Mathematics High School

Find the centroid of the triangle with these vertices: P (-1,7), Q (9,5), and R (4,3).
The coordinates of the centroid are?​

Answers

Answer 1

Answer:

The coordinates of the centroid are:

[tex]O\:=\:\left(4,\:5\right)\:\:[/tex]

The diagram is also attached below.

Step-by-step explanation:

Given the vertices

P (-1, 7)Q (9, 5)R (4, 3)

We know that the intersection of medians brings the centroid of the triangle.

The centroid of a triangle is given by

[tex]O\:=\:\left(\frac{P_x+Q_x+R_x}{3},\:\frac{P_y+Q_y+R_y}{3}\:\right)[/tex]

In this example,

[tex]P_x=-1,\:P_y=7[/tex]

[tex]Qx=9,\:Q_y=5[/tex]

[tex]Rx=4,\:R_y=3[/tex]

substituting in the formula

[tex]O\:=\:\left(\frac{-1+9+4}{3},\:\frac{7+5+3}{3}\:\right)\:\:[/tex]

[tex]O\:=\:\left(\frac{12}{3},\:\frac{15}{3}\:\right)\:\:[/tex]

[tex]O\:=\:\left(4,\:5\right)\:\:[/tex]

Therefore, the coordinates of the centroid are:

[tex]O\:=\:\left(4,\:5\right)\:\:[/tex]

The diagram is also attached below.

Find The Centroid Of The Triangle With These Vertices: P (-1,7), Q (9,5), And R (4,3). The Coordinates
Answer 2

We've been given with the co-ordinates of vertices of the triangle and asked to calculate the co-ordinates of the centroid.

★ Centroid of a triangle :-

[tex]\red{\boxed{ \sf{Centroid \: = \: \dfrac{x_1 \: + \: x_2 \: + \: x_3}{3} } \: , \: \dfrac{y_1 \: + \: y_2 \: + \: y_3}{3} }} \: \pink\bigstar [/tex]

We have :

x₁ = -1x₂ = 9x3 = 4y₁ = 7y₂ = 5y3 = 3

Substituting the values :

★ For x co-ordinate:-

[tex]: \: \implies \: \sf{x\: = \: \dfrac{x_{1} \: + \: x_2 \: + \: x_3}{3} } \\ \\ : \: \implies \: \sf{x\: = \: \dfrac{ - 1 \: + \: 9 \: + \: 4}{3}} \\ \\ : \: \implies \: \sf{x\: = \: \dfrac{ 8 \: + \: 4}{3} } \\ \\ : \: \implies \: \sf{x\: = \: \dfrac{ 12}{3} } \\ \\ : \: \implies \: \sf{x\: = \: \cancel\dfrac{ 12}{3} } \\ \\ : \: \implies \: \sf{x\: = \: 4 }[/tex]

★ For y co-ordinate:-

[tex]: \: \implies \: \sf{y\: = \: \dfrac{y_{1} \: + \: y_2 \: + \: y_3}{3} } \\ \\ : \: \implies \: \sf{y\: = \: \dfrac{ 7 + 5 + 3}{3}} \\ \\ : \: \implies \: \sf{y\: = \: \dfrac{ 10 \: + \: 5}{3} } \\ \\ : \: \implies \: \sf{y\: = \: \dfrac{ 15}{3} } \\ \\ : \: \implies \: \sf{y\: = \: \cancel\dfrac{ 15}{3} } \\ \\ : \: \implies \: \sf{y\: = \: 5 }[/tex]

★ Henceforth,

Co-ordinates are (4 , 5)

Additional Information :

★ Midpoint of two points:-

[tex]\boxed{ \sf{M \: = \: \dfrac{x_1 \: + \: x_2 }{2} \: , \: \dfrac{y_1 \: + \: y_2 }{2}}} \: \pink\bigstar[/tex]

★ Distance Formula :-

[tex]\huge \large \boxed{\sf{{d \: = \: \sqrt{(x _{2} - x _{1}) {}^{2} \: + \: (y _{2} - y _{1}) {}^{2} }}}} \: \red\bigstar[/tex]

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Related Questions

how are the triangles congruent ?

ASA , SSA , AAS , SAS , or Not enough information

Answers

Answer:

AAS

Step-by-step explanation:

Answer:

AAS

Step-by-step explanation:

1. (A) we know angle A is congruent to angle E

2. (A) angle B is congruent to D

3. (S) line BC is congruent to line DC

Rewrite 1/4 with the denominator of 100

Answers

Answer: 25/100= 1/4

Step-by-step explanation:

100/4=25

1*25=25

4*25=100

The fraction is now 25/100

One week, Ethan earned $391.00 at his job when he worked for 23 hours. If he is paid the same hourly wage, how many hours would he have to work the next week to earn $102.00?

Answers

Answer:

6 hrs.

Step-by-step explanation:

So 391.00 can just be converted to 391 because they mean the same thing, so since we have $391 for 23 hrs, we can divde those, which gives us 17, this answer would show that Ethan earns $17 a hour, so if we divide how much he earns by the hour by how much money he could earn by next week ( 102/17), that would give us 6, Therefore, Ethan would need to work 6 hours for $102.00

4. At a discount furniture store, Chris offers the salesperson $600 for a couch and a chair. The store charges 8% sales tax. If the salesperson accepts the offer, what is the cost of the furniture, including tax? Round your answer to the nearest hundredth.
5. Shelly earned 20% more money waitressing this week than last week. Last week, she earned $72. How much money did she earn this week? Round your to the nearest hundredth.
6. A 24 ounce box of Cinnamon Crunchers cereal costs $3.99. At this rate, what is the cost of a 36 ounce box of Cinnamon Crunchers? Round your to the nearest hundredth.

NEED THIS DONE ASAP DUE TOMORROW
worth 10 points​

Answers

Answer:

4. $648

5. $86.40

Step-by-step explanation:

You take the percent (we'll take 4 for example, so 8%) and change it to a decimal: .08. You then multiply the decimal (.08) by your other number (in this case $600) and the resulting number is your answer, but not final. Take whatever the answer was (in this case 48) and add it to the orignal number (600) to get $648.

This is a test my sister made to see how smart I am plz help.

Answers

Answer:

16.) second choice: (5,-6)

17.) third choice: (-10) (-8) (-5) (0) (1)

18.) fourth choice: (.18) (0.4) (1/4) (227)

What is the solutions of the following system of equations.

y = -2x + 2

y = x - 1

Answers

Answer:

x = 1, y = 0

Step-by-step explanation:

Given the 2 equations

y = - 2x + 2 → (1)

y = x - 1 → (2)

Substitute y = x - 1 into (1)

x - 1 = - 2x + 2 ( add 2x to both sides )

3x - 1 = 2 ( add 1 to both sides )

3x = 3 ( divide both sides by 3 )

x = 1

Substitute x = 1 into either of the 2 equations for corresponding value of y

Substituting into (2)

y = 1 - 1 = 0

Solution is (1, 0 )

True or False: The following relation is a function.
{(2,4), (3, 1), (- 3,2), (0,0), (1, 0), (0,4)}
O A. True
B. False

Answers

Answer:

false

Step-by-step explanation:

A dog drank ¼ quart of water from a birdbath. The birdbath now has ⅝ quart of water. How much water was in the birdbath before the dog’s drink?

Answers

Answer:

7/8 of a quart

The answer is 7/8ths

What is the volume of this figure?

Answers

Answer:

The total volume of this 3D Figure is 944.

Step-by-step explanation:

The volume of:

1. The above figure is 400.

2. The bottom figure is 544.

3. Add the total volume of those 2 figures (400+544).

4. You have found the final answer!

Brainliest? Thanks!

Answer:

So the first part of this shape is 400 ft and the secound part of this shape is 544 ft. Hence, since want the whole shape volume your answer would be and always will be 944 ft.

Step-by-step explanation:

since i'm pretty good at math I well tell you how I got this answer in this qustion I seen that this figure is 3-dimensional meaning that we have height,length, and width ( there is two more and were not going to talk about it ) prove we got to time not 2 but 3 times and since this figure has 2 part we would need to brake it into and mutlply both parts (sepertly) to get the answer right so for the first part (or what on the top).

1st part

since the height is 5 ft. that is the first part of our equation,I see that the width must be 10 ft., which well be the second part of our equation, and i see the length is  8 ft so our equation is , 8x10x5 witch mean the first part of the figure is 400 ft

2nd part

since the height is 4 ft. this mean we have the first part of our equation,the width is 8 ft so that the second part of our equation,and I see the length is 17 ft., means this equation is 4x8x17 so this part of the figure is 544 ft.

The whole figure

So with are info from the first and second part of our equation we can now add both parts of the figures  means if we add both of them the answer would be 944 ft.

if you don't other stand  here a tip:In geometry, a three-dimensional shape can be defined as a solid figure or an object or shape that has three dimensions – length, width and height. Unlike two-dimensional shapes, three-dimensional shapes have thickness or depth.

brainliest pls and thank you this is was all hard work

A wall 15 m long, 30 cm wide and 4 m high is made of bricks, each measuring
22 cm x 12.5 cm x 7.5 cm . If 1/12 of the total volume of the wall consists of mortar, how many
12
bricks are there in the wall​

Answers

l = 15m = 1500cm
b= 30cm
h= 4m= 400cm



So, total volume of the wall= l×b×h
= 1500×30×400= 1,80,00,000 cm^3


Now, volume of one brick= 22×12.5×7.5= 2062.5 cm^3


Volume of wall containing only bricks= total volume of the wall - volume of wall containing mortar
= 1,80,00,000 - (1,80,00,000 × 1/12)
= 1,65,00,000 cm^3


So, no. of bricks = volume of wall containing bricks ÷ volume of one brick
= 1,65,00,000 ÷ 2062.5
= 8000 bricks.

Please help its timed​

Answers

Answer:

give us the equation u donut

Answer:

c

Step-by-step explanation:

the conclusion ccxtryufrhhicycddtriv

Translate and solve:
m decreased by 12 is equal to negative 3.

Answers listed:
-9
15
-15
9

Answers

Answer:

The answer is C which is 15

Step-by-step explanation:

M decreased by 12 is equal to negative 6

That means:

12 - M = -3

or, 12 - (-3) = M

or, M = 12 + 3

. °. M = 15 Ans

Answer:

m=15

Step-by-step explanation:

m-12=3

add 12 both sides

m=15

The sum of a number and 16 times it's reciprocal is 10. Find the numbers

Answers

Answer:

The answer is 2 and 8!

Hope this helped :D

Mary Catherine makes 2 gallons of punch for her party. How many quarts of punch did she make?

Answers

Answer:

8

Step-by-step explanation:

1 gallon equals 4 quarts so 4*2=8

A=2.5
B=10
C=5
D=5 square root of 3

Answers

Answer:

B.

Step-by-step explanation:

I AM ON A TIMER!! HURRY PLEASE!!!!


What is the answer to this?



​

Answers

Answer:

(1,6) and (4,6)

Step-by-step explanation:

Answer:

(2,4)

Step-by-step explanation:

It's where the two lines cross, or where that black dot is.

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

[tex]\\ jn j j j[/tex]

Answers

Answer:

glhIblzikdjbgjdzgbobrgbzoerbgoernbs

Step-by-step explanation:

ur welcome ;)

Answer:

njjjj

Step-by-step explanation:

Jim is having a Halloween party for 60 children. He will give each child at least one candy bar. If each bag of candy contains 12
candy bars, which inequality gives the minimum number of bags, b, Jim will need to buy?
Yes

Answers

Answer:

5 bags of candy

Step-by-step explanation:

60/12= 5

Since there are 12 pieces of candy in each bag, 12*5= 60, so each kid can have 1 piece of candy.

Answer:

5<b

Step-by-step explanation:

Select the values that make b≥-3 true

Answers

Answer:

-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10+

Step-by-step explanation:

and anything above 10 would be true

HELP WILL MARK BRAINLIEST

Answers

Answer:

The answer is D: y = -2x + 6

Step-by-step explanation:

the y-intercept is 6, and the slope goes down 2 and right 1. -2/1 is the same as -2.

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

The perimeter of the polygon is 12 in. What is the length of side x?

Answers

Answer:

2in

Step-by-step explanation:

Since we are not given the type of polygon, let the polygon be an hexagon. An hexagon is a 6 sides shape. The perimeter of the shape will be the sum of all the sides of the polygon

Perimeter of the polygon = 6L

Length is the length of the side

Given

Perimeter of the polygon = 12in

Substitute and get L

P = 6L

12 = 6L

L = 12/6

L = 2in

Hence the length of side x of the polygon is 2in

A student is writing a research paper and must include sources from both magazines and books.
The student is required to have at least 15 sources.
• At least 6 sources must be magazines, m.
• No more than 7 sources can be books, b.
Which set of inequalities best represents the constraints on the number of sources for the research paper ?
m2 6
b20
m+bs 15
m>O
m+b 13
m+bs 15
m2 6
0 m + b 2 15
0< ms 6
db27
m+bs 15
No

Answers

B 100% is right answer

At a certain high school, about one in every 12 students have natural red hair. If a teacher has 179 students, how many students would they expect to have red hair?​

Answers

Answer:

look up alaskan pipeline

Step-by-step explanation:

Please explain easily or make sure you have the answer right

Answers

Answer:

D. 5:9

Because it's 5 sixth grade students and 9 seventh grade students so it asked you what is the ratio of sixth grade students to seventh grade students on the team.

Which fraction is not equivalent to 9/12
PLEASE HURRY

Answers

Answer:

1/2

1/2 = 50%

9/12 = 75%

Step-by-step explanation:

What is the percent of change of 25 when decreased to 18?

Answers

Answer:

your answer is that it decreases to 7%

Answer:

28% decrease

Step-by-step explanation:

(18−25)|25|×100

=−725×100

=−0.28×100

=−28%change

=28%decrease

Solve five ninths plus four sixths

sixty six fifty fourths

ten fifteenths

nine tenths

thirty ninths

Answers

Answer:

Your answer will be Sixty Six Fifty Fourths

Step-by-step explanation:

Make it the same denominator so you can add them (18.)

Multiply 5/9 by 2 and multiply 4/6 by 3.

10/18 + 12/18 = 22/18.

Since there is not 22/18 listed, you can use this fraction as a proportion. The only proportion that can be evident is answer A, as when you multiply 22/18 by 3, you get 66/54.

Hope this helps! ;)

Write an equivalent expression to 2x-1/2 - 4x + 4/3

Answers

Answer:

-4x+5/3

Step-by-step explanation:

-2x+5/6

multiply by 2

-4x+5/3

you can also check by plugging in a number for x and see if the answer is the same.

Ann received a $70 gift card for a coffee store. She used it in buying some coffee that cost $8.21 per pound. After buying the coffee, she had $45.37 left on her card. How many pounds of coffee did she buy?

Answers

Answer:

She bought 3 pound of coffee.

Step-by-step explanation:

70 - 45.37 = 24.63

24.63 ÷ 3 = 8.21

Answer:

3 pounds

Step-by-step explanation:

14.
Geographers keep track of how many people live in different areas of the world. They are
especially interested in how the populations of certain area change. The table below shows
the population of different regions in 1985 and in 2005.
Place
Earth
China
India
United States
Population
1985
2005
4.9 x 10
6.4 x 109
1.1 x 10° 1.3 x 10°
7.6 x108 1.1 x 10°
2.4 x108 3.0 x108
9. In 2005, how many times greater than China's population is the population of the world?
10. How many more people inhabited Earth in 2005 than in 1985?
15.

Answers

Answer:

`15

Step-by-step explanation:

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