21

y = 21/6

y = 3

explain how 5x-3y=2 and 5x-3y=8 are parallel without doing any calculations

Answers

Answer:

They're parallel because the first part of the equations have the same numbers/variables (can see down below in bold). This tells us whether or not it's parallel. There's no need for any calculations due to this.

5x - 2y = 2

and

5x - 2y = 8

The answer of the equations doesn't affect it, only is they're the same number. Then it becomes overlap.

For Example:

5x - 2y = 9

and

5x - 2y = 9

they're the same, meaning overlap.

Please help I’m struggling on this question.

Answers

Answer: [tex]\frac{2(y^2-4y+40)}{(y-8)(y+4)}[/tex]

Step-by-step explanation:

To solve this problem, we want to make sure the denominators are the same on both fractions. Once they are equal, we can dd them together.

[tex]\frac{y+4}{y-8} +\frac{y-8}{y+4}[/tex]                      [multiply first fraction by y+4 and second by y-8]

[tex]\frac{(y+4)(y+4)}{(y-8)(y+4)} +\frac{(y-8)(y-8)}{(y-8)(y+4)}[/tex]   [distribute by FOIL]

[tex]\frac{y^2+8y+16}{(y-8)(y+4)} +\frac{y^2-16y+64}{(y-8)(y+4)}[/tex]   [add numerator]

[tex]\frac{y^2+8y+16+y^2-16y+64}{(y-8)(y+4)}[/tex]         [combine like terms]

[tex]\frac{2y^2-8y+80}{(y-8)(y+4)}[/tex]                       [factor out 2 from numerator]

[tex]\frac{2(y^2-4y+40)}{(y-8)(y+4)}[/tex]                  

Now we know that [tex]\frac{2(y^2-4y+40)}{(y-8)(y+4)}[/tex] is the factored form after adding.

In the equation 4x - 8 = -12, the second step would be to...

Answers

Answer:

4x = -4

Step-by-step explanation:

4x = -12+8

4x = -4

x = -1

Step-by-step explanation:

4x - 8 = -12

4x = 8 - 12

4x = -4

x = (-4)/4

x = -1

What is the slope of the line parallel to y = 3x + 2
Zero
1
3
3
-3

Answers

Parallel lines have slopes which are equal to each other.

We know that y = 3x + 2 has a slope of 3, therefore, the line parallel to y = 3x + 2 has a slope of 3.

50 POINTS FOR THE ANSWER! Vanessa and Zack are playing a game where the player with the lower score wins. At the end of the game, Vanessa has a score of Negative 3 and StartFraction 5 over 8 EndFraction and Zack has a score of Negative 3 and two-thirds. Which statement explains who won? Comparing the decimal equivalents of their scores shows that Vanessa won because –3.625 is less than Negative 3.ModifyingAbove 6 with bar. Comparing the decimal equivalents of their scores shows that Vanessa won becauseNegative 3.ModifyingAbove 6 with bar is less than –3.625. Comparing the decimal equivalents of their scores shows that Zack won because –3.625 is less than Negative 3.ModifyingAbove 6 with bar. Comparing the decimal equivalents of their scores shows that Zack won becauseNegative 3.ModifyingAbove 6 with bar is less than –3.625.

Answers

Answer:

zack won. if you compare the decimal equivalents of their scores, -3.666<-3.625

Step-by-step explanation:

given: vanessa and zack are playing a game where the player with the lower score wins

score of vanessa=

[tex] - 3 \frac{5}{8} = - ( \frac{29}{8}) = - 3.625 [/tex]

score of zack:

[tex] -3 \frac{2}{3} = - ( \frac{11}{3} ) = - 3.666[/tex]

we can see -3.666<-3.625

zack has the lower score

Answer:

zack won. if you compare the decimal equivalents of their scores, -3.666<-3.625

Step-by-step explanation:

list a least two metric units that you can use to measure volume

Answers

Answer:

1-Rectangular prism

2-cube

Step-by-step explanation:

Rectangular prism - Multiply the measurement of the length times the width, then times the height.

Cube - Since all sides are the same measurement, it would be the measurement of any side, or edge, cubed, or a³

A parking garage charges $2 for the hour and $1 each additional hour. Fran has $9.90 to spend for parking. What is the greatest number of hours Fran can park

Answers

Answer:

Frank can park 8.9 hours at the highest

Step-by-step explanation:

Here, we want to know the greatest amount of time that Frank can park given the amount he has to spend on parking.

From the question, we are told that he pays $2 for the hour and an extra $1 per additional hour.

Now, let the number of additional hour he is going to park be x. The bill for the additional hours will be ; $1 * x = $x

By adding this to the initial $2, we have the total $9.90

So, mathematically;

2 + x = 9.90

x = 9.9 -2

x = 7.9 hours

Now, the initial hour he parked is 1 hour + number of incremental hours = 1 + 7.9 = 8.9 hours

PLEASE HELP I WILL MARK YOU BRAINLIEST

Answers

Answer:

33cm cubed

Step-by-step explanation:

6 blocks by 3 blocks by 2 blocks = 36 - 3 cause of the missing blocks = 33

17.
A $75 prize was to be awarded and split amongst a 6 person team. Which
representation best shows how much money each person will get, assuming the
prize is split equally?

Answers

Answer:

$12.5

Step-by-step explanation:

Since prize is split equally.

So, money received by each person

= 75/6

= $12.5

Other Questions
Which of the following examples describe an acceleration? (Check ALL that APPLY)Group of answer choicesA car has to slow down as it approaches a slower truck in front of itA car is sitting in a parking lotA car maintains a speed of 15 mph as it turns around a cornerA car is stopped at a stop light, and speeds up when it turns greenA car drives straight down a road at 60 mph Mark wants to put a fence around his square yard.He knows that his yard is shaped like a square and the area of the yard is 110. What would the perimeter be One important outcome of Edwin James' expedition reports is thatA. illustrations of bison encouraged Americans to hunt them to near extinctionB. accounts of rich, fertile soil encouraged Americans to settle the landC. descriptions of inhospitable land discouraged colonization for many yearsD. depictions of hostile native tribes discouraged colonization for many years Which of these is the best wayto avoid abusive peer relationships How to do this operation (11+1) -6 x8 + 16 Source: Dutch missionary John Megapolensis on the Mohawks (Iroquois), 1644, Smithsonian(John became the town's first pastor at Fort Orange (near Albany). As pastor he was not allowed to farm or trade, but received supportfrom the town, while diligently performing his duties, which included teaching the Indians about Christ.)The Women are obliged to prepare the land, to mow, to plant, and do every Thing: the Men do nothing except hunting, fishing, and goingto War against their Enemies: they treat their Enemies with great Cruelty in Time of War, for they first bite off the Nails of the Fingers oftheir Captives, and cut off some joints, and sometimes the whole of the Fingers; after that the Captives are obliged to sing and dancebefore them..., and finally they roast them before a slow Fire for some Days, and eat them. ... Though they are very cruel to theirEnemies, they are very friendly to us: we are under no Apprehensions from them....They are entire Strangers to alt Religion, but they have a Tharonhijouaagon, (which others also call Athzoockkuatoriaho) i.e. a Geniuswhich they put in the Place of God, but they do not worship or present offerings to him: they worship and present offerings to the Devilwhom they call Otskon or Airekuoni. ... They have otherwise no Religion: when we pray they laugh at us; some of them despise itentirely, and some when we tell them what we do when we pray, stand astonished. When we have a Sermon, sometimes ten or twelve ofthem, more or less, will attend, each having a long Tobacco Pipe, made by himself, in his Month, and will stand a while and look, andafterwards ask me what I was doing and what I wanted, that I stood there alone and made so many Words, and none of the rest mightspeak? I tell them I admonished the Christians, that they must not steal, ... get drunk, or commit Murder, and that they too ought not todo these Things, and that I intend after a while to preach to them. ... They say I do well in teaching the Christians, but immediately addDiatennon jawi Assyreoni hagiouisk, that is, why do so many Christians do these things. They call us Assyreoni, that is, Cloth-Makers, orCharistooni, that is, Iron Workers, because our People first brought Cloth and Iron among them...HIPP+:Historical Context:Intended Audience:Author's Purpose:Author's Point of View+Other Context (similar in kind, from a different time): Elmer Fudd is walking at 2.0 m/s. If he walks for 2.0 minutes, how far does he walk?(Can someone help with the answer due in 5min) Salgado speaks of a hunger for love as an overwhelming and constant desire for love, What are you hungry for right now (motivations, desires, passions)? Which property describes a mixture? It cannot be separated by physical methods. It has a single chemical composition. It cannot have more than one state of matter. It cannot be described by a chemical symbol or formula. The sum of two integers is -4. Can the two integers both be positive? If consumers start to believe they need a product, what is likely to happen? A. The demand becomes less elastic. B. The demand becomes more elastic. C. The supply decreases. D. The price decreases. Myoglobin transfers oxygen obtained from hemoglobin to mitochondrial proteins involved in the catabolism of metabolic fuels to produce energy for the muscle cell. Using what you have learned in this chapter about myoglobin and hemoglobin, what can you conclude about the structures of these mitochondrial proteins solve inequality and show work please What is the question to b(x)=3x-1. Please help me to prove this! Which conclusion about the Eldest Magician does this excerpt support?What makes Antigone a rebel? Question 3 of 10A__ sample is taken from the entire population, without a person choosingeach person.A. randomB. convenienceC. voluntaryO D. nonconvenienceSUBMITThe answer is A: random The Avogadro constant is defined as if f(x)=2x-1 and g(x)=x^2-3x-2, find (f+g)(x) Help pls i need help !!