Write a paragraph proof of the Quadrilateral Sum Theorem.
Given: Quadrilateral ABCD
Prove: m

After cutting the squares, the length of each shorter side (and the side length of each triangular quilt piece) is approximately 14√2 inches i.e. B.

What are squares?

A square is a two-dimensional shape with four straight sides that are of equal length and four right angles (90-degree angles) at the corners. It is a special case of a rectangle, where all four sides are the same length. A square can also be thought of as a special type of rhombus, where the angles are all right angles.

Now,

Since the hypotenuse of each triangle is 28 inches long, we know that this is also the longest side of the right triangle formed by the two shorter sides of the triangle. Let's call one of the shorter sides x.

Using the Pythagorean Theorem, we can find the length of the other shorter side:

c²= a² + b²

28² = x² + x²

784 = 2x²

x² = 392

x = √(392)

x=14√2 in

Therefore, the length of each shorter side (and the side length of each triangular quilt piece) is approximately 14√2 inches (rounded to two decimal places).

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answer is

512

Step-by-step explanation:

1.6x80=128

128x4=512

The length of OM, given that the triangles are similar to each other, is calculated as: 14.4.

Similar triangles are triangles that have the same shape but may have different sizes. They have the same angles, but the lengths of their sides are proportional. This means that corresponding sides of similar triangles are in proportion, and the ratio of their corresponding sides is constant.

Since triangle JKL is similar to triangle MNO, therefore:

JK/MN = JL/MO

Substitute:

5/24 = 3/x

Cross multiply:

5x = 72

5x/5 = 72/5

x = 14.4

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If Yin makes the maximum salary contribution to her 401(k), she will have made a total of $7,950.

Divide the part by the entire and multiply the result by 100 to obtain the percentage. A number can be expressed as a fraction of 100 by using the percentage, in other words.

If, for instance, there were 50 students in the class and 35 of them passed the test, and you want to know what percentage of those students passed the test, you may determine it by using the formula below.

% = (Number of students who passed / Total number of students) x 100 % = (35 / 50) x 100 % = 0.7 x 100 %

Percentage = 0.7 x 100

Percentage = 70%

If Yin may contribute up to 15% of her annual earnings to her 401(k) and her beginning salary is $50,000, her maximum annual contribution would be:

Maximum donation is = 15% of $50,000.

Maximum donation is 0.15 times $50,000.

Maximum annual contribution =  $7,500

Given that Yin's company will match up to 6% of her contributions, the maximum amount they might contribute annually is:

6% of $50,000 is the employer's contribution.

Employer contribution equals 0.6 times $50,000.

Annual employer contribution equals $3,000.

Hence, Yin's company will pay an additional $3,000 year if she contributes the maximum of $7,500 to her 401(k). Yin will contribute a total of $10,500 per year to her 401(k) ($7,500 + $3,000). (k).

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The volume of the cylinder in terms of π is  128π centimetres³.

The cylinder below has a height of 8 centimetres and a diameter of 8 centimetres. Therefore, the volume of the cylinder can be found as follows:

volume of the cylinder = πr²h

where

Therefore,

r = 8 / 2 = 4 centimetres

h = 8 centimetres

volume of the cylinder = π × 4² × 8

volume of the cylinder = 128π centimetres³

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Answer:

The inequality that represents this situation is 15x + 10y ≥ 1100, since Ezra needs to earn at least $1100 to buy the laptop.

To check if (60, 20) is a solution to this inequality, we need to substitute x = 60 and y = 20 into the inequality and see if it is true:

15(60) + 10(20) ≥ 1100

900 + 200 ≥ 1100

1100 ≥ 1100

Since 1100 ≥ 1100 is true, this means that (60, 20) is a solution to the inequality. This means that if Ezra works 60 hours mowing lawns and 20 hours walking dogs, he will earn enough money to buy the laptop.

The point (60, 20) represents the combination of hours worked for mowing lawns (x) and walking dogs (y) that will result in Ezra earning enough money to buy the laptop. The x and y values are the inputs or variables, while the inequality 15x + 10y ≥ 1100 is the constraint that must be satisfied. The solution (60, 20) is the output or result of the system of inequalities, and represents the combination of hours worked that will satisfy the constraint.

The linear equation in y=mx+b form that represents this scenario is:

y = -10x + 450.

What is a linear equation?

A linear equation is a mathematical equation in which the highest power of the variable(s) is one.

ax + b = 0

or

y = mx + b

where a, b, and m are constants and x and y are variables. In the first form, x is a variable and a and b are constants. In the second form, x and y are variables, m is the slope of the line, and b is the y-intercept.

Let x be the number of weeks that have passed since Todd started withdrawing money from his savings account. Initially, Todd had $450 in his savings, so the amount of money he has left after x weeks is:

450 - 10x

The rate of change of the amount of money Todd has with respect to time is -10, since he is withdrawing $10 per week. Therefore, the slope of the line that represents this situation is -10.

The y-intercept represents the initial amount of money Todd had in his savings, which is $450. Therefore, the linear equation in y=mx+b form that represents this scenario is:

y = -10x + 450

where y is the amount of money Todd has in his savings after x weeks.

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This report highlights the impact of human activity on three different locations: New York City, the Amazon Rainforest, and the Sahara Desert. The measurements were taken 50 years ago, in the present day, and the predicted future development impact.

## New York City

Water pollution in parts per million (ppm) was measured in New York City. Fifty years ago, the water pollution was 625ppm, and presently, it has increased to 893ppm. The predicted future development impact is 843ppm. To decrease human impact on this location, it is recommended to create gardens on all of the rooftops. The plants will help absorb some of the pollutants and reduce runoff into waterways.

## Amazon Rainforest

CO2 levels in parts per million (ppm) were measured in the Amazon Rainforest. Fifty years ago, the CO2 levels were 318ppm, and presently, it has increased to 402ppm. The predicted future development impact is 378ppm. To decrease human impact on this location, it is recommended to limit the amount of timber that can be removed per year. The Amazon Rainforest is often referred to as the "lungs of the planet" due to its ability to absorb carbon dioxide and produce oxygen. By limiting deforestation, the amount of carbon dioxide released into the atmosphere will decrease, and the rainforest will continue to produce oxygen, benefiting both the local and global environment.

## Sahara Desert

The loss of land by erosion in meters was measured in the Sahara Desert. Fifty years ago, the erosion was 1.2 meters, and presently, it has increased to 3.5 meters. The predicted future development impact is 2.6 meters. To decrease human impact on this location, it is recommended to build better enclosures to decrease overgrazing by livestock. Overgrazing leads to soil compaction, which makes it difficult for vegetation to grow and prevents the soil from holding water. By implementing better enclosures, the livestock will be limited to a smaller area, allowing the vegetation to recover and hold the soil in place.

## Conclusion

In conclusion, all three locations experienced an increase in human impact over the years. By analyzing the data, the location that could benefit the most from decreasing human impact is the Amazon Rainforest. Limiting the amount of timber that can be removed per year will have a positive impact on this location. However, it is important to continue monitoring all three locations to ensure that the human impact is decreasing and not increasing.

## Recommendations for Local Communities

To decrease the local effects of human impact on the environment, two recommendations are:

1. Reduce the use of single-use plastics, such as straws and bags, to decrease pollution. Single-use plastics are a major source of pollution in our oceans, and by reducing our reliance on them, we can help reduce the amount of plastic that ends up in our waterways.

2. Plant more trees and vegetation to increase the amount of oxygen in the air. Trees and plants produce oxygen through photosynthesis, which helps clean the air we breathe. By planting more trees and vegetation in our communities, we can help reduce the amount of pollution in the air and create a healthier environment for ourselves and future generations.

## Recommendations for Global Governments

To decrease the global effects of human impact on the environment, two recommendations are:

1. Invest in renewable energy sources, such as solar and wind power, to decrease the use of fossil fuels. Fossil fuels are a major contributor to greenhouse gas emissions, which are responsible for climate change. By investing in renewable energy sources, we can decrease our reliance on fossil fuels and reduce our carbon footprint.

2. Implement policies to decrease deforestation and promote reforestation to decrease the loss of wildlife habitats and increase the amount of oxygen in the air. Deforestation is a major contributor to climate change, as it releases carbon dioxide into the atmosphere and reduces the amount of oxygen produced by trees. By implementing policies to decrease deforestation and promote reforestation, we can help mitigate the effects of climate change and create a healthier environment for all living beings.

The volume of the solid is 7.58 thousandths when rounded to the nearest thousandth.

Area is a measure of the size of a given space or the amount of a given surface. It can be measured in square feet, square meters, acres, hectares, and other units. Area can be used to describe the size of a two-dimensional shape or the surface area of a three-dimensional object. Area can also be used to calculate the amount of material needed to cover a given space, such as for a roof, carpet, or other covering.

To find the volume of the solid, we will use the following formula:
V=∫baπ(y2−(x−1)2)dx

Where b is the upper bound of the integral, a is the lower bound of the integral and y is the height of the solid.

Since the region R is the base of the solid, we can set a = 0 and b = 2, since this is the x-value at which the two functions intersect. Additionally, we can set y = ln(x) + 1 since this is the height of the solid.

Therefore, the volume of the solid is:
V = ∫02π(ln(x)2 + 12 − (x−1)2)dx

Calculating the integral, we get:
V = [π(xln(x)2 + x − 2xln(x) − x + 1)]02

Substituting the bounds of the integral, we get:
V = [π(22ln(2)2 + 2 − 4ln(2) − 2 + 1)] − [π(02ln(0)2 + 0 − 2ln(0) − 0 + 1)]

Simplifying the equation, we get:
V = π(ln(2)2 + 1 − 2ln(2))

Finally, substituting the value of ln(2) into the equation, we get:
V = 3.14159 (2.386294 + 1 − 4.772188) ≈ 7.58 thousandths

Therefore, the volume of the solid is 7.58 thousandths when rounded to the nearest thousandth.

In conclusion, the volume of the solid whose base is the region R and each cross section perpendicular to the a-axis is a semicircle is 7.58 thousandths when rounded to the nearest thousandth. This was calculated by integrating the equation V=∫baπ(y2−(x−1)2)dx with the bounds of integration a=0 and b=2 and the height of the solid y=ln(x)+1.

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the total percentage increase in the investor's stock account is 22%.

In mathematics, a ratio or figure that can be expressed as a fraction of 100 is known as a percentage. If we want to calculate a percentage of a number, we should split it by 100 before multiplying it by the original number. Therefore, the percentage relates to a component per 100. The term percent means "per 100". It is represented by the symbol "%". In mathematics, a percentage is a number or ratio that is represented as a fraction of 100. Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most commonly used to denote it. A percentage is a number that has neither measurements nor a defined unit of measurement.

In the given question,

Increase in stock A= 24% of $5150 = 1236

Increase in stock = 20% of $5250 = 1050

The  total percentage increase in the investor's stock account= {(1236+1050)/(5150+5250)* 100=

= 21.98%

≈22%

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Answer:

183.3

Step-by-step explanation:

Since there were 1 angle and 2 sides, I used law of cosines

The value of x such that x - 4 and 2x + 1 are angles on a line is 61

x - 4 and 2x + 1 are angles on a line.

Using the theorem of sum of angles on a line that states that:

When two angles are on a line, they add up to 180 degrees.

So we have:

x - 4 + 2x + 1 = 180

Simplifying and solving for x:

3x - 3 = 180

So, we have

3x = 183

Divide both sides by 3

x = 61

Therefore, x = 61 is the value that makes x - 4 and 2x + 1 angles on a line.

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[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{8}}} \implies \cfrac{ 3 }{ -3 } \implies - 1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 1}(x-\stackrel{x_1}{8}) \\\\\\ y-5=-x+8\implies {\Large \begin{array}{llll} y=-x+13 \end{array}}[/tex]

Therefore , the solution of the given problem of function comes out to be the function's behavior on that range because it is not specified for negative values of x.

The midterm exam will include questions on design, geometry, numbers, each division, as well as actual and hypothetical geographic places. A piece of work describes the connections between variable elements that cooperate to produce the same outcome. A utility is a structure made up of numerous unique parts that work together to create unique outcomes for each input.

Here,

Given that the function in the graph you supplied is undefinable for negative values of x, its domain is (0, infinity).

Therefore, referring to the function as declining on the interval is illogical. (0, -infinity).

As we travel from right to left on the interval, we can observe that the function's values are indeed decreasing. (0, infinity).

We refer to this interval as the function's declining one because of this.

On the interval, we could state that the function is decreasing.

(-infinity, 0). However, in this specific instance, we are unable to discuss the function's behavior on that range because it is not specified for negative values of x.

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The chain rule is used when a function is composed of two or more functions, where one function is applied to the output of the other. In other words, it is used when a function is "nested" inside another function. Thus, option A is correct.

We can solve this problem by applying the chain rule and the product rule of differentiation. Let's begin by simplifying the expression inside the parentheses:

[tex]y = ex (e^-2x + 7)[/tex]

Now, let's apply the product rule:

[tex]dy/dx = (ex)'(e^-2x + 7) + ex(e^-2x + 7)'[/tex]

Using the chain rule, we can find (ex)':

[tex](ex)' = ex[/tex]

And using the chain rule again, we can find [tex](e^-2x + 7)':[/tex]

[tex](e^-2x + 7)' = (-2e^-2x)[/tex]

Substituting these values back into the original equation, we get:

[tex]dy/dx = ex(e^-2x + 7) + ex(-2e^-2x)[/tex]

Simplifying, we get:

[tex]dy/dx = ex(e^-2x + 7 - 2e^-2x)[/tex]

[tex]dy/dx = ex(e^-2x - e^-2x + 7)[/tex]

[tex]dy/dx = ex(7)[/tex]

Therefore, the answer is A) 7.

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Answer:

64, 69, 88, 88, 91, 92, 93, 95, 97, 97, 100

Median= 92

Mode= 88, 97

Mean= 88.55

Range= 36

Quartile 1= 88

Quartile 2= 92

Quartile 3= 97

Interquartile range= 9

Minimum= 64

Maximum= 100

Not sure if this helped but I hope it did

Answer:

To find the real and imaginary parts of the complex number 26 = a + bi, we can use the fact that:

a + bi = 26

Taking the complex conjugate of both sides, we get:

a - bi = 26

Adding the two equations, we get:

2a = 52

Solving for a, we get:

a = 26

Substituting this value into one of the equations, we get:

26 + bi = 26

Therefore, b = 0.

Therefore, the real part of 26 is a = 26, and the imaginary part is b = 0.

The parallelogram ABCD's congruency can be proven using Side-Angle-Side (SAS) congruence theorem.

Prove that ΔABC ≅ ΔDCB using the Side-Angle-Side (SAS) congruence theorem.

Given that ABCD is a parallelogram, AB || CD and BC || AD. Therefore, ∠ABC ≅ ∠DCB and ∠ACB ≅ ∠DCA because they are corresponding angles.

AB ≅ CD and BC ≅ AD because opposite sides of a parallelogram are congruent.

Lastly, AC ≅ AC because it is a shared side between the two triangles.

Therefore, the following congruent parts:

∠ABC ≅ ∠DCB (by corresponding angles)

AB ≅ CD (by opposite sides)

BC ≅ AD (by opposite sides)

AC ≅ AC (shared side)

The SAS congruence theorem concludes that ΔABC ≅ ΔDCB.

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Image transcribed:

Prove ΔABC ≅ ΔDCB

The answer of the given question based on rational parent function , to identify a correct transformation of the function, The correct answer choice is (c) Left 5.

A function is  mathematical relationship that assigns  unique output value for each input value. It describes relationship between two variables, where  output value is dependent on input value. A function can be represented by  equation, a graph, or  table. In its simplest form,  function takes  input value, performs a specified operation on that value, and produces  corresponding output value.

Functions are used to model real-world phenomena, to solve problems, and to analyze and understand complex systems. They are  fundamental concept in mathematics and are used in  wide variety of fields, like science, engineering, economics, and finance.

The given equation is y = 12/(x + 5), which represents the rational parent function. To identify a correct transformation of the function, we can consider the effect of each transformation on the parent function.

a) Vertical reflection: This transformation would change the sign of the function, resulting in y = -12/(x + 5). This is not the given equation, so it is not a correct transformation.

b) Vertical stretch by 12: This transformation would multiply the function by 12, resulting in y = 12(12/(x + 5)) = 144/(x + 5). This is not the given equation, so it is not a correct transformation.

c) Left 5: This transformation would shift the function to the left by 5 units, resulting in y = 12/(x + 10). This is a correct transformation of the function, as it represents a horizontal shift of 5 units to the left.

d) Down 5: This transformation would shift the function down by 5 units, resulting in y = 12/(x + 5) - 5. This is not the given equation, so it is not a correct transformation.

Therefore, the correct transformation of the rational parent function as described by the given equation is a horizontal shift of 5 units to the left. The answer choice is (c) Left 5.

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The correct transformation of the function on rational parent function as described by the given equation. The correct answer choice is (c) Left 5.

A function is  mathematical relationship that assigns  unique output value for each input value. It describes relationship between two variables, where  output value is dependent on input value. A function can be represented by  equation, a graph, or  table. In its simplest form,  function takes  input value, performs a specified operation on that value, and produces  corresponding output value.

The given equation is y = 12/(x + 5), which represents the rational parent function. To identify a correct transformation of the function, we can consider the effect of each transformation on the parent function.

a) Vertical reflection: This transformation would change the sign of the function, resulting in y = -12/(x + 5). This is not the given equation, so it is not a correct transformation.

b) Vertical stretch by 12: This transformation would multiply the function by 12, resulting in y = 12(12/(x + 5)) = 144/(x + 5). This is not the given equation, so it is not a correct transformation.

c) Left 5: This transformation would shift the function to the left by 5 units, resulting in y = 12/(x + 10). This is a correct transformation of the function, as it represents a horizontal shift of 5 units to the left.

d) Down 5: This transformation would shift the function down by 5 units, resulting in y = 12/(x + 5) - 5. This is not the given equation, so it is not a correct transformation.

Therefore, the correct transformation of the rational parent function as described by the given equation is a horizontal shift of 5 units to the left. The answer choice is (c) Left 5.

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The cost to operate Lee's Tv is 2.88 dollars.

Lee watches TV for 4 hours per day. During that time, the TV consumes 200 watts per hour. Electricity costs (12 cents)/(1 kilowatt-hour).

Therefore, the cost for Lee to operate in 30 days can be calculated as follows:

200 watt = 0.2 kilowatt

Therefore,

1 day = 4 hours

30 days = ?

cross multiply

number of hours = 120 hours.

Therefore, in 30 days he watches television for 120 hours.

Let's find the cost

0.12 dollars  = 12 cent

1 hour  = 0.2 kilowatt

120 hours =

kilowatt use in 30 days = 0.2 × 120 = 24 kilowatts

Therefore,

1 kilowatts = 0.12 dollars

24 kilowatts = ?

cost of Tv for a month of 30 days = 24 × 0.12

cost of Tv for a month of 30 days = 2.88 dollars

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Answer:

Numbers between 100 and 200 which are also equal to a square number multiplied by a prime number are:

Step-by-step explanation:

A square number is a number that has been multiplied by itself.

For example, 25 is a square number as 5 × 5 = 25.

The square numbers between zero and 200 are:

A prime number is a whole number greater than 1 that cannot be made by multiplying other whole numbers (its only factors are 1 and itself).

Since the smallest square number is 4, and our final number needs to be between 100 and 200, we only need to list the primes numbers that are less than 50 as 4 × 50 = 200.

Begin with the smallest prime number, 2. If we divide 100 and 200 by this prime number, we get 50 and 100. Therefore, to find a number between 100 and 200 that is equal to a square number multiplied by a prime number, the square number should be more than 50 and less than 100.  Therefore:

The next smallest prime number is 3. If we divide 100 and 200 by 3 we get 33.33.. and 66.66...  Therefore, the prime number 3 should be multiplied by a square number that is more than 33 and less than 67:

The next prime number is 5. If we divide 100 and 200 by 5 we get 20 and 40.  Therefore, the prime number 5 should be multiplied by a square number that is more than 20 and less than 40:

Continuing this way, all the numbers that are between 100 and 200, which are also equal to a square number multiplied by a prime number are:

Number between 100 and 200 which is also equal to a square number multiplied by a prime number is 147.

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In simpler terms, a prime number is a number that can only be evenly divided by 1 and itself.

To find this number, I first looked for square numbers between 100 and 200. The square numbers within this range are 121 (11 squared) and 169 (13 squared).

I then checked if either of these square numbers could be multiplied by a prime number to equal a number between 100 and 200. After some calculation, I found that 169 cannot be multiplied by a prime number to give a number between 100 and 200. However, 121 can be multiplied by 2 to give 242, which is greater than 200.

Finally, I checked if there were any other square numbers I missed. I found that 7 squared is equal to 49, which when multiplied by 3 (a prime number) gives 147, a number between 100 and 200 that satisfies the problem.

Therefore, the number between 100 and 200 which is also equal to a square number multiplied by a prime number is 147.

I hope this helps!

Answer:

Step-by-step explanation:

Part A:

Let's assume that the velocity of the runner changes linearly over time. We can use the slope-intercept form of a linear equation, y = mx + b, to describe the velocity of the runner at different times. In this case, the y-axis represents the velocity in km/h and the x-axis represents time in hours. We can define:

y = velocity of the runner in km/h

x = time in hours

The velocity of the runner changes by -2/3 km/h for every hour that passes. This gives us a slope of -2/3. We can use the point-slope form of a linear equation to find the equation of the line:

y - 5 = -2/3(x - 1)

Simplifying this equation, we get:

3y - 15 = -2x + 2

Rearranging to standard form, we get:

2x + 3y = 17

So the equation in two variables in standard form that can be used to describe the velocity of the runner at different times is 2x + 3y = 17.

Part B:

To graph the equation obtained in Part A for the first 5 hours, we can simply plot points for different values of x and y. For example, we can use x = 0, 1, 2, 3, 4, and 5 to find the corresponding values of y using the equation 2x + 3y = 17. Then we can plot these points on a graph and connect them with a straight line.

Here are the values of y for different values of x:

x = 0, y = 17/3

x = 1, y = 5

x = 2, y = 13/3

x = 3, y = 3

x = 4, y = 7/3

x = 5, y = 1

Plotting these points and connecting them with a straight line, we get the graph of the equation 2x + 3y = 17 for the first 5 hours:

|

6.0 -| .

| .

5.5 -| .

| .

5.0 -| .

|.

4.5 -|

|

4.0 -| .

| .

3.5 -| .

| .

3.0 -| .

|.

2.5 -|

|

2.0 -| .

| .

1.5 -| .

| .

1.0 -|.

|

0.5 -|

|

--------------

0 1 2 3 4 5

The y-intercept of the line is 17/3, which represents the initial velocity of the runner at time 0. The slope of the line is -2/3, which represents the rate of change of the velocity over time.

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Part A:

Let v be the velocity of the runner in km/h and let t be the time elapsed in hours. We can use the two given data points to form a system of two equations:

v = 5 when t = 1

v = 3 when t = 3

To find the equation in standard form, we can first use point-slope form:

v - 5 = m(t - 1) (using the point (1, 5))

v - 3 = m(t - 3) (using the point (3, 3))

Simplifying both equations:

v - 5 = m(t - 1)

v - 3 = m(t - 3)

v = mt + (5 - m)

v = mt + (3m - 3)

Setting the right-hand sides equal to each other:

mt + (5 - m) = mt + (3m - 3)

Simplifying and rearranging:

-m = -2

m = 2

Substituting m = 2 into one of the equations above:

v = 2t + 3

This is the equation in two variables in standard form that describes the velocity of the runner at different times.

Part B:

To graph the equation v = 2t + 3 for the first 5 hours, we can plot points for different values of t and then connect them with a line. For example:

When t = 0, v = 3, so the point (0, 3) is on the line.

When t = 1, v = 5, so the point (1, 5) is on the line.

When t = 2, v = 7, so the point (2, 7) is on the line.

When t = 3, v = 9, so the point (3, 9) is on the line.

When t = 4, v = 11, so the point (4, 11) is on the line.

When t = 5, v = 13, so the point (5, 13) is on the line.

Plotting these points on a coordinate plane and connecting them with a line, we get the graph of the equation v = 2t + 3 for the first 5 hours:

    |

 15 +-------*

    |       |

 13 +           *

    |           |

 11 +               *

    |               |

  9 +                   *

    |                   |

  7 +                       *

    |                       |

  5 +                           *

    |                           |

  3 +---------------*-----------*

    0   1   2   3   4   5   6   7

The x-axis represents time (t) in hours, and the y-axis represents velocity (v) in km/h. The line starts at (0, 3) and has a slope of 2, indicating that the velocity is increasing by 2 km/h for every hour that passes.

Step-by-step explanation:

Answer:

Step-by-step explanation:

5/9 + (-4/9) - (-2)

5/9 - 4/9 + 2

[tex]5-4+18/9[/tex]

19/9 or 2.1, 2 1/9

Answer:

i did this in 8th grade. (I'm homeschooled)

Step-by-step explanation:

Heres the best i got

So the probability that Angela gets to go to the meeting is 2/5.

Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain. Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is an important concept in many fields, including mathematics, statistics, physics, and engineering, and is used to make predictions, analyze data, and make decisions under uncertainty.

Here,

There are a total of 5 people in the club, so there are 10 possible pairs of people that could be chosen to go to the meeting. Since each pair is equally likely to be chosen, the probability of any particular pair being chosen is 1/10.

To determine the probability that Angela gets to go to the meeting, we need to count the number of pairs that include Angela. There are 4 other people in the club, so there are 4 possible pairs that include Angela. Therefore, the probability that Angela gets to go to the meeting is:

P(Angela) = number of pairs that include Angela / total number of pairs

= 4 / 10

= 2 / 5

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Answer:

3.7

Step-by-step explanation:

1.5, 2.2, 2.8, 3.4, 5, 5.6, 6.8, 7

Q1 = 2.2+2.8 = 5.0 divided 2 = 2.5

Q3 = 5.6+6.8 = 12.40 divided 2 = 6.2

IQR = 6.2 - 2.5 = 3.7

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f(x) = [tex]x^{2}[/tex] -> f(x) = [tex]x^2[/tex] - 18 (translation) -> f(x) = [tex](x-3)^2[/tex] - 18 (horizontal translation) -> f(x) = -6[tex](x-3)^2[/tex] + 18 - 6x (vertical stretching)

To transform the function f(x) =[tex]x^{2}[/tex] into f(x) = [tex]x^{2}[/tex] - 6x + 18, we need to apply a series of transformations. Here are the steps:

Translation: We need to shift the graph of f(x) = [tex]x^{2}[/tex] down by 18 units to obtain f(x) = [tex]x^{2}[/tex] - 18. This can be done by subtracting 18 from the function, which results in f(x) = [tex]x^2[/tex]- 18.

Horizontal translation: Next, we need to shift the graph of f(x) = [tex]x^{2}[/tex] - 18 to the right by 3 units to obtain f(x) =[tex](x-3)^2[/tex] - 18. This can be done by replacing x with (x-3) in the function, which results in f(x) =[tex](x-3)^2[/tex]- 18.

Vertical stretching: Finally, we need to vertically stretch the graph of f(x) = [tex](x-3)^2[/tex] - 18 by a factor of -6 to obtain f(x) = [tex](x-3)^2[/tex] - 6x + 18. This can be done by multiplying the function by -6, which results in f(x) = -6[tex](x-3)^2[/tex] + 18 - 6x.

So, the series of transformations required to transform f(x) = [tex]x^{2}[/tex] into f(x) = [tex]x^{2}[/tex] - 6x + 18 is:

f(x) = [tex]x^{2}[/tex] -> f(x) =[tex]x^{2}[/tex] - 18 (translation) -> f(x) =[tex](x-3)^2[/tex] - 18 (horizontal translation) -> f(x) = -6[tex](x-3)^2[/tex]+ 18 - 6x (vertical stretching)

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Using a trigonometric relation we can see that  the balloon’s vertical distance above the ground is 430.8ft

We can see this as a right triangle, such that we know one angle of 39°, and the adjacent cathetus of that angle has a measure of 532 feet, then we can use a trigonometric relation to find the opposite cathetus, which is the height.

tan(a) = (opposite cathetus)/(adjacent cathetus)

Then we can write:

tan(39°) = H/532ft

532ft*tan(39°) = 430.8ft

That is the vertical height.

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