A sending host will retransmit a TCP segment if it ________. Group of answer choices none of the above receives an RPT segment receives an ACK segment receives an NAC segment

Answers

Answer 1

A sending host will retransmit a TCP segment if it receives an ACK segment.

Transmission Control Protocol (TCP) is a core communication protocol in the Internet Protocol (IP) suite. It is a connection-oriented protocol that provides reliable, ordered, and error-checked delivery of data between applications that run on hosts that may be located on different networks.

TCP requires an end-to-end handshake to set up a connection before transmitting data, and it uses flow control and congestion control algorithms to ensure that network resources are utilized efficiently. Retransmission of lost packets is also a significant feature of TCP.

If a sending host detects that a packet has been lost, it will retransmit the packet. TCP utilizes a form of go-back-n retransmission, in which packets that are transmitted but not acknowledged by the receiving host are retransmitted.

When the sender detects that an ACK segment has not arrived within a reasonable amount of time, it will assume that the segment has been lost and retransmit the segment. This is accomplished using the Retransmission Timeout (RTO) algorithm, which dynamically adjusts the timeout period based on the network conditions.

If a sending host receives an RPT segment, it will retransmit the packet, which is a packet containing a retransmission request from the receiving host. This occurs when the receiving host detects that a packet has been lost and requests that the sender retransmit it. TCP retransmission is also triggered by the receipt of a NAC segment, which is a packet containing a notification of no available buffer space in the receiver's buffer.

Finally, none of the above is an option that does not apply to TCP retransmission.Therefore, a sending host will retransmit a TCP segment if it receives an ACK segment.

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Related Questions

Find the equation of the line that passes through the given points. (1, 4.5) and (3, 6)

Answers

Answer:

y=0.75x+3.75

Step-by-step explanation:

The slope is

[tex] \frac{6 - 4.5}{3 - 1} = \frac{3}{4} [/tex]

Substituting into point-slope form,

y - 6 = 0.75(x - 3)

y - 6 = 0.75x - 2.25

y = 0.75x + 3.75

Plss help give brainiest if right!

the speed of the boat going with a current is 20 mph. when the
boat goes against the current, the speed is 16 mph. find the speed of
the boat in still water and the speed of the current.

Answers

Answer:

The speed of the boat in still water is 18 mph.

The speed of the current is 2 mph

Step-by-step explanation:

Let x constitute the charge of the boat in nonetheless water.

Let y constitute the rate of the contemporary.

When the boat is going against the modern-day, the rate is sixteen mph. Assuming it traveled against the modern at the equal time as going upstream, its general speed may be (x - y) mph. It way that

x - y = 16  (equation 1)

Going downstream, the boat averages 20 mph. Assuming it traveled with the current, its standard pace would be (x + y) mph. It way that

x + y = 20  (equation 2)

Adding each equation, it becomes

2x = 36

x = 36/2

x = 18 mph

Substituting x = 18 into equation 1, it will become

18 - y = 16

y = 18 - 16

y = 2 mph

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find the slope of a line parallel to the line through the given points. E(5, 7), F(3, 1) •-3
•-1/3
•1/3

Answers

Answer:

3

Step-by-step explanation:

slope = (y_2 - y_1)/(x_2 - x_1)

slope = (1 - 7)/(3 - 5)

slope = -6/(-2)

slope = 3

Parallel lines have equal slopes.

Answer: 3

The perimeter of a parallelogram is 180 cm. One side exceeds the other by 10 cm.
What are the lengths of adjacent sides of the parallelogram?

Answers

Answer:

One side is 40 cm and the adjacent side is 50 cm

Step-by-step explanation:

We can use a rectangle because a rectangle is a parallelogram.  Draw a rectangle.  Write the width as x and the length as x + 10.  We find the perimeter by adding all 4 side lengths.

Two side lengths are x and two side lengths are x + 10.  If we add all of this together we get 180

x +x +x+10+x+10 = 180

4x + 20 = 180  Combine the like terms.  There are 4 x's and 10+10 is 20

4x = 160  Subtract 20 from both sides

x  = 40  Divide both sides by 4

So, two sides are 40 and two sides are 50, this will add up to 180

Answer:

40 cm & 50 cm

Step-by-step explanation:

one side = X cm (??)

the other side =X+10 cm

Solve

2(x+x+10)=180

x+x+10=90

2x=80

x = 80/2

x=40

therefore

x+10=50cm

Select all the correct systems of equations. Which systems of equations have infinite solutions? 2x + 5y = 31 6x - y = 13 y = 14 - 2x 6x + 3y = 42 2x + y = 14 x = 13-2y Reset 2x + y = 10 -6x = 3y + 7 y = 13-2x 4x - 3y = -19 2x + y = 17 Next -6x = 3y - 51​

Answers

Answer:

The system of equations y=14-2x and 6x+3y=42.

Step-by-step explanation:

Please see attachment to see the answer as a graph.

Hope this helps!

Ed records the temperature of two pots of water. The pots are the same size and material. Pot X has a temperature of 56 degrees Fahrenheit, and pot Y has a temperature of 49 degrees Fahrenheit. What conclusion can Ed make about the pots of water

Answers

Answer:

The water in pot X is hoter than that of pot Y

Answer:

A is the answer

Step-by-step explanation:

Equivalent ratios what’s the answer
3:6=

Answers

Step-by-step explanation:

you multiply both sides by the same factor, so that the main message or information, the ratio, stays the same :

3:6 × 2/2 = 6:12

3:6 × 1/3 / 1/3 = 1:2

3:6 × 4/3 / 4/3 = 4:8

3:6 × 100/100 = 300:600

so, these are all equivalent ratios. and there are infinitely more, as you can see.

explain how the following problem could be solved. then, solve the problem. a full-grown dog is about one-eighth as heavy as a cow. together, they weigh 360 kg.

Answers

The problem could be solved using the linear equation in one variable, x/8 + x = 360, where x kg is the weight of a cow.

The weight of the cow, on solving the equation, is found to be 320 kg.

The weight of the full-grown dog = (1/8)*320 kg = 40 kg.

We assume the weight of the cow to be x kg.

The weight of a full-grown dog is given to be one-eight of a cow, that is, the weight of a full-grown dog = (1/8)*x = x/8 kg.

Thus, the sum of the weights of the full-grown dog and the cow = x/8 + x kg.

But, we are given that together, they weigh 360 kg.

This can be shown as the linear equation in the one variable:

x/8 + x = 360.

Thus, the problem could be solved using the linear equation in one variable, x/8 + x = 360, where x kg is the weight of a cow.

To solve the problem, we solve the equation as follows:

x/8 + x = 360,

or, (9/8)x = 360 {Simplifying},

or, x = 360*8/9 {Cross-Multiplying},

or, = 320.

Thus, the weight of the cow, on solving the equation, is found to be 320 kg.

The weight of the full-grown dog = (1/8)*320 kg = 40 kg.

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successor of -501 is​

Answers

Answer:

-500

Step-by-step explanation:

since 501 has a negative sign,add 1 to to the number,the next number will be -500

-501 +1 = -500

successor in this case means a number that succeeds another

Find the center and radius of the circle with the equation: (x-0^2 + (y+1)^2 = 4

a.
center: (-5, 1)
radius: 4
c.
center: (-5, 1)
radius: 2
b.
center: (5, -1)
radius: 4
d.
center: (5, -1)
radius: 2

Answers

The center and radius of the circle is (b) center: (-5, 1) radius: 2

How to determine the center and the radius?

The circle equation is given as:

(x-5)^2 + (y+1)^2 = 4

The circle equation is represented as:

(x-a)^2 + (y-b)^2 = r^2

Where:

Center = (a,b)

Radius = 4

By comparison, we have:

(a, b) = (-5, 1)

r^2 = 4

This gives

(a, b) = (-5, 1)

r = 2

Hence, the center and radius of the circle is (b) center: (-5, 1) radius: 2

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A teacher gave a test to a class in which 10% of the students are juniors and 90% are seniors. The average score on the test was 84. The juniors all received the same score, and the average score of the seniors was 83. What score did each of the juniors receive on the test

Answers

Each junior  receives 93 score on the test. It is also the average score of the juniors.

Given Information

It is given that 10% of the strength of the class consists of juniors and 90% consists of seniors.

Let us assume the total strength of the class is 100, then,

Number of seniors = 90

Number of juniors = 10

It is also given that the average score of the class = 84

And, average score of the seniors = 83

Another given information is that all the juniors all received the same score, which is their average score. Let it be x.

Average Score of Juniors

Total marks obtained by the seniors = Number of seniors × Average score of seniors

= 90 × 83

= 7470

Total marks obtained by the juniors = Number of juniors × Average score of juniors

= 10x

Average marks on the test = Total marks / Total number of students

⇒ 84 = (7470 + 10x)/100

⇒ 84 × 100 = 7470 + 10x

⇒ 10x + 7470 = 8400

⇒ 10x = 8400-7470

⇒ 10x = 930

⇒ x = 930/10

⇒  x = 93

Thus, each junior scores 93 on the test.

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Derrick had a 0.250 batting average at the end of his last baseball season, which means he got a hit 25% of the times he was up to bat. if derrick had 47 hits last season, how many times did he bat?

Answers

The number of times that Derrick batted last season is 188 times.

How many times did Derrick bat?

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. Percentage is a measure of frequency. The sign used to denote percentage is %.

A percentage of 25% here means that twenty five times out of hundred times, Derrick hit the ball. In order to convert a percentage to a decimal, divide the percentage by 100.

Number of times Derrick bat last season = Number of hits last season / percentage of his batting average

47 / 25%

47 / 0.25 = 188

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Find the digits x and y such that number 90x0y07 is divisble by 2017

Answers

No digit with the format 90x0y07 is divisible by 2017

How do determine the digits x and y?

The given parameters are:

Dividend = 90x0y07

Divisor = 2017

The dividend is a 7-digit number, and the divisor is a 4-digit number

So, the quotient must be 3 to 4 digits.

Comparing the first and last digits of 90x0y07 and 2017;

The first and last digits of the quotient must be 4 and 1, respectively

So, we have:

90x0y07 = 2017 * 4a1

Assume a = 9.

So, we have:

90x0y07 = 2017 * 491

90x0y07 = 990347

The above is 6-digit.

So, we make use of a 4-digit quotient

This gives

90x0y07 = 2017 * 4ab1

Next, we make use of trial by error.

After several attempts, we conclude that no digit with the format 90x0y07 is divisible by 2017

The closest attempt is

90x0y07 = 2017 * 4471

90x0y07 = 9018007

Where:

x = 1, y = 0 and the digit between x and y is 8, not 0

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22. If 1 m,m/19 - 118°, and m/16 - 48°, calculate m/12.
0 0
103"
98
109⁰
110"
18
17
19 20
14
16
13
15
11
10
12
9
63
5
m

Answers

Answer: [tex]110^{\circ}[/tex]

Step-by-step explanation:

[tex]m\angle 20=62^{\circ}[/tex] (linear pair)

[tex]m\angle 11=70^{\circ}[/tex] (angle sum in a triangle)

[tex]m\angle 12=110^{\circ}[/tex] (linear pair)

True or false: the mayans wrote the digits in their numerals in a vertical format

Answers

Answer:

True

Step-by-step explanation:

(03.01 MC)
Simplify
the square root of 4 divided by 3 to the third power , the square root of 4

Answers

Answer:  [tex]\frac{2}{9}[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt{4} }{3^{3} }[/tex]
The square root of 4 can be written as 2
3 to the third power can be written as 9

So, the answer is
[tex]\frac{2}{9}[/tex]

Find the missing side length of the triangle.

Answers

Answer:

c = 10

Explanation:

Use Pythagoras theorem: a² + b² = c²

where 'a' and 'b' are legs and 'c' is the hypotenuse (the longest side)

Here given: a = 8 cm, b = 6 cm, c = ?

Substituting values:

8² + 6² = c²

c² = 64 + 36

c² = 100

c = √100

c = 10

Answer:

10 cm

Step-by-step explanation:

[tex]a^2=b^2+c^2[/tex]

[tex]a^2=6^2+8^2[/tex]

[tex]a^2=100[/tex]

[tex]\sqrt{a^2}=\sqrt{100[/tex]

a=10

Analyze the diagram below and complete the instructions that follow. (7x - 3) (12x -7) Solve for x.

Answers

Answer:

Step-by-step explanation:

(7x-3)(12x-7)

we are solving for x and we are multiplying.

we start with the x's 7x*12x=  84x

-3*-7=21

so now we have

84x+21=0

the 0 is a placer for answering the question

we minus 21 to both sides

84x=-21

now we divide

84/-21= -4

x=-4

Hi Guys!
I need help ASAP

Answers

Answer:

8.

Step-by-step explanation:

P/Q = 3.125 = 3 1/8

- looks like the denominator Q could be 8.

It could not be any of the other choices.

25/8 = 3.125.

Solve 3[-x + (2 x +1)]=x-1

Answers

The result of the evaluation of the equation given in the task content is; x =-2.

What is the solution of the equation?

It follows from the task content that the equation given whose solution is to be determined is;

3[-x + (2 x +1)]=x-1

The equation can be solved as follows;

-3x + 6x +3 = x-1

2x = -4

x = -2

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250-{(135+34)÷(46-33)}-15 simplify​

Answers

Answer:

222

Step-by-step explanation:

Hey there!


250 - {(135 + 34) ÷ (46 - 33)} - 15 

= 250 - 169/(46 - 44) - 15

= 250 - 169/13 - 15

= 250 - 13 - 15

= 237 - 15

= 222


Therefore, your answer should be:

222


Good luck on your assignment & enjoy your day!



~Amphitrite1040:)


23. Which equation translates y = | x | by 8 units to the left?
y = |x-81
y = |x + 81
y = |x|-8
y = |x | +8

Answers

Answer:

y = |x + 8|

Explanation:

Please see the table attached below.

Answer:y=|x+8|

Step-by-step explanation:

From points a and b on level ground the angles of elevation of the top of a building are 25degree and 37 degree respectively. if [ab] =57m, calculate to the nearest metre, the distances of the top of the building from a and b if they are both on the same side of the building

Answers

The distance of the top of the building from a is 163m and that from b is 115m .

Calculating the Perpendicular Distance of the Top From Ground

It is given that the angle of elevations of the building top from a and b are 25° and 37° respectively.

ab = 57m

Let the top of the building be point c and the distance between the building and the point b be x. Then, from the figure, we can deduce the following,

In Δacd, tan 25° = cd/ad

⇒ 0.4663 = cd /(x+57)

⇒ cd = 0.4663(x+57)             ......................... (1)

In Δbcd, tan 37° = cd/x

⇒ 0.7536 = cd/x

⇒ x =cd / 0.7536                   .......................... (2)

Solving for the Distance cd

Substitute the value of in equation (2) to equation (1) to get,

cd = 0.4663 ((cd/0.7536)+57)

cd = 0.4663(cd+42.9552)/0.7536

0.7536cd = 0.4663cd + 20.03

0.7536cd - 0.4663cd = 20.03

0.2906cd = 20.03

cd = 20.03/0.2906

Thus, the distance cd ≈ 68.93m

Finding the Distance cb and Distance ca

In Δacd, sin25° = cd/ca

⇒ 0.4226 = 68.93/ca

ca = 68.93/0.4226

ca = 163.10

∴ The distance ca ≈ 163m

Similarly, in Δbcd, sin37° = cd/cb

⇒ 0.6018 = 68.93/cb

cb = 68.93/0.6018

cb =114.54m

∴ The distance cb ≈ 115m

Therefore, the points a and b are at a distance of 163m and 115m respectively from the top of the building.  

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Hi I don't know how to do this

Answers

Using a system of equations, the weight of 5 apples, 2 oranges are 4 bananas is given as follows:

B. 1147 gm.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Variable x: Weight of an apple.Variable y: Weight of an orange.Variable z: Weight of a banana.

Considering the data given, the equations are:

3x + 5y = 928.4y + 6z = 1088.5x + 3z = 799.

From the first equation:

3x = 928 - 5y.

x = 309.33 - 1.667y.

From the second equation:

6z = 1088 - 4y

z = 181.33 - 0.667y

Replacing in the third equation:

5x + 3z = 799

5(309.33 - 1.667y) + 3(181.33 - 0.667y) = 799

10.336y = 12961.64

y = 1291.64/10.336

y = 125 gm.

The other weights are:

x = 309.33 - 1.667y = 309.33 - 1.667 x 125 = 101 gm.z = 181.33 - 0.667y = 181.33 - 0.667 x 125 = 98gm.

The weight of 5 apples, 2 oranges are 4 bananas is:

5x + 2y + 4z = 5 x 101 + 2 x 125 + 4 x 98 = 1147 gm, option B.

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Solve 5x=125 using the one-to-one property of exponents.

A) X=In(125)
B) x = 1
C) x = 3
OD) x = 5

Answers

Answer:

C)  x = 3

Step-by-step explanation:

Given equation:

[tex]5^x=125[/tex]

Rewrite 125 with base 5:  125 = 5³

[tex]\implies 5^x=5^3[/tex]

[tex]\textsf{Apply the one-to-one property of exponents}: \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]

[tex]\implies x=3[/tex]

Since 125 is 25 times 5, I may rewrite it as 125 is 5 times 5 times 5. Add the exponents one plus one plus one using the same base. Simply put, this is five to the third power. because their bases are each five. Technically, since the university exponent is log, u could take the log, base five, of both sides, making X equal to 3.

Find all solutions to 2w^4 - 5w^2 + 2 = 0
asap please

Answers

Answer:

w = ±[tex]\sqrt{1/2}[/tex] or w= ±[tex]\sqrt{2}[/tex]

Step-by-step explanation:

if we say some variable y = w^2, we can rewrite the equation to:

2y^2 - 5y + 2 = 0

this can be factored into (2y-1)(y-2) = 0

putting w^2 back in the place of y, that's (2w^2 - 1)(w^2 - 2) = 0

The equation is a fourth degree polynomial, so there are four roots, or four values of w that will cause the equation to equal 0.

If 0 is multiplied by anything, the result is 0, so we set 2w^2 - 1 = 0 and solve for w, which is ±√1/2, then set w^2 - 2 = 0 to get w = ±√2 as our roots

the four solutions are ±√1/2 and ±√2

(because the positive counts as one solution and the negative another solution)

Help with these two problems and show work please !!

Answers

Answer:

1) [tex]x_1=-1-2\sqrt{2},\ x_2=-1+2\sqrt{2}[/tex]

2) [tex]x_1=\dfrac{-5 - \sqrt{13}}{6},\ x_2=\dfrac{-5 + \sqrt{13}}{6}[/tex]

Step-by-step explanation:

[tex]{\large \textsf{ Quadratic Formula: }}x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\ \Bigg{\|}\ \textsf{when }ax^2+bx+c=0[/tex]

Given quadratic equations:

1. [tex]x^2+2x-7=0[/tex]

2. [tex]4x^2-3=x^2-5x-4[/tex]

1. x² + 2x - 7 = 0

[tex]\implies a=\textsf{1},b=\textsf{2},c=\textsf{-7}[/tex]

Step 1: Substitute the given values into the formula and simplify.

[tex]\begin{aligned}\implies x&=\dfrac{-(\textsf{2})\pm \sqrt{(\textsf{2})^2-4(\textsf{1})(\textsf{-7})}}{2(\textsf{1})}\\\implies x&=\dfrac{-2\pm \sqrt{4-4(-7)}}{2}\\\implies x&=\dfrac{-2\pm \sqrt{4+28}}{2}\\\implies x&=\dfrac{-2\pm \sqrt{32}}{2}\end{aligned}[/tex]

Step 2: Simplify the radicand (under the square root).

[tex]\begin{aligned}x&=\dfrac{-2\pm \sqrt{16\times2}}{2}\\x&=\dfrac{-2\pm 4\times\sqrt{2}}{2}\\x&=\dfrac{-2\pm 4\sqrt{2}}{2}\end{aligned}[/tex]

Step 3: Separate into two solutions and simplify them.

[tex]\implies x_1&=\dfrac{-2 - 4\sqrt{2}}{2},\ x_2&=\dfrac{-2 + 4\sqrt{2}}{2}[/tex]

[tex]\begin{aligned}\implies x_1&=\dfrac{-2}{2}+\dfrac{- 4\sqrt{2}}{2},\ x_2=\dfrac{-2 + 4\sqrt{2}}{2}\\\implies {x_1&=\boxed{-1-2\sqrt{2}},\ x_2=\boxed{-1+2\sqrt{2}} \end{aligned}[/tex]

----------------------------------------------------------------------------------------------------------------

2. 4x² - 3 = x² - 5x - 4

Step 1: Set the equation to zero (by moving the "x² - 5x - 4" to the left).

4x² - 3 - x² + 5x + 4 = 0 [ Combine like terms. ]

3x² + 5x + 4 = 0

[tex]\implies a=\textsf{3},b=\textsf{5},c=\textsf{1}[/tex]

Step 2: Substitute the given values into the formula and simplify.

[tex]\begin{aligned}\implies x&=\dfrac{-(\textsf{5})\pm \sqrt{(\textsf{5})^2-4(\textsf{3})(\textsf{1})}}{2(\textsf{3})}\\\implies x&=\dfrac{-5\pm \sqrt{25-12}}{6}\\\implies x&=\dfrac{-5\pm \sqrt{13}}{6}\end{aligned}[/tex]

Step 3: Separate into two solutions.

[tex]\implies x_1=\dfrac{-5 - \sqrt{13}}{6},\ x_2=\dfrac{-5 + \sqrt{13}}{6}[/tex]

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Your dad says you can have a new puppy if you build the dog house. Before building, you need to determine the dimensions. Choose the dimensions of the base, the length, and the width of the dog house. Choose dimensions that you think are reasonable for whatever type of puppy you would get. Once you plan the base and walls, you need to decide on the height of the roof (represented by the dotted line in the image below). The roof is a triangle with two sides that are the same length.
Find the height of the roof using the dimensions you chose. You are hoping to put shingles on the roof and need to know what the square footage of the roof will be. Use the dimensions to calculate the area of the roof.

Hint: Remember to find the area of the entire roof.

Answers

Answer is 12 sq feet
Step by step
Roof is 36” x 24” which is 3’ x 2’
So 3 x 2 = 6 multiplied by 2 sides of roof
Total is 12 sq feet
————-
I made the roof peak with a 3” overhang over the entrance
I made the roof overhang the sides with 4”
—————-
So to find the hypotenuse (diagonal of the roof) I used the Pythagorean theorem.
a^2 + b^2 = c ^2
15^2 + 13^2 = c^2
394 = c^2
Take square root of both sides
C= 19.8 rounded to 20
I then added 4” overhang to each side for total diagonal of 24”

The area of Entire roof is 12 feet².

What is Pythagorean theorem?

The well-known Pythagorean Theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its legs (the side opposite the right angle)

Given:

As, the roof peak with a 3 and the roof overhang the sides is 4.

Now, Using Pythagorean theorem.

a² + b² = c ²

15² + 13² = c²

c² = 225+ 169

c = 19.8 (or 20)

So, the length of diagonal is 24.

Roof Dimension 36 x 24 or (

Area of Roof = 3 x 2

                      = 6 unit²

and, area of the entire roof = 2 x6 = 12 ft²

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Graph and label each of the ordered pairs in the coordinate plane. Then state the quadrant
or axis in/on which the point is located.
55. A(2, 4)
56. B(0, -3)
57. C(1, -1)
59. E(-4,1)
61. G(-3,-2)
63. I(0, 2)
58. D(3, 3)
60. F(2,0)
62. H(-2, 3)
64. J(-1,-4)

Answers

The quadrants of the points are

Quadrant 1: Points A and DQuadrant 2: Points E and HQuadrant 3: Points G and JQuadrant 4: Points Cx-axis: Point Fy-axis: Point B and I

How to determine the quadrants?

The points are given as:

A(2, 4)    B(0, -3)   C(1, -1)

E(-4,1)     G(-3,-2)   I(0, 2)

D(3, 3)     F(2,0)    H(-2, 3)

J(-1,-4)

Next, we plot each coordinate on a graph (see attachment)

From the attached graph, we have the following categories

Quadrant 1: Points A and D

Quadrant 2: Points E and H

Quadrant 3: Points G and J

Quadrant 4: Points C

x-axis: Point F

y-axis: Point B and I

Read more about quadrants at

https://brainly.com/question/863849

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Can someone help me with the first question please

Answers

Answer:

  (c)  5y -17x +99 = 0

Step-by-step explanation:

The median of a triangle is the line through a vertex and the midpoint of the opposite side. The median of ΔXYZ from vertex Y will be the line through point Y and the midpoint of XZ.

Midpoint

The midpoint of XZ is the average of the coordinates of X and Z.

  M = (X +Z)/2

  M = ((1, -2) +(8, -7))/2 = (9, -9)/2 = (4.5, -4.5)

Line through two points

The slope of the median can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

The slope of line YM is ...

  m = (-4.5 -4)/(4.5 -7) = -8.5/-2.5 = 17/5

The point-slope form of the equation of a line is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

The line with slope 17/5 through point Y(7, 4) is ...

  y -4 = 17/5(x -7)

Subtracting the right side, and multiplying by 5 gives ...

  5(y -4) -17(x -7) = 0

  5y -17x +99 = 0 . . . . equation of the median through Y

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