unit test: line and triangle relationships - part 1

question 8

What are the coordinates of the centroid of a triangle with vertices P(−4, −1), Q(2, 2), and R(2, −3)?




Enter your answers in the boxes.


( , )

Answers

Answer 1

Answer:

[tex]G(0, -\dfrac{2}{3})[/tex]

Step-by-step explanation:

Given that:

The coordinates of the vertices of a triangle [tex]\triangle PQR[/tex] are given as:

[tex]P(-4, -1)[/tex], [tex]Q(2, 2)[/tex], and [tex]R(2, - 3)[/tex].

To find:

The coordinates of the centroid of the triangle.

Solution:

The coordinates of the centroid of a triangle is given as:

[tex]G(\dfrac{x_1+x_2+x_3}{3}, \dfrac{y_1+y_2+y_3}{3})[/tex]

Where [tex](x_1,y_1), (x_2,y_2)\ and\ (x_3,y_3)[/tex] are the coordinates of the vertices of the triangle.

As per the given values, we have:

[tex]x_1 = -4\\y_1 = -1\\x_2 = 2\\y_2 = 2\\x_3 = 2\\y_3 = -3[/tex]

Putting the values,we can find the coordinates of centroid as:

[tex]G(\dfrac{-4+2+2}{3}, \dfrac{-1+2-3}{3})\\\Rightarrow G(0, -\dfrac{2}{3})[/tex]

Therefore, the coordinates of the centroid is:

[tex]G(0, -\dfrac{2}{3})[/tex]


Related Questions

Question 9
10 pts
Identify whether the equation has no solution, infinite solution or one solution
2x +3 = 2x + 3

Answers

infinite solutions. 2x + 3 = 2x + 3 can be solved out to get 0 = 0, which is true no matter what the x value is. that means that there are infinite solutions.

I SERIOUSLY NEED THIS NOW- 100 POINTS

(The unanswered question :D)

Answers

Answer:

its b i did this before

Step-by-step explanation:

Answer:

The answer will be C.

Step-by-step explanation:

PLEASE PLEASE PLEASE HELP ASAP
solve using the elimination process and SHOW ALL STEPS
5x+4y=2
3x+3y=-3

IM LITERALLY BEGGING FORN HELP RN

Answers

Answer:

x = 6, y = -7 or (6, -7)

Step-by-step explanation:

Given system of equations

5x+4y=2 3x+3y=-3

Solving as follows:

Simplify the second equation by dividing all terms by 3

3x+3y=-3    divide by 3⇒ x + y = -1

Now, considering the coefficient of x of 5 in the first equation, we will multiply the simplified second equation by 5 and subtract from the first equation:

x + y = -1 multiply by 5⇒5x + 5y = -5

Subtract it from 5x + 4y = 2

5x + 4y - 5x - 5y = 2 - (-5)-y = 7y = -7

Finding x using simplified second equation:

x + (-7) = -1x = - 1 + 7x = 6

Answer is (6, -7)

What is 12p+3q−5−5q−8p written in simplest form?

Answers

The answer is C, 4p-2q-5

Answer:

C.

Step-by-step explanation:

Samia y su hija fueron a una obra de teatro musical, ella pago $90 por su boleto y $45 por el de su hija. Ese dia el cajerovendio 100 boletos y cuenta con $8190, pero necesita saber cuantos adultos y menores de edad entraron al evento?

Answers

Answer:

Al evento entraron 82 adultos y 18 menores de edad.

Step-by-step explanation:

De acuerdo a la información proporcionada, puedes plantear las siguientes ecuaciones:

x+y=100 (1)

90x+45y=8190 (2), donde:

x es el número de adultos

y es el número de menores de edad

Puedes despejar x en (1):

x=100-y (3)

Después, puedes reemplazar (3) en (2):

90(100-y)+45y=8190

9000-90y+45y=8190

9000-8190=90y-45y

810=45y

y=810/45

y=18

Ahora, puedes reemplazar el valor de y en (3) para encontrar x:

x=100-y

x=100-18

x=82

De acuerdo a esto, la respuesta es que al evento entraron 82 adultos y 18 menores de edad.

Write the equation for the Graph in Vertex form ( `y=a\left(x-h\right)^{2}`+ k) below by first determining the values of h and k.
List all of the equations, numbers, and units that they gave us? Helppppppp answer this.

Answers

Answer:

I this all for the question

y = 4 + 6x
Siope-interce
What linear equation form is this equation written in?

Answers

Answer:

We can write this equation in slope-intercept form

y

=

m

x

+

b

where

m

is the slope and

b

is the

y

-intercept.

We know

m

=

4

and

b

=

6

, so we can insert these into the equation to get

y

=

4

x

+

6

Hope this helps!

hey there, random person? Mind to answer?

Answers

your answer is 512 feet squared.

Which fraction has a value that’s equal to7/8? A.49/64
B.56/8. D.15/8
C.22/24

Answers

Answer:

a 49/64

Step-by-step explanation:

7/8 multiply 7 ×7 = 49 then 8×8 is 64 so yeah a

Answee a 49/64 is the best answer

Why am I using negative numbers in 6th grade science?

Answers

Answer:

Try stopping at nothing to avoid them

2(4.50 - x) + 8y
This might be easy for u guys but a little for me :/

Answers

Answer:

-2x+8y+9

Step-by-step explanation:

Answer:

9-2x+8y

Step-by-step explanation:

Distribute 2*4.50=9

2(x)=2x

Now you have: 9-2x+8y

Hope this helps!

Mrs. Rodrigues was seling two kinds of raffle tickets for $1.50 and $3.50. The number of 1.50 tickets sold was 5 more than three times the number of $3.50 tickets sold. She earned of $1,607.50. How many $1.50 tickets did he male?

Answers

Step-by-step explanation:

पति ऑफिस से घर आया... और खाना खाने बैठा

खाते-खाते उसने अपनी पत्नी से कहा कि

"खाना ठीक नहीं है, कोई टेस्ट नहीं आ रहा है।"

पत्नी चुपचाप उठी, और उसने कॉरपोरेशन मेंं कॉल किया और एम्बुलेंस को बुला ली

और कहा..

"इन्हे टेस्ट नहीं आ रहा है.."

एम्बुलेंस पति को ले गयी और उसे क्वॉरंटाइन कर दिया

अस्पताल में पत्नी ने पति को फोन किया और पूछा: अब आया स्वाद??

यहाँ तक की कहानी सबने सुनी होगी। अब देखिये कहानी में नया मोड़:

⬇️

.

.

.

.

.

.

.

.

उधर पति को पूछा गया कि

"आपके संपर्क में कौन-कौन आया था ?"

पति ने बड़ी ही शांति से कहा..

- मेरी पत्नी

- मेरा ससुर

- मेरी सास

- मेरा साला

- मेरी साली

बस अब ये सब भी अस्पताल के बिस्तर पर बैठे-बैठे पति को घूर रहे हैं!

Moral of the story is

बेजुबान को ज्यादा सताना भी ठीक

Answer:

605 tickets were sold.

Step-by-step explanation:

I took the test.

Find the slope of the line passing through the points (-8, 2) and (9, 2)

Find the slope of the line passing through the points (-8, 5) and (-8, -4)

Answers

Answer:

1/17  and  No slope

Step-by-step explanation:

2-2=1

9--8=17

-4-5=-9

-8--8=0

Answer:

1. 0/-17 no slope

21/0 indefinite

Step-by-step explanation:

2-2

-8-9

5-4

-8--8

Which of the following congruence statements must be true based on the diagram shown?

Multiple Choice: (Select Two Correct Answers)
A. ∠V≅∠U
B. ∠T≅∠W
C. ∠S≅∠X
D. TU¯¯¯¯¯¯¯≅XW¯¯¯¯¯¯¯¯¯¯
E. ST¯¯¯¯¯¯¯≅VX¯¯¯¯¯¯¯¯

Answers

I’m pretty sure D and E

Which expression represents the phrase, "five more than the quotient of a number and 16?"
A 16-n + 5
C. 5+ n - 16
B. 16n + 5
D. n/16 +5

Answers

B i thinkkkkk..........

A realtor is paid $24 per hour and $20 for each sale she makes. She wants to earn $2,000 in a 10-hour work period. Write an equation that represents the number of sales, x, the saleswoman must make in a 10-hour period to earn $2,000. How many sales must she earn to reach her goal?

Answers

Answer:

2000 = 24x + 20y (x represents hours and y represents money per sale)

she must make 88 sales

Step-by-step explanation:

2000 = 24(10) + 20y

2000 = 240 + 20y

-240  = -240

1760 = 20y

/20   = /20

88 = y

simplify 10 divided by 7 divided by 8

Answers

Answer:

10 ÷ 7 ÷ 8

Step-by-step explanation:

10 ÷ 7 = 1.428571428571429

1.428571428571429 divided by 8

0.1785714285714286

Hope this helps :)

what's the correct answer?​

Answers

Answer: I believe the answer to your question is Yes by SAS. I believe my coucelations are right but if not I'm sorry. I tryed:)

Step-by-step explanation:

Answer:

Yes, by SSS

Step-by-step explanation:

This theorem states that if two triangles have proportional sides, they are similar.

Since they share 2/3 sides, and the diagram tells us that the bases are parallel, we can assume all three sides are proportional to one another. Thus, the two triangles are similar.

x=2y-4
7x+5y=-66
what is the x- value​

Answers

Answer:

x = -8

Step-by-step explanation:

x = 2y - 4 --- Equation 1

7x + 5y = -66 --- Equation 2

I will be using the substitution method to solve this.

Substitute x = 2y - 4 into Equation 2:

7x + 5y = -66

7(2y - 4) + 5y = -66

Evaluate.

14y - 28 + 5y = -66

Evaluate like terms.

19y - 28 = -66

Isolate 19y.

19y = -66 + 28

     = -38

Find y.

y = -38 ÷ 19

y = -2 --- Equation 3

Substitute y = -2 into Equation 1:

x = 2y - 4

x = 2(-2) - 4

Evaluate.

x = -4 - 4

x = -8

(Help needed I don’t understand due soon) Larry is evaluating the best way to invest $5000 how much more money to the nearest dollar will he earn on his investment and 1% compound interest for 10 years then at 1% simple interest for 10 years?
A) $23
B) $500
C) $523
D) $51

Answers

Answer:

23

Step-by-step explanation:

I=5000x1

There are 62 girls in the seventh grade and 58 boys in the eighth grade. Each grade
has 120 students. Which statement correctly compares the
ratios of boys to girls in each grade?

Answers

Answer:

1:1

Step-by-step explanation:

since there are120 girls and120 boys

120:120

1:1

29:34
Boys:Girls
GCF of each number gives u this

Esther is doing some onlne
shopping. She has to spend a
momum of $125 to get free
shipping. If she adds a $30
water bottle
to her cert,
how many $5 stickers will she
have to order to meet the
free shoong
recurement?

Answers

Answer:

Needs to order 19 stickers

Step-by-step explanation:

5x+30=125

5x=95

x=19

x=stickers

Your answer for that question is 19

Here are two graphs representing function f and g.

Select all statements that are true about functions f and g.

Answers

Answer:

The correct answer is B, C, D

Step-by-step explanation:

Thanks to Onbadbshedo, who was in the comments giving the correct answer. Props to you.

The statements about functions f and g that are true are f (-3) > g (4)

What is meant by functions?A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain. In mathematics, a function is a mathematical expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.A function is a relationship between a set of inputs and one output. Every function has its own domain, codomain, and range.When working on a project, it is common for some tasks to need to be repeated with different input. To ensure that the analyses are performed consistently, it is critical to wrap the code in a named function that is called each time it is required.

Therefore,

The two graphs representing functions f and g are shown below. Option D) f (-3) > g (4)

To learn more about functions, refer to:

https://brainly.com/question/28193969

#SPJ2

Line n is defined by the equation y = 3x - 5. If line n undergoes a dilation with a scale factor of 3 and center P, which equation will define the image of the line?


A. y = 3x + 13

B. y = 3x - 23

C. y = 9x - 5

D. y = 9x - 15

Answers

i think the answer is B pls don’t get mad if it wrong . and i tried

The required equation for the dilated image of the line is y = 9x - 15. Option D is correct.

What is the scale factor?

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
Line n is defined by the equation y = 3x - 5.
Line n undergoes a dilation with a scale factor of 3 and center P,
Since the dilation of line n with factor 3, increase the slope of a line by 3 times and change the intercept simultaneously.

y = 3(3x - 5)

y = 9x - 15

Thus, the required equation of dilated image of the line is y = 9x - 15.

Learn more about Scale factors here:

https://brainly.com/question/22312172

#SPJ6

3. You have spent a total of $440 total on your gym membership so far. If the gym charges a
monthly membership fee of $30 and a sign-up fee of $50, how many months have you gone to
the gym for?

Answers

Answer:

13 months

Step-by-step explanation:

Total spent: $440

Sign-up fee: $50 (a one-time fee)

Membership fee: $30/month

[tex](440 - 50) \div 30 = 13 \: months[/tex]

The first two terms in an arithmetic progression are -2 and 5. The last term in the progression is the only number in the progression that is greater than 200. Find the sum of all the terms in the progression.

Answers

Given:

The first two terms in an arithmetic progression are -2 and 5.

The last term in the progression is the only number in the progression that is greater than 200.

To find:

The sum of all the terms in the progression.

Solution:

We have,

First term : [tex]a=-2[/tex]

Common difference : [tex]d = 5 - (-2)[/tex]

                                      [tex]= 5 + 2[/tex]

                                      [tex]= 7[/tex]

nth term of an A.P. is

[tex]a_n=a+(n-1)d[/tex]

where, a is first term and d is common difference.

[tex]a_n=-2+(n-1)(7)[/tex]

According to the equation, [tex]a_n>200[/tex].

[tex]-2+(n-1)(7)>200[/tex]

[tex](n-1)(7)>200+2[/tex]

[tex](n-1)(7)>202[/tex]

Divide both sides by 7.

[tex](n-1)>28.857[/tex]

Add 1 on both sides.

[tex]n>29.857[/tex]

So, least possible integer value is 30. It means, A.P. has 30 term.

Sum of n terms of an A.P. is

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

Substituting n=30, a=-2 and d=7, we get

[tex]S_{30}=\dfrac{30}{2}[2(-2)+(30-1)7][/tex]

[tex]S_{30}=15[-4+(29)7][/tex]

[tex]S_{30}=15[-4+203][/tex]

[tex]S_{30}=15(199)[/tex]

[tex]S_{30}=2985[/tex]

Therefore, the sum of all the terms in the progression is 2985.

Umm I don’t remember this please help. I will give correct answer brainliest

Answers

Answer:

Option D

Step-by-step explanation:

[tex]F=\frac{9}{5}C+32\\\\F-32=\frac{9}{5}C \\\\5(F-32)=9C\\\\\frac{5(F-32)}{9}=C \\\\C=\frac{5}{9}( {F-32})[/tex]

For F=77°F

[tex]C=\frac{5}{9}(F-32) \\\\C=\frac{5}{9}(77-32)\\\\C=\frac{5}{9}(45)\\\\C=\frac{225}{9} \\\\C=25[/tex]

Solve: 6/9-(8/72)??????????????

Answers

Answer:

0.55555556

Step-by-step explanation: i searched it up!

Answer

7/9

Step-by-step explanation:

Renee spent $15.50 on Amazon today and Alex spent $9.69. How much more did Renee spend than Adam

Answers

Answer:

$5.81

Step-by-step explanation:

15.50-9.69=5.81

Answer:

$5.81

Step-by-step explanation:

Subtract. Hope this helped you!! Do you have a calculator

There are 6 red marbles, 5 green marbles, and 4 yellow marbles in a bag. If Joe picks 2 marbles one after the other without replacement, then what is the probability that both are red?

Answers

Answer:

2 out of 6

Step-by-step explanation:

if this is wrong try 2 out of 15

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