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The coordinates of a centroid of a triangle with vertices  [tex](x_1,y_1),(x_2,y_2),(x_3,y_3)[/tex]  are [tex](\frac{x_1+x_2+x_3}{3}, \frac{{y_1+y_2+y_3} }{3})[/tex].

Centroid of a triangle

For a triangle, the centroid is obtained by the intersection of its medians. The line segments of medians join vertex to the midpoint of the opposite side. All three medians meet at a single point (concurrent). The point of concurrency is known as the centroid of a triangle.

Let KLM be a triangle with the vertex coordinates [tex](x_1,y_1),(x_2,y_2),(x_3,y_3)[/tex] as K,L and M respectively.

Let the midpoints of the side LM, KL and KM are D, E, and F, respectively. The centroid of a triangle is represented as “G.”

As D is the midpoint of the side LM, we can write,

D = ((x2+x3)/2, (y2+y3)/2)

Now, we know that, G intersects AD in the ratio 2:1 , we get

Hence, using section formula we can write,

The x-coordinates of G will be:-

x = (2(x2+x3)/2 + 1.x1 )/ (2+1) =  (x2+x3+x1)/3  = (x1+x2+x3)/3

The y-coordinates of G will be :-

y =(2(y2+y3)/2 + 1.y1 )/ (2+1) =  (y2+y3+y1)/3 =  (y1+y2+y3)/3

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Answer: 7 units

Step-by-step explanation:

AE and BE are congruent lines or we can say lines with same length.

What are congruent lines?

Congruent line segments are geometrical figures in one dimension with identical dimensions. In terms of congruent lines, the word "congruent" refers to the equality of the two line segments. When two lines are the same length, they are said to be congruent.

As given in the question,

AC = BD, and

EC = ED

We can see in the figure that:

AC - EC = AE ___(1)

BD - ED = BE ___(2)

Substituting the value of AC and EC in equation (1):

AE = BD - ED ___(3)

From equations (2) and (3), we can conclude that,

AE = BC

Therefore, AE and BE are congruent lines.

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9. Option b. The two lines are perpendicular to each other

  Given:

   6x+10y = 20

   5x- 3y = 21

Consider the first line,

10 y = -6x+ 20

y = -3/5 x + 2

This is of the form y = mx+ b

where, slope =m = - 3/5

Consider the second line,

5x- 3y = 21

3y = 5x- 21

y = 5/3 x - 21

This is of the form y = mx+ b

where, slope= m = 5/3

Since the slopes of the two lines are negative reciprocals ,they are perpendicular.

10. Option a. The equation of the line  passing through (2, -9) with a slope -5 is y = - 5x + 1

Given:

slope = m= -5

point = (2,-9)

We know that ,the slope -intercept form is given by ,

y = mx+ b ---(1)

Substituting the given values in (1)

-9 = -5(2)+b

10- 9 = b

b = 1

Substituting m and b in (1)

y = -5x+1

Thus, the slope-intercept form equation of the line is y = -5x + 1

11. The  equation of the line perpendicular to y= -2x+8 and passing through the point (4,-7) is y = 1/2x- 9

Given:

line = y = -2x+8

point = (x, y)= (4, -7)

The given equation is of the form,

y = mx+ b  ---- (1)

m = -2

The line perpendicular to this line will have a negative reciprocal slope,

m = 1/2  

The new line is of the form,

y = 1/2 x+ b   ----(2)

Substituting the given point (4, -7) in (2)

- 7= 2 + b

b = - 9

Substituting b in (2)

y = 1/2x- 9 is the perpendicular line equation

12.  The  equation of the line parallel to 3x- 2y = 14 and passing through the point (-6,-11) is y = 3/2 x -2

Given:

line = 3x- 2y = 14

point = (x, y)= (-6,-11)

The slope - intercept form of the given line is ,

2y = 3x- 14

y = 3/2x - 7  

slope = m = 3/2

The line parallel to this line will have the same slope,

m = 3/2  

The new line is of the form,

y = 3/2 x+ b   ----(1)

Substituting the given point (-6, -11) in (1)

- 11= -9 + b

b = - 2

Substituting b in (1)

y = 3/2 x -2 is the parallel line equation.

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The depreciation equation is given by

where x represents the number of years. Here, the initial value of the car corresponds to x=0, then we have

After one year, the car value corresponds to x=1, that is,

Now, let's find the depreciation percentage by means of a rule of three:

so we have

So the difference between 100% and 86% is 14% This means Nichole's car depreciate 14% each year

It's (1, 0) - first option

Hope this helps!

Answer:

45 levels

Step-by-step explanation:

60% of 75 is 45 i think

Answer:

B and C

Step-by-step explanation:

I think that you mean -1 -1.  That would equal -2

-2 is an integer and a rational number.

An integer are the whole numbers 0,1,2,3 and so on and their opposites, -1, -2, -3 ,-4 and so on

Rational number is when you can write a number as an integer over and integer.  You can write -2 as  -2/1

Answer: a,b,c

I did it in the test

Answer: 5/3

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.

Answer:

Subtract 66.5 from Devon's total to find how much he has left

well, her husband makes "x" in salary, hmmm hers is 16% more than that, so

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{16\% of x}}{\left( \cfrac{16}{100} \right)x}\implies 0.16x[/tex]

so she really makes x + 0.16x = 1.16x, and we know their total is 72,360, so

[tex]\stackrel{husband}{x} + \stackrel{hers}{1.16x} = 72360\implies 2.16x=72360\implies x=\cfrac{72360}{2.16}\implies \boxed{x = 33500}[/tex]

Answers to your questions with explanations are below. You can ask a question, feel free. I wish you success!

This answer should be Vertical Angles.

Vertical angles are angles that are opposite of each other when two lines cross and equal each other. [tex](a^o=b^o)[/tex]

A pair of vertical angles is formed when two lines intersect each other at a single point. They are said to be linear if the angles are adjacent after the intersection of the two lines. The sum of the angles of a linear pair is always equal to [tex]180^o[/tex]. Such angles are also known as complementary or supplementary angles.

The answer is [tex]2^{nd}+4^{th}+5^{th}[/tex]

The answer is the first option. Adjacent angles. The rule is simple. If [tex]a+b=90^o[/tex] if they're adjacate angles.

The answer is the third option. Supplementary angles. The rule is simple. If [tex]a+b=180^o[/tex] if they're supplementary angles.

Based on the results of Mean and Median, we can say that Mean is larger than median in value .

Mean of n observations can be calculated using the formula

Mean = (sum of all observations)/(number of observations) .

After arranging the data in ascending or descending order , the middle value can be called as Median .

In the question ,

the set of numbers is given as 4, 5, 11, 12, 5, 38, 44

rewriting them in ascending order ,we get 4, 5, 5, 11, 12 ,38 ,44   .

the sum of all the number = 4+5+5+11+12+38+44

                                           = 119

number of observations = 7

hence the mean = 119/7 = 17

So, mean = 17

from the set of numbers 4, 5, 5, 11, 12 ,38 ,44 we can see that

the middle value of the set of numbers is 11 .

So , median = 11 .

On comparing the mean = 17  and the median = 11 ,

we can say that the mean is greater than median.

Therefore , based on the results of Mean and Median, we can say that

Mean is larger than median in value .

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Answer:

54 cm

Step-by-step explanation:

A cube has six sides. The area of each face is found by squaring the length of a side. To get the total surface area of the cube, you'll multiply the area of one face by the number of faces.

a = edge

Area = 6a to the power of 2

The line a and b from the given line diagram is parallel since <2 and <3 are corresponding angles.

An angle is the point where two lines meet or intersect. From the given line diagram, we are told that <1 and <2 are supplementary.

Since the sum of supplementary angles is 180 degrees, hence;

<1 + <3 = 180 degrees

Also <1 + <2 = 180 degrees (sum of angles on a straight line)

<1 = 180 - <3

<1 = 180 - <2

Equate

180 - <3 = 180 - <2

-<3 = -<2

<2 = <3 (corresponding angle)

Since <2 is equivalent to <3, hence the line a is parallel to b

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The measure of each angle is 34.1° and 55.9°

complementary angles are angles that gives 90° when added to together.

if the first angle is x and the other complementary angle is y,

then x+y=90

x= y-21.8

representing y-21.8 for x in equation x+y=90

y+ y-21.8= 90°

2y= 111.8

y= 55.9°

and x= 34.1°

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Hence the average rate of change, in simplest form is -10 .

What is average rate of change?

Using the coordinate points from the table  ( 4,53) ( 8, 13 )

Substitute the coordinate into the expression

Average rate of change  = y₂ - y₁/x₂ - x₁

                                         = 13 - 53/8 - 4                    

                                         = -  4 0/4 ⇒ -10

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Answer:

11

Step-by-step explanation:

A whole number is an integer greater than 0.

-76 , -34 , -57 are all negative so they are not whole numbers.

0 is too small so it also is not a whole number.

By ruling out those numbers you are left with 11 which is positive and greater than 0. Therefore, the correct answer is 11.

Answer:

0 and 11

Step-by-step explanation:

Whole numbers are set yo to be real numbers that include zero and all positive numbers while it excludes fractions, negative integers and decimals.

Therefore, from our question, 0 and 11 are whole numbers while -76, -34 and -57 are excluded because they are negative integers.

The largest number of rods that the pole can be cut into is 86.

Given:

Length of Metal Pole = 500 cm

The pole is cut into rods.

Length of each rod = 5.8 cm

To determine the number of rods we can divide the total length of the pole by the length of each rod.

Number of rods that the pole can be cut into = (Length of Metal Pole) ÷ (Length of each rod )

⇒ Number of rods = 500 ÷ 5.8 = 86.2 ≈ 86

Therefore, the largest number of rods that the pole can be cut into is 86.

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Answer:

Step-by-step explanation:

8(2+3)

Compute the Laplace transform of [tex]f(t)=t^n[/tex], where [tex]n[/tex] is a non-negative integer.

[tex]\displaystyle L\left\{t^n\right\} = I_n = \int_0^\infty t^n e^{-st} \, dt[/tex]

Integrate by parts with

[tex]u=t^n \implies du = nt^{n-1} \, dt[/tex]

[tex]dv = e^{-st} \, dt \implies v = -\dfrac1s e^{-st}[/tex]

[tex]\displaystyle I_n = \frac ns \int_0^\infty t^{n-1} e^{-st} \, dt = \frac ns I_{n-1}[/tex]

By substitution,

[tex]\displaystyle I_n = \frac ns I_{n-1} = \frac{n(n-1)}{s^2} I_{n-2} = \cdots = \frac{n(n-1)\cdots(n-(k-1))}{s^k} I_{n-k}[/tex]

so that for [tex]k=n[/tex], we end up with

[tex]\displaystyle I_n = \frac{n(n-1)\cdots1}{s^n} I_0 = \frac{n!}{s^n} \int_0^\infty e^{-st} \, dt = \frac{n!}{s^{n+1}}[/tex]

We then have the inverse transform relation

[tex]\displaystyle L^{-1}\left\{ \frac1{s^n} \right\} = \frac{t^{n-1}}{(n-1)!}[/tex]

and so

[tex]L^{-1}\left\{ \dfrac1{s^3} + \dfrac1s \right\} = \dfrac{t^2}{2!} + \dfrac{0!}{t^0} = \boxed{\dfrac{t^2}2 + 1}[/tex]

Answer:

yes

Step-by-step explanation:

Answer:

11, 110

Step-by-step explanation:

Constant of proportionality: Ratio of distance to time, which is 11.

Distance at 10s: Multiply time by the constant of proportionality, giving 110.

Answer:

Option 4

Step-by-step explanation:

Each x-value corresponds to only one y-value

Answer:

Option 2

Step-by-step explanation:

Using point-slope form, the line passes through (3, 1).

Option 2 is the only choice that satisfes this.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: Graph \:\: 2[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The equation is given in its point slope form :

[tex]\qquad \tt \rightarrow \:y - 1 = \dfrac{2}{3} (x - 3)[/tex]

And the general equation in point slope form is :

[tex]\qquad \tt \rightarrow \:y - y_1 = m(x - x_1)[/tex]

by comparing these two, we can get

And [tex]{ (x_1 , y_1) } [/tex] satisfies the equation, so the line (graph) of this equation should have point (3 , 1) lying on it.

And the only graph satisfying this condition is graph 2, therefore The graph 2 is the required graph.

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The probability of a lizard living for more than 2.5 years is 16%.

The average lifespan of a lizard is 3.1 years, with a standard deviation of 0.6 years.

Average lizard u = 3.1,

standard deviation σ = 0.6

To calculate the likelihood of a lizard living for more than 2.5 years;

p(X<2.5)

μ + aσ = 2.5

3.1 + a(0.6) = 2.5

a(0.6) = −0.6

a = −1

To calculate the probability, apply the empirical rule.

The total area = 100% (since total probability always is 1)

Area from  μ to ∞  =  p(X > μ)  = 50%

Area between  (μ−σ)  and  (μ+σ)  = 68%  

Area between  (μ−σ)  and  μ  is  p((μ−σ) < X < μ)  =34%  

Thus,

p(X< (μ−σ)) = 1 − (p((μ−σ) < X < μ) + p(X > μ))

                  = 1 − (0.34 + 0.5)

p(X< (μ−σ)) = 0.16  

Therefore, the probability that a lizard will live longer than 2.5 years 16%.

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The decimal is equal to (294117647)/(1000000000).

Answer:its D

Step-by-step explanation:

Answer:

43°

Step-by-step explanation:

Alternate interior angle are congruent.