the coordinatinates of the centroid of a triangle with the given vertices 3,3 5,-1 -2,1​

Answers

Answer 1

Answer:

Therefore, the coordinates of the centroid of a triangle is

[tex]G(x,y)=(2,1)[/tex]

Step-by-step explanation:

Given:

Let,

point A( x₁ , y₁) ≡ ( 3, 3)  

point B( x₂ , y₂) ≡ (5 , -1)  

point C( x₃ , y₃) ≡ (-2 , 1)

To Find:

Centroid, G (x,y) = ? (say)

Solution:

Centroid:

Centroid is a point where all the three medians of the triangle intersect.

It is denoted as G and the coordinates are give by

[tex]G(x,y)=(\dfrac{x_{1}+x_{2}+x_{3}}{3},\dfrac{y_{1}+y_{2}+y_{3}}{3})[/tex]

Substituting the values we get

[tex]G(x,y)=(\dfrac{3+5+-2}{3},\dfrac{3+-1+1}{3})[/tex]

[tex]G(x,y)=(\dfrac{6}{3},\dfrac{3}{3})=(2,1)[/tex]

Therefore, the coordinates of the centroid of a triangle is

[tex]G(x,y)=(2,1)[/tex]


Related Questions

if The price tag on a trumpet says 104 how much did the store pay for it

Answers

Without the markup percentage or discount percentage, it is impossible to calculate the actual cost price the store paid for the trumpet. One needs this additional information to provide a precise answer.

The question "if the price tag on a trumpet says $104, how much did the store pay for it" cannot be answered with the information provided. To calculate how much the store paid for the trumpet, we need additional details such as the markup percentage or the discount percentage. Retail stores typically apply a markup to the cost of the goods they purchase from suppliers to cover their operating expenses and make a profit.

Let's assume the markup percentage is known. For example, if a store generally marks up items by 50%, and the selling price of the trumpet is $104, we can calculate the store's cost using the formula: Cost Price = Selling Price / (1 + Markup Percentage). So the cost would be $104 / (1 + 0.50), which is $69.33.

Without the markup or discount information, it is impossible to determine the exact cost price that the store paid for the trumpet.

HELP PLEASE
The sum of the roots of 5 - 2m - 3m^2 = 0 is:
A) -2/3
B) 1
C) 5/3

Answers

Answer:

A) -2/3

Step-by-step explanation:

We are given the equation;

5 - 2m - 3m² = 0

We are required to get the sum of the roots of the equation;

We will solve the equation to get the two roots,Using factor method;

Rearranging the equation;

3m² + 2m - 5 = 0

product = -15 m²

sum = 2 m

Terms = 5m and -3m

Therefore;

3m² + 5m - 3m - 5 = 0

Factorizing by pairing

m(3m + 5) - 1 (3m + 5) = 0

Thus;

(m - 1) (3m + 5) = 0

This means;

m - 1 = 0 or 3m + 5 =0

Hence; the roots of the equation are;

m = 1 or m = -5/3

Thus, the sum of the roots is;

= 1 + -5/3

= -2/3

Hence, the sum of the roots of the equation is -2/3

What is three tenths of six thousand

Answers

Answer:

1,800

Step-by-step explanation:

Evaluate the expression 1/3 (4+18) 4

Answers

Answer:

29 1/3

Step-by-step explanation:

1/3 (4 + 18) 4

1/3 (22) 4

7 1/3 x 4

29 1/3

Twenty nine and one third is your answer.

Final answer:

The expression 1/3 (4+18) 4 evaluates to approximately 29.333 following the order of operations; first the addition inside the parentheses, then multiplication by 1/3, and lastly by 4.

Explanation:

When evaluating the expression 1/3 (4+18) 4, it's essential to follow the orders of operation, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication, and Division (from left to right), Addition and Subtraction (from left to right)). Let's break down the problem step by step:

First, handle the operations inside the parentheses: 4 + 18 = 22.Multiply by the fraction outside, which is 1/3 of 22: (1/3) * 22 = 22/3.Finally, multiply by the last number, which is 4: (22/3) * 4.

Now, perform the multiplication: 22 * 4 = 88. Since we are multiplying by a division by 3 (22/3), it is the same as dividing 88 by 3, which gives us the final answer: 88 divided by 3 equals 29 with a remainder of 1, or as a decimal, approximately 29.333.

The correct answer to the expression 1/3 (4+18) 4 is therefore approximately 29.333. It is crucial to always follow the order of operations in any math problem to get the correct result.

PLEASE HELP WILL MARK BRAINLIEST What is the solution to 2x2 + 3x - 1 = 0?

Answers

Answer:12

Step-by-step explanation:

Answer:

X=-1

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

what is the side of equilateral triangle is altitude is 10




Answers

Answer:

11.55

Step-by-step explanation:

An equilateral triangle is one which all it sides are equal.

10cm altitude means the height is 10cm.

Using Pythagoras theorem,

x² = 10² + (x/2)²

Assume that the side of the triangle is xcm

x² - x²/4 = 100

3x²/4 = 100

x = √(400/3)

x = 11.55cm

? Help please and thanks

Answers

Answer:

The similarity statement: FGHI ~ BCDE

Similarity ratio: 5:1

Step-by-step explanation:

The similarity statement is quite obvious, as there are only two rectangles shown, and the other one is "BCDE".

The similarity ratio is 5:1 because everything in the 1st (FGHI) rectangle is multiplied 5 times the values in the 2nd (BCDE) rectangle.

!HELP!

Look at the figure below:

*look at image attached*

Make a two-column proof showing statements and reasons to prove that triangle ABD is similar to triangle ACB.

(please show in a two-column proof)

Answers

I hope this help you with what you need

X^2 + Y^2 +4y =3 complete the square on the x and y terms to find the radius and center of a circle

Answers

Answer:

Center = (0, -4)

Radius = [tex]\sqrt{7}[/tex] units

Step-by-step explanation:

We are given;

The equation of a circle;

[tex]x^2+y^2+4y=3[/tex]

We are required to determine the radius and the center of the circle;

To do this we are going to use completing square method;

[tex]x^2+y^2+4y=3[/tex]

Since we don't have the x term then;

[tex]x^2+ox+y^2+4y=3[/tex]

We add the square of half the coefficients of x and y on both sides of the equation;

That is;

[tex]x^2+0x+(0^2)+y^2+4y + (2^2)=3+0+(2^2)[/tex]

We get;

[tex]x^2+0x+(0^2)+y^2+4y + (2^2)=7[/tex]

Taking the squares;

[tex](x+0)^2+(y+4)^2=7[/tex]

But we know when the equation of a circle is written in the form of;

[tex](x-a)^2+(y-b)^2=r^2[/tex], where (a,b) is the center and r is the radius of the circle.

Thus, in this case;

[tex](x+0)^2+(y+4)^2=7[/tex]

Center = (0, -4)

Radius = [tex]\sqrt{7}[/tex] units

Tell me the correct answer to get brainliest.

Answers

Good evening

Answer:

RM ≈ 8.25

Step-by-step explanation:

√((10-2)^2+(6-4)^2)

= √(8^2+2^2)

=√(64+4)

=√(68)

=8.246211251235

Distance RM To the nearest hundredth 8.25

:)

Jenna drove 35 miles in 30 minutes. At this rate, how many miles will she drive in 1 hour?

Answers

Answer:

70 miles

Step-by-step explanation:

30 minn+30 min=1 hour/60 min

30 min=35 miles

add the minutes together then add the miles together witch will give you

1 hour/60 min=70 miles

Answer:

70 miles

1 hour= 60 minutes

[tex]60 \div 30 = 2[/tex]

Take 35 and multiply it by your first equations sum

[tex]35 \times 2 = [/tex]

=70

3/4 times what equals 9/8?

Answers

Answer:

I believe the answer to this question is: 3/2 simplified to 1  1/2.

If a rectangle has an area of 2x^2+7x+3 find the perimeter

Answers

Perimeter of a rectangle = 6x + 8

Solution:

Given area of a rectangle = [tex]2x^2+7x+3[/tex]

Let us first factor the given polynomial.

[tex]2x^2+7x+3=2x^2+x+6x+3[/tex]

                    [tex]=(2x^2+x)+(6x+3)[/tex]

Taking out common terms in the above expression

                    [tex]=x(2x+1)+3(2x+1)[/tex]

Taking out common term [tex]2x+1[/tex] in the above expression

                    [tex]=(2x+1)(x+3)[/tex]

[tex]2x^2+7x+3=(2x+1)(x+3)[/tex]

Area of a rectangle = l × b

Therefore, [tex]l=2x+1[/tex] and [tex]b=x+3[/tex]

Perimeter of a rectangle = 2(l + b)

                                         [tex]=2[(2x+1)+(x+3)][/tex]

                                         [tex]=2(2x+1+x+3)[/tex]

                                         [tex]=2(3x+4)[/tex]

                                         [tex]=6x+8[/tex]

The answer is same if you take l = x + 3 and b = 2x + 1.

Hence, perimeter of a rectangle = 6x + 8.

Ninety-eight percent of the mules who were surveyed said that stubbornness was a good character trait. If 343 mules gave this response, how many were surveyed in total?

Answers

Answer:

350 people

Step-by-step explanation:

you would cross multiply

98/100 times 343/x

98x = 34300

34300/98= 350

So the answer is 350 people

Do you have to simplify 1/8 as a fraction

Answers

Answer:no

Step-by-step explanation:

Because it can not get any smaller

No you can’t simplify it more.

if everything costs $25.30 and there is an 8% meals tax, how much does the meal cost ?

Answers

Answer:

Total cost of the meal is $ 27.32.

Step-by-step explanation:

Given:

Cost of the meal = $25.30

Tax levied on it = 8%

We have to find the total cost.

Total cost of the meal = Summation of cost of the meal and levied tax.

So,

We have to calculate the tax.

⇒ [tex]8\%\ of\ \$25.30[/tex]

⇒ [tex]\frac{8}{100}\times \$25.30[/tex]

⇒ [tex]0.08\times \$25.30[/tex]

⇒ [tex]\$2.024[/tex]

Tax imposed = [tex]\$2.024[/tex]

Now,

Total cost of the meal =Tax + Meal cost

⇒ [tex]\$(2.024+25.30)[/tex]

⇒ [tex]\$27.324[/tex]

Total cost of the meal is $ 27.32.

The variable y is directly proportional to the variable x. If y = 32 when x = 20, what is the value of x when y = 40?

A)
20


B)
20.5


C)
25


D)
30

Answers

Answer:

The Correct option is C ) 25

Therefore the value of x is 25 when y =40.

Step-by-step explanation:

Given:

Variable 'y' is directly proportional to the variable 'x'.

[tex]\therefore y=kx[/tex]     ......Direct Variation

Where,

k = Constant of proportionality

To Find:

value of x = ? when y = 40

Solution:

First we need to find Constant of proportionality

When x = 20 and y = 32

Substituting the values we get

[tex]32=k\times 20\\k=\dfrac{32}{20}=1.6\\\\k=1.6[/tex]

Now when k =1.6 , y = 40 then x will be

[tex]40=1.6\times x\\\\x=\dfrac{40}{1.6}=25\\\\x=25[/tex]

Therefore the value of x is 25 when y =40.

Final answer:

The value of x when y is 40 is C) 25.

Explanation:

The variable y is directly proportional to the variable x.

This means that as x increases or decreases, y does so at a constant rate.

This relationship can be written as y = kx, where k is the constant of proportionality.

To find k, we use the information that y = 32 when x = 20, leading to the equation 32 = k * 20.

Solving this gives us k = 32 / 20 or k = 1.6.

With the constant k known, we can find the value of x when y = 40 by setting up the equation 40 = 1.6x.

Dividing both sides by 1.6 gives us x = 40 / 1.6, which results in x = 25.

Therefore, the correct answer is C) 25.

Convert 2671(in base 9), to base 3 without first converting to base 10.​

Answers

Since 9 is 3², each digit in base nine takes two digits in base 3.

2₉ = 02₃

6₉ = 20₃

7₉ = 21₃

1₉ = 01₃

Putting it together

2671₉ = 2202101₃

Show that x+2​ is a factor of f(x)=x^4+2x^3−27x−54​ . Then factor f(x) completely.
f(x)=

Answers

Answer:

Step-by-step explanation:

Final answer:

The polynomial f(x)=x^4+2x^3−27x−54 has x+2 as a factor. The complete factorization of f(x) after polynomial division and analysis is (x + 2)(x^2 - 3x + 9)(x + 3).

Explanation:

To show that x+2 is a factor of f(x)=x^4+2x^3−27x−54, we need to use the Factor theorem which states that if a polynomial f(x) has a factor of the form x - k, then f(k) = 0.

So, if x + 2 is a factor of the function, then f(-2) should equal 0. Let's apply this to our function:

f(-2) = (-2)^4 + 2(-2)^3 - 27(-2) -54 = 16 -16+54 -54 = 0. So x+2 is indeed a factor.

To factor f(x) completely, we will perform polynomial division of f(x) by the factor (x+2) which will give us g(x) = x^3 - 27. This can be further factored to x^3 - 3^3 which is a difference of cubes. Consequently, the complete factorization of f(x) would be:

f(x) = (x + 2)(x^2 - 3x + 9)(x + 3).

Learn more about Factorization here:

https://brainly.com/question/34290719

#SPJ3

A commercial jet liner hits an air pocket and drops 282 feet. After climbing 143 feet up it drops another 161 feet. What is its overall vertical change?

Answers

Answer:

Therefore the overall vertical change is a drop of 300 feet.

Step-by-step explanation:

i) The overall vertical change is given by = -282 feet + 143 feet - 161 feet = -300 feet.

ii) Therefore the overall vertical change is a drop of 300 feet. A drop is represented as negative and a climb is represented as positive.

Find the value of the polynomial 3xy+7x2−3x2y+3y2x−2x2−2xy+4x2y−2y2x, when x=1 and y=−2

Answers

9514 1404 393

Answer:

  5

Step-by-step explanation:

The evaluation can be easier if terms are collected first.

  3xy+7x^2−3x^2y+3y^2x−2x^2−2xy+4x^2y−2y^2x

  = x^2y(-3+4) +xy^2(3-2) +x^2(7-2) +xy(3-2)

  = x^2y +xy^2 +5x^2 +xy

  = x(xy +y^2 +5x +y)

Filling in the numbers, we have ...

  = (1)(1(-2) +(-2)^2 +5(1) +(-2))

  = -2 +4 +5 -2

  = 5

The value of the polynomial is 5.

Looking at Yari's equation below, what
do you notice about both sides of the
equation?
2(x + 10)-17=5+2x-2
2x + 20-17=3+2x
2x +3=3+2x

A) Only the constants are the same on both sides.

B) Both sides are exactly the same.

C) The variable terms on each side of the equation are different.

D) Only the variable terms are the same on both sides.

Answers

Answer:

B, hope this helps you!

Final answer:

Both the variable and constant terms in Yari's equation are identical on each side after simplification, leading to the conclusion that both sides are exactly the same.

Explanation:

Analysing Yari's equation step-by-step, we can see that after expanding and simplifying both sides of the equation:

2(x + 10) - 17 becomes 2x + 20 - 17, which simplifies to 2x + 3.5 + 2x - 2 simplifies directly to 3 + 2x.

Comparing both sides of the simplified equation 2x + 3 = 3 + 2x, we notice that both the variable terms (2x) and the constant terms (3) are identical on each side.

Therefore, the correct answer is:

B) Both sides are exactly the same.

the sum of 45% of a number and 55% of the same number is 200. what is the number?

Answers


.45x+.55x=200
Combine like terms
1x=200
So x is 100

Or you can do 45%+55%=100%
And 100% of 200 is 200

Lamont works for an electric utility and is installing a 40 foot utility pole as shown. Lamont drills the anchor of a support cable into the ground 15 feet from the base of the pole. What is the minimum length of cable Lamont needs?

Answers

Answer:

Approximately 43 feet of minimum cable is needed.

Step-by-step explanation:

This problem can be solved using Trigonometry and Pythagorean theorem. Pythagorean theorem applies on right-triangles (which are known to have one 90° angle). The theorem states that the square of the Hypotenuse is obtained by the squared sum of the other two sides of the triangle (i.e the two sides forming the 90° angle - with the hypotenuse side being across it as:

[tex]h^2=a^2+b^2[/tex]           Eqn. (1)

where

[tex]h[/tex] is the hypotenuse

[tex]a[/tex] is a side

[tex]b[/tex] is a side

Now in this case, the utility pole must be perpendicular to the ground and the anchor being parallel to the ground, and a 90° angle formed between them. Conclusively the cable length will be represented by the hypotenuse in a right triangle. So here we have [tex]a=40ft[/tex] and [tex]b=15ft[/tex]. Plugging in Eqn.(1) and solving for [tex]h[/tex] we have:

[tex]h^2=40^2+15^2\\h=\sqrt{40^2+15^2} \\h=\sqrt{1600+225}\\ h=\sqrt{1825}\\ h=5\sqrt{73}\\ h=42.72ft[/tex]

So we conclude that the minimum length of cable needed by Lamont is

43 feet (rounded up).

3x2 – 18x + 225 = 6
What’s the answer

Answers

Answer:

12.5

Step-by-step explanation:

1) Original equation: 3(2) - 18x +225 = 6

2) Simplify: 6 - 18x + 225 = 6

3) Move 18x over to the right: 6 + 225 = 6 + 18x

4) Move the 6 on the right over to the left: 225 = 18x

5) Divide both sides by 18 to isolate x: 225/18, 18x/18

6) x = 12.5

How do I work this
-(-3)-[-(-4]-2+7

Answers

Answer:

4

Step-by-step explanation:

-(-3)-[-(-4)]-2+7 = 3 - [4] - 2 + 7 = 3 - 4 - 2 + 7 = (3+7) - (4+2) = 10 - 6 = 4

Sarah sold a total of 178 t shirts and posters at a festival. She sold 46 more tshirts than poster. How many posters did she sell

Answers

Sarah sold 66 posters

Solution:

Let "a" be the number of shirts sold

Let "b" be the number of posters sold

Sarah sold a total of 178 t shirts and posters at a festival

Therefore,

number of shirts sold + number of posters sold = 178

a + b = 178 ----------- eqn 1

She sold 46 more tshirts than poster

Number of shirts sold = 46 + number of posters sold

a = 46 + b --------- eqn 2

Substitute eqn 2 in eqn 1

46 + b + b = 178

2b = 178 - 46

2b = 132

b = 66

Thus she sold 66 posters

Final answer:

Sarah sold 66 posters at the festival.

Explanation:

Let's represent the number of posters Sarah sold as P. Since she sold 46 more t-shirts than posters, we can represent the number of t-shirts as P + 46. The total number of t-shirts and posters sold is 178, so we can write the equation: P + (P + 46) = 178.

Combining like terms, we get: 2P + 46 = 178. Subtracting 46 from both sides, we have: 2P = 132. Dividing both sides by 2, we find: P = 66.

Therefore, Sarah sold 66 posters at the festival.

What can 8/6 be simplified to

Answers

Answer: 4/3

Explanation: To write the fraction 8/6 in lowest terms, we divide the numerator and the denominator by the greatest common factor of 8 and 6.

Since the factor of 8 are 1, 2, 4, and 8 and the factors of 6 are 1, 2, 3, and 6, the greatest common factor of 8 and 6 is 3 so we divide the numerator and the denominator of 8/6 by 2 and we get 4/3.

So 8/6 can be simplified to 4/3.

4/3 can also be changed to the mixed number 1 and 1/3.

Find altitude of a triangle whose area is 22.86m square and base is 2.4m

Answers

Answer:

H = 21.7

Step-by-step explanation:

A = 1/2 x b x h

26 = 1/2 x2.4xh

26= 1.2h

divide both sides by 1.2

26/1.2 = 1.2/1.2 h

h = 21.7

9a+4b+4(-4a+2b)-7
What the answer

Answers

My work to your question.
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