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Which method and additional information would prove ΔONP and ΔMNL similar by the AA similarity postulate?


A. Use a rigid transformation to prove ∠NOP ≅ ∠NML.

B. Use a rigid transformation to prove ∠NOP ≅ ∠ONP.

C. Use rigid and nonrigid transformations to prove segment LN over segment ON = segment PN over segment MN.

D. Use rigid and nonrigid transformations to prove segment LM over segment ON = segment PN over segment MN.

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

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.

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 :-

We have :

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,

Additional Information :

★ Midpoint of two points:-

★ Distance Formula :-

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Answer:

B=4

Step-by-step explanation:

The Y intercept is where the line meets with the middle of the graph

Answer:

I think its B 216

Step-by-step explanation:

Because you multiply 12×9×2 and get 216 (I dont know if im right)

Answer:

Um... ithink it would be 3 but please tell me and correct me if im wrong

Step-by-step explanation:

Answer:

may be 5 times is answer but I am not sure I have done 5 times I got like this

Answer:

6

Step-by-step explanation:

Answer:

The Correct Answer is 2

Step-by-step explanation:

Trust me for I have the skills of a scientist

Answer:

no correlation

Step-by-step explanation:

the dots are all scattered randomly

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A number is divisible by 9 if the sum of its digits is divisible by 9.

Look :

[tex] \frac{1 + 8 + 6 + 4 + 2 + 6}{9} = \frac{27}{9} = 3 \\ [/tex]

Thus 186,426 is divisible by 9 .

_________________________________

Also a number is divisible by 3 if the sum of its digits is divisible by 3.

Look :

[tex] \frac{1 + 8 + 6 + 4 + 2 + 6}{3} = \frac{27}{3} = 9 \\ [/tex]

Thus 186,426 is divisible by 3 .

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Answer: 140?

I am not really sure but I think 140......

Answer:

4

Step-by-step explanation:

2^2 - (2)(-2) - (-2)^2

=4+4-4

=4

2² - (2 × -2) - (-2²)

= 4 - (-4) - 4

= 4 + 4 - 4

= 8 - 4

= 4

Answer:

Let's solve your inequality step-by-step.

−15>−16+y

Step 1: Simplify both sides of the inequality.

−15>y−16

Step 2: Flip the equation.

y−16<−15

Step 3: Add 16 to both sides.

y−16+16<−15+16

y<1

Answer:

y<1

Answer:

−3, 8, 32, 7, -5

Step-by-step explanation:

Answer:

The number of people living in both countries is 1.704 x 10⁹

Step-by-step explanation:

Given;

Population of people in China, = 1.381 x 10⁹

Population of people in united states, = 3.23 x 10⁸

The total number of people living in both countries is given as;

Total population = 1.381 x 10⁹ + 3.23 x 10⁸

Total population = 1.381 x 10⁹ +  0.323 x 10⁹

Total population = (1.381 + 0.323) x 10⁹

Total population = 1.704 x 10⁹

Therefore, the number of people living in both countries is 1.704 x 10⁹

Answer:

Step-by-step explanation:

Proportion can be defined as the effect of changing one quantity on the other.

Given that

‘c’ is directly proportional to‘d’

It can mathematically be written as:

c∝d

A constant is introduced in the equation when the proportionality symbol will be removed. The constant is called constant of proportionality

[tex]c =kd[/tex]

Given that

c = 24 when d = 4

Putting the values

[tex]24 = k(4)\\k = \frac{24}{4}\\k = 6[/tex]

Putting the value of k

[tex]c = 6d[/tex]

Putting d = 8

[tex]c = 6(8) = 48[/tex]

Putting c = 54

[tex]54 = 6d\\d = \frac{54}{6}\\d = 9[/tex]

Hence,

Answer:

-27 °C

Step-by-step explanation:

-15 -12 = -27

we will eat chocolate of rupee 1 and divide other amount ofoney equally

Answer:

140 beads.

Step-by-step explanation:

Hope this helps. :)

Answer:

: an equation obtained by equating to zero a sum of a finite number of terms each one of which is a product of positive integral powers (including the zero power) of the variables.

Step-by-step explanation:

includeing zero

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Answer:

An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign.

Step-by-step explanation:

Answer:

They should pay $12 each

Answer:

about 12 dollars probably more with tax maybe around 12.03

Answer:

Commutative

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Resposta:

Primer rectangle:

Amplada = 11

Longitud = 14

Segon rectangle:

Amplada = 12

Longitud = 15

Tercer rectangle:

Amplada = 13

Longitud = 16

Explicació pas a pas:

Donat que:

Primer rectangle:

Amplada = x

Longitud = x + 3

2n rectangle:

Augment de la dimensió d'1 cm respecte al primer rectangle;

Amplada = x + 1

Longitud = x + 4

3r rectangle:

Augment de la dimensió de 2 cm respecte al primer rectangle;

Amplada = x + 2

Longitud = x + 5

Suma dels tres perímetres del rectangle:

Perímetre d'un rectangle: 2 (l + O)

Primer rectangle:

2 (x + x + 3) = 2 (2x + 3) = 4x + 6

2n:

2 (x + 1 + x + 4) = 2 (2x + 5) = 4x + 10

3r:

2 (x + 2 + x + 5) = 2 (2x + 7) = 4x + 14

Suma de perímetres = 162

(4x + 6 + 4x + 10 + 4x + 14) = 162

12x + 30 = 162

12x = 162 - 30

12x = 130

x = 11

Per tant,

Primer rectangle:

Amplada = 11

Longitud = 11 + 3 = 14

2n rectangle:

Amplada = 11 + 1 = 12

Longitud = 11 + 4 = 15

3r rectangle:

Amplada = 11 + 2 = 13

Longitud = 11 + 5 = 16

Answer:

The answer to this is 7.

a+2

5+2

7

Answer:

600

Step-by-step explanation:

Last years enrollment was 100% of the number.

This year, the enrollment went up by 10%, so now, it's 110% of last years number.

Let last year's enrollment be x.

110% of x is 660

1.1x = 660

x = 660/1.1

x = 600

Answer: 600

Answer:

600

Step-by-step explanation:

Answer:

70 miles per hour

Step-by-step explanation:

Answer:

A car can travel up to 240 km in 4 hours.

Step-by-step explanation:

A car travels 60 MPH meaning 60(miles) times 4(hours) is 240.

Answer:

3/4

Step-by-step explanation:

Answer: 105 Cars

Step-by-step explanation: To get an increase of 25% you need to multiply 84 by .25 then add the product of that to 84 to get 105

The number of cars dealership need to sell to reach their goal is, 105 cars

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

A car dealership sold 84 cars in April,

The dealership wants to increase the number of cars sold by 25% in May

The number of cars dealership need to sell to reach their goal = ?

This represents a 25% increase, which is the same as adding one quarter to the original number of cars sold.

The car dealership wants to increase the number of cars sold by 25% in May, which means that they want to sell,

⇒ 84 x 1.25 = 105 cars

So, the dealership will need to sell 105 cars in May in order to reach their goal of increasing the number of cars sold by 25%.

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Answer:

The time when walking is 5/v hours

The walking speed is 4 26/31 km/hr

Step-by-step explanation:

Mathematically;

time = distance/speed

So the time taken when walking will be;

5/v

The time taken when cycling will be:

15/2v

The term 2h 35 minutes is same as 2 35/60

= 2 7/12

If we add the whole times together, we get 2 7/12

Thus;

5/v + 15/2v = 2 7/12

5/v + 15/2v = 31/12

(10 + 15)/2v = 31/12

25/2v = 31/12

12 * 25 = 2v * 31

31v = 6 * 25

v = 150/31

= 4 26/31