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The point of concurrency of the three angle bisectors of a triangle is  incenter

The three angle bisectors of a triangle are concurrent in a point equidistant from the sides of a triangle. The point of concurrency of the angle bisectors of a triangle is known as the incenter of a triangle.

The point where the triangle's angle bisectors cross is known as the incenter, which is equidistant from the triangle's three sides. It is a crucial location in triangle geometry, and numerous incenter properties are applied in various triangle-related constructions and proofs.

Therefore, the point at which the three angle bisectors of a triangle meet is called its Incentre.

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The costs and areas of the mat are

Represent the dimensions of the frame with

Length = x

Width = y

So, the frame area is

Area = xy

When the mat is 1 inch from the frame, we have

Whole Area = (x + 1 + 1) * (y + 1 + 1)

Whole Area = (x + 2) * (y + 2)

Expand

Whole Area = xy + 2x + 2y + 4

So, the mat area is

Mat area = xy + 2x + 2y + 4 - xy

Mat area = 2x + 2y + 4

The cost is

Cost = 0.05 * (2x + 2y + 4)

Cost = 0.1x + 0.1y + 0.2

When the mat is 2 inches from the frame, we have

Whole Area = (x + 4) * (y + 4)

Expand

Whole Area = xy + 4x + 4y + 16

So, the mat area is

Mat area = xy + 4x + 4y + 16 - xy

Mat area = 4x + 4y + 16

The cost is

Cost = 0.05 * (4x + 4y + 16)

Cost = 0.2x + 0.2y + 0.8

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Answer:

Below

Step-by-step explanation:

N, the number can be anything   greater than or equal to 11.5 and less than 12.5  

11.5 ≤  n < 12.5

Answer: The pants cost more than $34.5

Step-by-step explanation:

The requried representative sample for the survey would consist of 385 people randomly selected from the city's population.

The statistic is the study of mathematics that deals with relations between comprehensive data.

Here,
To obtain a representative sample of the population, the sample should be randomly selected to ensure that each person in the city has an equal chance of being chosen. The size of the sample will depend on the level of precision required, the confidence level desired, and the margin of error that is acceptable. However, as a general rule, a sample size of at least 385 people would be required to obtain a margin of error of plus or minus 5% with a 95% confidence level.

Therefore, a representative sample to the survey would consist of 385 people randomly selected from the city's population.

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Using the formula to convert pounds to kilogram,

We know that :

1 lb/ Pound = 0.453592 kilogram

therefore,

250 lbs/ Pound = 113.398 kilogram.

Using the formula to convert pounds to kilograms, you find that 250 pounds equals 113.398 kilograms

To convert 250 pounds (pounds) to kilograms (kg), you must use the conversion factor 1 pound = 113.398 kilogram.

Therefore,

we multiply 250 pounds by 86.18 kg/lb to get the equivalent weight in kilograms:

250 pounds x 0.45359237 kg/lb = 113.398 kilogram

Therefore,

250 pounds is 113.4 kilogram.

To understand the conversion factor, you need to know that pounds and kilograms are units of mass, but are used in many parts of the world. In the United States and some other countries, the accepted unit of mass is the pound, while most other countries use the kilogram.

A conversion factor connects the number of pounds to the number of kilograms, so you can easily convert from one unit of measure to another. It is important to use the correct conversion factor for accurate conversion.

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Answer: B - $6,098.35

Step-by-step explanation:

This is a compound interest question. The compound interest formula is:

A = P ( 1 + r/n)^nt

A = Future amount of investment

P = Starting amount of investment

r = Rate of interest

n = Number of times interest compounds per year

t = Time (Years)

You must turn the percentage (1%) into a decimal by dividing by 100

1/100=.01

So, the equation for this question is:

A = 4,800(1+[tex]\frac{.01}{2}[/tex])^(2)(24)

A = 4800(1.005)^48

A = 4800(1.2704891611)

A = 6,098.35

By using effective text features and text structure, the author can help the reader to better understand and remember the central idea of the text. These elements can also make the text more engaging and interesting to read. Overall, text features and text structure are essential tools for conveying information effectively and conveying the author's intended message to the reader.

Generally, Text features and text structure are important components of a written text that contribute significantly to its overall meaning. The central idea of a text is the main message or thesis that the author wants to convey to the reader. The text structure is the way the author organizes the information within the text, and the text features are the visual and organizational elements of the text that help the reader navigate and understand the content.

Text features such as headings, subheadings, and bullet points help the reader to quickly identify the main ideas and subtopics of the text. Bold and italicized fonts may be used to emphasize important concepts or ideas. Images, charts, and graphs can provide visual aids that help the reader understand complex information. In addition, text features like footnotes, citations, and a bibliography can help to establish the credibility of the author and the information presented in the text.

Text structure also plays a critical role in conveying the central idea of a text. The author may use a variety of text structures, such as chronological order, cause and effect, problem-solution, or compare and contrast, to organize the information and present it in a logical and coherent manner. For example, a text about the causes and effects of climate change might use a cause and effect structure to explain how human activities are contributing to global warming and the impacts that result from this phenomenon.

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Absolutely, because they show how big a number is, average leading zeros are regarded as significant digits. Leading zeros are counted as important figures since they help determine the decimal point's location and the size of the number.

Leading zeros in a number are important figures. This implies that when counting the total number of significant figures in a number, they are taken into account. The reason for this is that preceding zeros reveal the location of the decimal point and, hence, the size of the number. Because the leading zero signifies that the number is in hundredths, the number 0.002, for instance, has three significant figures. The number would be read as two rather than two hundredths without the leading zero. Due to their significance in assessing a number's precision, leading zeros should always be counted among the significant figures.

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{2x + y = 2

{5x + 3y - 9

Solution: We can solve this system of equations either by substitution or elimination method. Here, let's use substitution method.

From equation 1, we have: y = -2x + 2

Substituting this in equation 2, we get: 5x + 3(-2x + 2) - 9 = 0

Expanding the right-hand side, we get: 5x - 6x + 6 - 9 = 0

Simplifying further, we get: -x + (-3) = 0

Adding x to both sides, we get: -3 = x

Substituting this value of x in y = -2x + 2, we get: y = -2(-3) + 2 = 6

So, the solution to the system of equations is (x, y) = (-3, 6)

{5x - 2y = -2

{3x + 4y - 30

Solution: We can solve this system of equations by either substitution or elimination method. Here, let's use elimination method.

We can multiply equation 1 by 3 and equation 2 by 2, to make the coefficients of y same in both equations. Doing this, we get:

15x - 6y = -6

6x + 8y - 60 = 0

Adding these two equations, we get: 21x + 2y - 60 = 0

Simplifying further, we get: 21x = 60 + 2y

Dividing both sides by 21, we get: x = (60 + 2y)/21

Substituting this in equation 1, we get: 5((60 + 2y)/21) - 2y = -2

Expanding the right-hand side, we get: 60/21 + 10/21 y - 2y = -2

Simplifying further, we get: 60/21 + (-12/21) y = -2

Adding 12/21 y to both sides, we get: 60/21 = (-2) + (12/21) y

Subtracting -2 from both sides, we get: 62/21 = (12/21) y

Dividing both sides by 12/21, we get: y = 62/12 = 5 1/6

Substituting this value of y in x = (60 + 2y)/21, we get: x = (60 + 2(5 1/6))/21 = (60 + 11 1/3)/21 = (71 1/3)/21 = 71/21 + 1/63

So, the solution to the system of equations is (x, y) = (71/21 + 1/63, 5 1/6)



The description of the graph of the system of inequalities, including shading and the types of lines graphed, and the description of the solution set is given below:

2x + y <= 8 is the inequality for the cost.

x + y >= 4 is the inequality for the number of cupcakes or pieces of fudge that she wants to buy.

using the desmos dot com calculator, you would graph the OPPOSITE of the inequalities.

the area on the graph that is NOT shaded is the feasible region

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Answer:

y = -3 or (2, -3)

Step-by-step explanation:

For x = 2 :

(2 ⋅ 2) + y = 1

4 + y = 1

4 − 4 + y = 1 − 4

0 + y =−3

y = −3 or (2, -3)

The statements supported by the random samples of the amount of time spent shopping, as shown on the box plot are :

For Group A, the box begins at 30 minutes. This means that 25 % of those in group A spent 30 minutes or less when shopping. For Group B, this can be said to be less than 25 %.

Group A had a longer box than Group B and what this is meant to show is that Group A had greater variability in the data ( number of minutes spent shopping ) than Group B.

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The magic number is calculated as G + 1 − [tex]W_{A}[/tex] − [tex]L_{B}[/tex], where G represents the season's overall number of games. The total victory for Team A is represented by the WA. LB is the total number of defeats Team B has suffered this year.

The "magic number" in baseball is used to estimate how likely a club is to advance to the postseason or win the division. Every year, in September, when teams get closer to clinching, it gains attention. The total number of victories and losses that must occur by a team's closest rival in order for that team to achieve a certain goal is known as its magic number. A team's magic number drops by one with each victory. The magic number additionally drops by one each time the team's closest rival for the division (or Wild Card) loses.

This is the precise formula: Games left in season: +1 (Losses by second place team - losses by first place team)

The magic number changes to reflect any further changes in the second-place team.

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Answer:

186

Step-by-step explanation:

Division will yield 186 .

Given,

372 divided by 2.

Now,

For division firstly the common factors of 372 and 2,

372 = 2 * 2 *3 * 31

2 = 2 * 1

So common factor is 2,

Now divide 372 by 2

= 372/2

= 186

Thus the value of 372 divided by 2 is 186 .

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Answer: To determine which vehicle received the greater force, we need to calculate the momentum change for each vehicle during the collision. The force experienced by a vehicle during a collision is equal to the rate of change of its momentum.

First, let's calculate the initial momentum for each vehicle:

The car has a mass of 1,000 kg and a velocity of 30 m/s, so its initial momentum is 1,000 kg * 30 m/s = 30,000 kg m/s.

The truck has a mass of 2,000 kg and a velocity of 20 m/s, so its initial momentum is 2,000 kg * 20 m/s = 40,000 kg m/s.

Next, let's calculate the final momentum for both vehicles after the collision:

The car and truck collide head-on, so their velocities will become zero after the collision. So the final momentum for both vehicles will be zero.

Finally, we can calculate the rate of change of momentum for each vehicle:

The rate of change of momentum for the car is equal to its final momentum minus its initial momentum, or 30,000 kg m/s - 0 kg m/s = 30,000 kg m/s.

The rate of change of momentum for the truck is equal to its final momentum minus its initial momentum, or 0 kg m/s - 40,000 kg m/s = -40,000 kg m/s.

Since the magnitude of the rate of change of momentum for the truck is greater than the magnitude of the rate of change of momentum for the car, the truck has received the greater force.

Step-by-step explanation:

[tex] \sf \frac{5^{4} \times {10}^{4x ^{7} } }{8 \times 43 \times {5}^{3} } [/tex]

The expression that represents the area of each section is 14.2z - 9.8.

What is area ?

To find the area of each section, we need to divide the total area of the garden plot by the number of sections, which in this case is six.

The expression for the area of each section can be obtained by dividing the expression for the total area by 6:

(area of each section) = (total area of garden plot) / 6

(area of each section) = (85.2z - 58.8) / 6

Simplifying this expression, we can divide both terms by 6:

(area of each section) = 14.2z - 9.8

Therefore, the expression that represents the area of each section is 14.2z - 9.8.

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Triangle PST is congruent to triangle QSR based on side-angle-side congruency theorem

A triangle is a polygon that has three sides and three angles. Types of triangles are equilateral, isosceles, scalene, right angled triangle. In an equilateral triangle, two sides are equal.

Two triangles are said to be congruent, if all angles and all sides are congruent to each other.

From the diagram:

ΔPQR is equilateral (given)

QR = PT (Given)

∠SPT = ∠RQS (Given)

PS = QS (Definition of equilateral triangle)

ΔPST ≅ ΔQSR (Side angle side congruency theorem)

Triangle PST is congruent to triangle QSR

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The correct statements about the given isosceles triangle are: (B) YQ = XP, (C) ∠WXY = ∠WYX, (D) WQ/QX = WP/PY, (E) PQ ║ XY, and (F) ∠PXY = ∠QYX.

An isosceles triangle in geometry is a triangle with two equal-length sides.

It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

The isosceles right triangle, the golden triangle, the faces of bipyramids, and some Catalan solids are all examples of isosceles triangles.

Isosceles triangles were first studied mathematically in Babylonian and Egyptian mathematics.

Isosceles triangles are commonly employed in architecture and design, such as in building pediments and gables, and have been utilized as ornamentation since much earlier periods.

Then, according to the given image, the true statements for the following isosceles triangle can be:

YQ = XP

∠WXY = ∠WYX

WQ/QX = WP/PY

PQ ║ XY

∠PXY = ∠QYX

Therefore, the correct statements about the given isosceles triangle are: (B) YQ = XP, (C) ∠WXY = ∠WYX, (D) WQ/QX = WP/PY, (E) PQ ║ XY, and (F) ∠PXY = ∠QYX.

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Answer: The line y = 3x - 5 can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, m = 3 and b = -5.

When a line is reflected across the x-axis, the slope of the line changes sign, but the y-intercept remains the same. This means that if the original line has slope m and y-intercept b, the reflected line will have slope -m and y-intercept b.

For the image, y = 1 - 3x, the slope is -3 and the y-intercept is 1.

To find the value of a, we can set the two lines equal to each other and solve for x:

3x - 5 = 1 - 3x

Solving for x, we get:

4x = 6

x = 3/2

So the line of reflection, x = a, passes through

Step-by-step explanation:

The graph of the function [tex]g(x) = 6.(\frac{8}{3})^x[/tex] is an exponentially growing function.

The formula for exponential growth is [tex]y = y_0.e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_0.e^{(-kt)}[/tex].

Given, An exponential function [tex]g(x) = 6.(\frac{8}{3})^x[/tex].

The graph of the function has a y-intercept of 6 and it is an exponentially growing function for all positive values of 'x'.

To obtain the intercept we set x = 0, Therefore, [tex]g(0) = 6.(\frac{8}{3})^0[/tex],

[tex]g(0) = 6[/tex].

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The value of x in the triangle s 16√2

From the question, we have the following parameters that can be used in our computation:

The triangle

The vertical side (y) can be calculated using the following equation

y/2 = (18 - 2)/y

So, we have

y^2 = 32

Take the square roots

y = 4√2

The length x is then calculated as

x^2 = y^2 + (18 - 2)^2

Substitute the known values in the above equation, so, we have the following representation

x^2 = (4√2)^2 + (18 - 2)^2

Evaluate

x^2 = 288

Take the square root

x = 16√2

Hence, the value of x is 16√2

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Answer:

I'm 90% sure it's B.

Step-by-step explanation:

sorry if its not correct-

Answer: figure b

Step-by-step explanation:

this is because all of figure b's sides are congruent but the other figures sides are different lengths

Answer:

Step-by-step explanation:

Answer:

I believe the solution is -12

Step-by-step explanation:

Answer:

(-5,1) and (0,3)

in this first one the distance of x is -5 and y is 1, similarly in second x is in origin which means 0 and y is 3.....

The equation of this circle include the following: C. (x - 8)² + (y - 4)² = 16.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²

Where:

Substituting the given points into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - 8)² + (y - 4)² = 4²

(x - 8)² + (y - 4)² = 16.

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