the area of a rectangle is 14 square units. it has the side length of x and y. given each value for x, find y.

1. x = 4 and 1/5
2. x = 2 and 1/3
3. x = 7/6​

Answer:

Step-by-step explanation:

To simplify this expression, we will distribute the -4 and -3 to the terms inside the parentheses:

-4(-11+4n) - 3(-2n+9)

= 44 - 16n + 6n - 27

= -16n - 17

Therefore, the simplified expression is -16n - 17.

Answer:

Step-by-step explanation:

y = 3x + 9

Answer:

x = 0

Step-by-step explanation:

9x - 7 = -7

Add 7 to both sides.

9x - 7 + 7 = -7 + 7

9x = 0

Divide both sides by 9.

9x/9 = 0/9

x = 0

Answer:

x=0

Step-by-step explanation:

60 adult tickets and 45 children tickets were sold.

Let's use algebra to solve the problem:

Let x be the number of adult tickets sold.

Let y be the number of children tickets sold.

From the problem, we know that:

x + y = 105 (total tickets sold)

10x + 6y = 870 (total amount raised)

We can solve this system of equations by using elimination:

Multiply the first equation by 6: 6x + 6y = 630

Subtract the second equation from the first: 4x = 240

Solve for x: x = 60

Now we can use x to find y:

x + y = 105

60 + y = 105

y = 45

Therefore, 60 adult tickets and 45 children tickets were sold.

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The coordinates of the point P on the directed line segment from A to B such that P is 2/3 the length of the line segment from A to B are (-1, 2).

The coordinates of point P are obtained applying the proportions in the context of the problem.

P is 2/3 the length of the line segment from A to B, hence the equation is given as follows:

P - A = 2/3(B - A)

Then the x-coordinate of P is obtained considering the x-coordinates of A and B as follows:

x - 9 = 2/3(-6 - 9)

x - 9 = -10

x = -1.

The y-coordinate of P is obtained considering the y-coordinates of A and B as follows:

y + 8 = 2/3(7 + 8)

y + 8 = 10

y = 2.

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Answer:

146.82 yards is the distance from tee to hole.

Step-by-step explanation:

Let A is the position of tee and where the golfer is standing.

C is the position of hole.

CB is the vertical distance between greens and tee.

Angle of elevation,

To find: side AC.

Using trigonometric functions, we know that value of sine is:

[tex]sin\theta=\dfrac{\text{Perpendicular}}{\text{Hypotenuse}}[/tex]

Here [tex]\theta=\angle BAC=15^\circ[/tex]

Perpendicular is side CB.

Hypotenuse is side AC.

[tex]\text{sin}12^\circ=\dfrac{\text{CB}}{\text{AC}}[/tex]

[tex]\implies\text{CB}=\dfrac{38}{\text{sin}15^\circ}[/tex]

[tex]\implies\text{CB}=146.82[/tex]

Hence, 146.82 yards is the distance from tee to hole.

Answer:

We can rewrite the function as:

f(x) = 3(8√3)^(2x) = 3(2^3√3)^(2x)

Using the properties of exponents, we can rewrite this as:

f(x) = 3(2^(3*2x)√3^(2x)) = 3(2^(6x)√(3^(2x)))

Therefore, the base of the exponent is 2.

It would take approximately 115.38 minutes to drive 125 miles at a rate of 65 miles/hour.

Speed is simply referred to as distance traveled per unit time.

Mathematically, Speed = Distance ÷ time.

Given that, the speed or rate is  65 miles/1 hr, how many minutes will it take to drive 125 miles.

First, we need to find the time it takes to travel 125 miles at a rate of 65 miles/hour.

We can use the formula:

Speed = Distance ÷ time.

time = distance / rate

time = 125 miles / 65 miles/hour

time = 25/13 hours

Now we can convert hours to minutes by multiplying by 60:

= 25/13 hours × 60 minutes/hour

= 115.38 minutes

Therefore, the required time is approximately 115.38 minutes.

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According to the question approximately 83.89% of professors make more than $75,000 calculated by forming the equation.

When the roots and solutions of two equations match, they are said to be equivalent. The same number, symbols, or expression must be added to or subtracted from both the equation's two sides to produce an equivalent equation. By multiplying or dividing both sides of an equation by a nonzero number, we can also obtain an analogous equation.

This issue can be resolved using the conventional normal distribution. First, we need to standardize the value of $75,000 using the formula:

z = (x - μ) / σ

where x is indeed the value we wish to standardise, is indeed the mean, and is the deviation.

z = (75,000 - 85,900) / 11,000

z = -0.99

Next, we look up the area to the right of z = -0.99 in the standard normal distribution table or by using a calculator. The area to the left of z = -0.99 is 0.1611, so the area to the right of z = -0.99 is:

1 - 0.1611 = 0.8389

Therefore, approximately 83.89% of professors make more than $75,000.

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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.

Answer: CLICK THANKS IF YOU LIKE MY ANSWER. HAVE A GOOD DAY SIR/MAAM #KEEPSAFE

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:

Alright

Step-by-step explanation:

50/1.428

Multiply the numerator by the denominator to get 50000/1428

Set equation up in long division format

Divide 50000 by 1428 to get 3

Divide 7160 by 1428 to get 5

Divide 200 by 1428 to get 0

Divide 2000 by 1428 to get 1

Divide 5720 by 1428 to get 4

Divide 80 by 1428 to get 0

Divide 800 by 1428 to get 0

35.014

Answer:

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

Step-by-step explanation:

Heres the best i got

Answer:

0 (-72522)

Step-by-step explanation:

ahora tienes negativo manzanas

Answer: x= 6241/2

Step-by-step explanation:

Answer:

183.3

Step-by-step explanation:

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

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 corresponding point on the graph is (9, 21). This point is within the normal respiratory rate region, which is defined by the system of linear inequalities. Therefore, model breakdown has not occurred.

The given problem involves the normal respiratory rates of children aged 3 to 15 years. The respiratory rate, measured in breaths per minute, is represented as a function of age using a system of linear inequalities. The graph depicts a normal respiratory rate region that models the respiratory rate ranges shown in the table. The problem requires us to identify a specific point on the graph that corresponds to a respiratory rate of 21 breaths per minute for a 9-year-old child. The ordered pair (9, 21) represents the corresponding point on the graph.

Further, we need to determine if this point lies within the normal respiratory rate region or if model breakdown has occurred. The system of linear inequalities defines the normal respiratory rate region, and we can determine if the point (9, 21) satisfies these inequalities. In this case, the point (9, 21) lies within the normal respiratory rate region and satisfies the system of linear inequalities. Therefore, model breakdown has not occurred, and the given model is an appropriate approximation of the normal respiratory rate region for children aged 3 to 15.

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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.

answer is

512

Step-by-step explanation:

1.6x80=128

128x4=512

[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]

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

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.

13

First, we divide to figure out how much Jane makes an hour

143 ÷ 11 = 13

Second, we multiply multiply by 13 until we get 169

13 × 13 = 169

So Jane will make 169 dollars in 13 hours

Answer:

13 Hours

Step-by-step explanation:

$143 ÷ 11hrs = $13/hr that Jane is paid, so to find how many hours she will need to work to make $169

$169 ÷ $13 = 13 hours

Total volume of shape is =144cu.cm

By knowing the length of the cube's edges, we can quickly determine its volume (V). Assume that "a" is the cube's edge length. The product of length, height, and breadth will then be the V. The cube's volume formula is as follows:

Cube Volume = Length× Width× Height

Volume equals= a× a× a =a³

where "a" denotes the cube's side or edges' length.

Length of each cube = 2cm

Volume of each cube=a³

=2³

=8cm³

Total number of cubes=18

Total volume of shape=18×8

=144 cu.cm

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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

Answer:

The first term of the sequence is -3 and the common difference is -1/3. Therefore, the second term of the sequence can be found by adding the common difference to the first term:

second term = first term + common difference

second term = -3 + (-1/3)

second term = -10/3

Similarly, we can find the third term by adding the common difference to the second term:

third term = second term + common difference

third term = -10/3 + (-1/3)

third term = -11/3

And we can find the fourth term by adding the common difference to the third term:

fourth term = third term + common difference

fourth term = -11/3 + (-1/3)

fourth term = -4

Therefore, the first four terms of the sequence are -3, -10/3, -11/3, and -4.

Answer:

[tex]yeah \: 2 + 2 = 4[/tex]

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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Answer:

-2 ( 2x - 3 )

Step-by-step explanation:

We know that,

( + ) × ( + ) = ( + )

( - ) × ( - ) = ( - )

( + ) × ( - ) = ( - )

Accordingly,

-4 ( x - 1 ) + 2

First, solve the brackets. That is, multiply each term inside the brackets by -4.

- 4x + 4 + 2

Combine like terms.

- 4x + 6

You can take the common factor out of the brackets.

-2 ( 2x - 3 )