find the coordinates of the points of intersection of the graph y=13-x with the axes. Find the area of the right triangle formed by this line and the coordinate axis

The rational function that best models the data in the table is: y = 72/x.

To determine the rational function that best models the given data, we can analyze the relationship between the number of full-time staff (x) and the number of days needed to complete the project (y).

Let's examine the data in the table:

People Working, x: 36, 18, 8, 6

Days, y: 2, 4, 9, 12

Based on the data, we can observe that as the number of full-time staff increases, the number of days needed to complete the project decreases. This suggests an inverse relationship between x and y.

One rational function that represents an inverse relationship is of the form y = k/x, where k is a constant. This function implies that as x increases, y decreases, and vice versa.

To find the specific value of k, we can use one of the data points from the table. Let's use the first data point (x=36, y=2):

2 = k/36

To solve for k, we can cross-multiply:

2 * 36 = k

k = 72

Therefore, the rational function that best models the data in the table is:

y = 72/x

This function suggests that the number of days needed to complete the project is inversely proportional to the number of full-time staff. As the number of staff increases, the number of days decreases, following a hyperbolic trend.

Please note that while this rational function provides a reasonable approximation of the data, it may not perfectly fit all the data points. Further analysis and additional data points could refine the model for greater accuracy.

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The function f(x) in standard form is 3x³ - 12x² + 16x -2

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

We have:

The function = f(x)

dividend = (x-1)

quotient = 3x²-9x+7

remainder = 5

Thus, the function f(x) in standard form will be:

f(x) = (x - 1)(3x² - 9x + 7) + 5

Expand the left-hand side:

f(x) = (3x³ - 9x² + 7x - 3x² + 9x - 7) + 5

f(x) = 3x³ - 12x² + 16x -7 + 5

f(x) = 3x³ - 12x² + 16x -2

Therefore, the function f(x) in standard form is 3x³ - 12x² + 16x -2.

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Answer:240

Step-by-step explanation:

divide 480 by the amount of gift everybody gets . 2

Answer:

I think the answer would be 240 people that received a gift.

Step-by-step explanation:

If there were 240 people at the party that received gift then we would check by dividing 480 and 2.

Why?

Simply because if there was 480 gifts and 2 were given to each person then it would only make sense that , that’s as the amount.

(2 persons would have 4 gifts, and if there was 240 people then there would be 480 gift brought to the party)

Answer:

Answer is simple

Step-by-step explanation:

just apply the Pythagoras theorem if u have Hypo nd perpendicular given than B(base) square will be B²=5²-13²

B²=✓144

=12

A rectangular tank measuring 40 cm long, 30 cm wide and 35 cm high was filled with water to a hight of 15 cm. 4800 cm3 of water were poured into water ,The new height of the water in the tank is approximately 19.83 cm.

To find the new height of water in the tank after pouring in 4800 cm³ of water, we can use the concept of ratios.

First, let's calculate the initial volume of water in the tank before pouring in the additional water. The initial volume can be calculated as the product of the length, width, and initial height:

Initial volume = 40 cm * 30 cm * 15 cm = 18,000 cm³

Next, we add the volume of the water poured in:

Total volume = Initial volume + Volume poured in = 18,000 cm³ + 4800 cm³ = 23,800 cm³

To find the new height, we divide the total volume by the base area of the tank (length * width):

New height = Total volume / (Length * Width) = 23,800 cm³ / (40 cm * 30 cm) = 19.83 cm (rounded to two decimal places)

As a result, the tank's new water level is roughly 19.83 centimetres high.

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The chi-square test of independence is a useful statistical method that can be used to test the null hypothesis that there is no association between two categorical variables. When the assumptions of the test are satisfied, this hypothesis can be tested using the chi-square statistic. The following problem can be solved using the chi-square test of independence:

Is gender associated with a person's environmental awareness? Two hundred randomly selected individuals were surveyed about their environmental awareness. Participants were asked about recycling, use of aerosol sprays, and various other environmental concerns.

A point system was developed to score the individuals' responses. Once the points were tallied, individuals were broken up into categories of environmental awareness.

Those with scores of 8 to 10 were considered to be very environmentally aware, scores of 4 to 6 moderately aware, and 3 or less not aware.

The results are shown in the following table: Very environmentally aware Moderately environmentally aware Not environmentally aware Male 302145 Female 423428 We will use a chi-square test of independence to test the null hypothesis that gender is not associated with one's environmental awareness.

We begin by specifying the null and alternative hypotheses: H0: Gender and environmental awareness are independent.

Ha: Gender and environmental awareness are dependent. We choose a significance level of α = 0.05. We can now proceed with the chi-square test of independence.

First, we will calculate the expected frequencies. The expected frequency for each cell can be found by multiplying the row total by the column total and then dividing by the sample size.

The expected frequencies are shown in the following table: Very environmentally aware Moderately environmentally aware not environmentally aware Male 22.5716.6176.81 Female 49.424.826.19 Next, we calculate the chi-square statistic using the formula: X2 = ∑(O - E)2/E where O is the observed frequency and E is the expected frequency.

The chi-square statistic is 18.66. We now need to find the degrees of freedom.

The degrees of freedom for a chi-square test of independence are given by df = (r - 1)(c - 1) where r is the number of rows and c is the number of columns. In this case, there are 2 rows and 3 columns, so df = (2 - 1)(3 - 1) = 2.

We can now use a chi-square distribution table to find the critical value of the chi-square distribution with 2 degrees of freedom and a significance level of 0.05.

The critical value is 5.99. Since the calculated value of the chi-square statistic (18.66) is greater than the critical value (5.99), we reject the null hypothesis.

We have sufficient evidence to conclude that gender and environmental awareness are dependent. Therefore, we can conclude that gender is associated with a person's environmental awareness.

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Step-by-step explanation:

The quadratic expression f(x) = 2x^2 - 9x - 18 can be factored as (2x + 3)(x - 6). So, the missing values in the given expression (2x + [?])(x - [ ]) are 3 and 6, respectively.

Answer:

(2x + 3)(x -6)

Step-by-step explanation:

2x² -9x -18

2 × -18 = -36

Find factors of -36 which you multiply will give -36 but when same factors are added will give -9.

-12 × 3 = -36

-12 + 3 = -9

2x²-12x +3x -18

2x(x - 6) + 3(x -6)

(2x + 3)(x -6)

Answer:

Step-by-step explanation:

no

Answer:

$16,453.80

Step-by-step explanation:

5 × 12 months = 60 months (the time she payed the monthly payments in months)

219.23 × 60 = 13, 153.8

13,153.8+3,300= $16,453.80.

None of the answer choices (2,4), (2,-4), (4,2), or (4,-2) are applicable to the function f(x) = 3/(x-4) + 2. The function does not have a center point in the traditional geometric sense. Option E.

he function f(x) = 3/(x-4) + 2 does not have a center in the traditional sense. The concept of a center is typically associated with geometric figures such as circles or ellipses.

The function f(x) = 3/(x-4) + 2 represents a rational function. It does not have a central point or location like a circle, which has a center at (h, k). In this case, we are dealing with a rational expression involving x.

The equation f(x) = 3/(x-4) + 2 describes a vertical shift of the graph of the function 3/(x-4) by 2 units upward. However, this vertical shift does not correspond to a center point.

The function f(x) = 3/(x-4) + 2 does not have a center point. The concept of a center is not applicable in this context as it is commonly associated with geometric figures rather than rational functions. Option E is correct.

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Answer:

204

Step-by-step explanation:

Sum: 816

Count: 4

Median: 199

Geometric Mean: 202.92942642991

Largest: 238

Smallest: 180

Range: 58

Certainly! I can help you with trigonometry. To find the lengths of a triangle and the angles, we typically use the trigonometric ratios: sine, cosine, and tangent. These ratios relate the angles of a right triangle to the lengths of its sides.

To find the lengths of a triangle:

To find the angles of a triangle:

Remember to use the appropriate trigonometric ratio or trigonometric formula depending on the given information. Also, keep in mind the restrictions and conventions for angles and sides in triangles, such as the Pythagorean theorem and the sum of angles in a triangle.

I hope this helps! Good luck with your exam. If you have any specific questions or examples, feel free to ask.

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Answer:

the volume of 8 identical cubes is approximately 386.744 cm³.

Step-by-step explanation:

Let's assume the side length of a cube is represented by "s."

The total shaded area of two identical cubes is given as 162 cm². Since there are two cubes, each cube contributes half of the total shaded area.

Area of a single cube = (Total shaded area) / 2

= 162 cm² / 2

= 81 cm²

The area of each face of a cube is equal to the side length squared. Therefore, we can set up the equation:

6s² = 81 cm²

Dividing both sides by 6:

s² = 81 cm² / 6

= 13.5 cm²

Taking the square root of both sides:

s = √(13.5 cm²)

≈ 3.674 cm (rounded to three decimal places)

Now that we know the side length of a single cube, we can calculate the volume of 8 identical cubes.

Volume of a single cube = s³

= (3.674 cm)³

≈ 48.343 cm³ (rounded to three decimal places)

Volume of 8 cubes = Volume of a single cube * 8

= 48.343 cm³ * 8

= 386.744 cm³

The solution for the system of equations is (x, y) = B. (3, -5).

The correct option is B. (3, -5).

To find the solution for the system of equations:

{4x + y = 7

{2y + 3 = 3x - 16

We can solve it using the method of substitution or elimination. Let's use the method of elimination:

First, let's multiply the second equation by 2 to eliminate the variable y:

2(2y + 3) = 2(3x - 16)

4y + 6 = 6x - 32

Rearranging this equation, we get:

6x - 4y = 38 ----(1)

Now we have the system of equations:

4x + y = 7 ----(2)

6x - 4y = 38 ----(1)

Next, let's multiply equation (2) by 4 to eliminate the variable y:

4(4x + y) = 4(7)

16x + 4y = 28

Now we have the system of equations:

16x + 4y = 28 ----(3)

6x - 4y = 38 ----(1)

Adding equations (3) and (1) eliminates the variable y:

(16x + 4y) + (6x - 4y) = 28 + 38

22x = 66

x = 66/22

x = 3

Substituting the value of x into equation (2), we can solve for y:

4(3) + y = 7

12 + y = 7

y = 7 - 12

y = -5

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The Growth functions are:

[tex]N = 2000(1.12)^{t}[/tex]

[tex]N = N_{0} e^{kt}[/tex] where k > 0

The Decay Functions are:

[tex]A = A_{0}(0.95)^{t}[/tex]

[tex]N = N_{0} e^{kt}[/tex] where k < 0

[tex]A = Pe^{-rt}[/tex]

[tex]A = A_{0}(1 - \frac{r}{n})^{nt}[/tex]

Exponential growth and decay function:

Exponential growth refers to when the quantity is increasing over time, while exponential decay refers to when the quantity is decreasing over time.

The general form of growth functions is:

y = [tex]ab^{kt}[/tex]

where: a ≠ 0 and b ≠ 0

The conditions for the functions are:

1) When b > 1, k > 0, it represents exponential growth function

2) When 0 < b < 1, k > 0, it represents exponential decay function

3) When b > 1, k < 0, it represents exponential decay function

Thus:

Growth functions are:

[tex]N = 2000(1.12)^{t}[/tex]

[tex]N = N_{0} e^{kt}[/tex] where k > 0

Decay Functions are:

[tex]A = A_{0}(0.95)^{t}[/tex]

[tex]N = N_{0} e^{kt}[/tex] where k < 0

[tex]A = Pe^{-rt}[/tex]

[tex]A = A_{0}(1 - \frac{r}{n})^{nt}[/tex]

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Alright, so let's assume your phone number has no repeated digits. The first task is to select the first digit of the two-digit number. Since phone numbers don't start with zero, you have 9 choices (1 through 9).

The next task is to select the second digit. Because we've already used one digit, and we're assuming there are no repeats in the phone number, we have 9 choices left (0 and the 8 digits that were not selected first).

That gives us a total of 9 * 9 = 81 possible two-digit numbers.

Now, your phone number has a specific first two digits, right? There's only one such combination that matches your phone number.

So the probability that the two-digit number you've selected matches the first two digits of your phone number is 1 in 81, or 1/81.

Think of it this way, my friend: Imagine you have a bag with 81 marbles, each marble has a unique two-digit number on it. You close your eyes and reach into the bag to pick a marble. The chance that you'll pick out the marble with your phone number's first two digits is just like finding one special marble in a bag of 81. It's quite the quest, isn't it? But that's what makes the game of probability so interesting!

The ratio of 6/5 and 8/7 is 21/20

A ratio is a relationship between two things when it is expressed in numbers or amounts.

For example if the ratio of boys to girls In a class is 4: 5 , this means that there are 4 boys to 5 girls in the class , i.e for every 4 boys there are 5 girls.

For example if two boys are to share 10 mangoes in the ratio 1:4 , this means one will take 2 and the other will take 8

2:4 can also be expressed as 2/4 = 1/2

Similarly, 6/5 : 8/7

= 6/5)/8/7

= 6/5 × 7/8

= 42/40

= 21/20

Therefore the ratio of 6/5 : 8/7 is 21/20

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Answer: $204

Step-by-step explanation:

203 plus 195 plus 180 plus 238 equals 816

816 divided by 4 equals 204

203+195=398

398+180=578

578+238=816

816/4=204

Answer:

No

Step-by-step explanation:

Slope is [tex]\frac{-9-5}{-12-8}=\frac{-14}{-20}=\frac{7}{10}[/tex]

[tex]y-y_1=m(x-x_1)\\y-5=\frac{7}{10}(x-8)\\y-5=\frac{7}{10}x-\frac{28}{5}\\10y-50=7x-56\\10y+6=7x\\6=7x-10y[/tex]

Therefore, 7x-10y=3 would not be a good model, but it's very close

The value of x and the measure of the intercepted arc of the circle is 2 and 140 degrees respectively.

An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.

The relationhip between an an inscribed angle and intercepted arc is expressed as:

Inscribed angle = 1/2 × intercepted arc.

From the image:

Inscribed angle Q = 70 degrees

Intercepted arc = 69x + 2

Value of x = ?

To solve for x, plug the given values into the above formula and solve for x:

Inscribed angle = 1/2 × intercepted arc.

70 = 1/2( 69x + 2 )

Multiply both sides by 2

2 × 70 = 2 × 1/2( 69x + 2 )

140 = 69x + 2

140 - 2 = 69x

138 = 69x

x = 138/69

x = 2

Now, to find the value of the intercepted arc:

Intercepted arc = 69x + 2

Plug in x = 2

Intercepted arc = 69( 2 ) + 2

Intercepted arc = 138 + 2

Intercepted arc = 140 degrees.

Therefore, the Intercepted arc measure 140 degrees.

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Joseph needs to determine the thesis and topic sentences. Each topic sentences will explain one aspect of the thesis. Option C

To start making sense of the reading on the physical laws that keep airplanes in the air, Joseph can follow a systematic approach to enhance his understanding and alleviate his nervousness about flying. While options (a) and (b) might have some merit, option (c) is a more effective strategy for comprehending and synthesizing the information.

Option (a) suggests repeatedly reading the article until Joseph knows it well. While repetition can help reinforce understanding, it might not be the most efficient method for Joseph.

Reading the same material multiple times without actively engaging with the content may not result in deeper comprehension. It's important for Joseph to actively process the information and apply critical thinking.

Option (b) suggests reading the entire article once and then bringing questions to his professor during the next class period. While seeking clarification from the professor is beneficial, reading the article only once might not provide a solid foundation for asking insightful questions. Joseph could benefit from a more comprehensive understanding of the material before seeking clarification.

Option (c) is a more effective approach. Joseph should begin by identifying the thesis and topic sentences of the article. The thesis statement will outline the main idea or argument, while the topic sentences will provide an overview of the key points discussed in the article.

Once Joseph has identified the thesis and topic sentences, he can focus on each topic sentence individually. By breaking down the content into manageable segments, Joseph can ensure that he comprehends each aspect of the thesis before moving on to the next.

Moreover, Joseph can actively engage with the material by taking notes, summarizing each section in his own words, and making connections to real-world examples or personal experiences. This active approach will enhance his understanding and help him internalize the concepts.

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Answer:

x = 1/2

Step-by-step explanation:

-3x + 1 + 10x = x + 4

7x + 1 = x + 4

6x + 1 = 4

6x = 3

x = 3/6

x = 1/2

Answer:

the solution to the equation is x = 1/2.

Step-by-step explanation:

To solve the equation -3x + 1 + 10x = x + 4, we can start by simplifying both sides of the equation:

Combine like terms on the left side:

(-3x + 10x) + 1 = x + 4

7x + 1 = x + 4

Next, we want to isolate the x term on one side of the equation. We can do this by subtracting x from both sides and subtracting 1 from both sides:

7x - x + 1 - 1 = x - x + 4 - 1

6x = 3

Finally, to solve for x, we divide both sides of the equation by 6:

6x/6 = 3/6

x = 1/2

So, the solution to the equation is x = 1/2.

The kinetic energy of this car is equal to 77160.49 Joules.

In Mathematics, the kinetic energy of a physical object can be calculated by using the following equation (formula):

K.E = 1/2 × mv²

Where:

Note: 50 km/h to m/s = 50 × 1000/3600 = 13.89 m/s

By substituting the given parameters into the formula for the kinetic energy of a physical object, we have the following:

Kinetic energy, K.E = 1/2 × 800 × 13.89²

Kinetic energy, K.E = 400 × 192.90

Kinetic energy, K.E = 77160.49 Joules.

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Complete Question:

An 800 kg car travels at 50 km/h, what will its kinetic energy be?

Answer:

AA Postulate

Step-by-step explanation:

To prove that two triangles are similar in problem 6-7, we would use the Angle-Angle (AA) postulate. This postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

The system has infinitely many solutions, and they can be expressed in the form (x, y) = (x, x - 27), where x can take on any real value.

The given system of equations is:

x - 27 - 8 = 0

x - 27 = 8

To solve this system, let's start by simplifying the second equation:

x - 27 = 8

Adding 27 to both sides, we get:

x = 35

Now we can substitute the value of x into the first equation

x - 27 - 8 = 0

35 - 27 - 8 = 0

8 - 8 = 0

0 = 0

We see that the equation is satisfied, which means that the system is consistent. However, the system is not unique because it has infinitely many solutions. This is because when we simplified the second equation, we obtained a value for x (x = 35) that satisfies both equations.

The system can be represented by the equation y = x - 27. Since x can take on any value, y will also vary accordingly. Therefore, the solutions to the system can be written as (x, y) = (x, x - 27), where x is any real number.

In summary, the system has infinitely many solutions, and they can be expressed in the form (x, y) = (x, x - 27), where x can take on any real value.

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Answer:  

Step-by-step explanation:

The degree is 4 the leading coefficient is even/positive.  There are 3 distinct real 0's and 3 relative extreme values

Explanation:

4th degree.   Degree is the highest exponent.  The number of 0's (times it hits the curve)tells you the degree.  The curve goes through the x 2 times, which means 2 x's. Then it bounces off x 1 time which means there are 2 x's there too but because this one bounces off it means it's not a distint solution it's a multiplicity ex (x-3)².  So that accounts for 4 solutions

Even/positive coefficient.  That's the first number in the equation.  Because it's facing up it's a positive but all the ends are both facing up so that tells you it's even.  Think of a parabola that is an even function, this follows those rules too.

3 distinct zeroes.    This is explained in 4th degree.   Zeroes are solutions, when it hits x axis.  Goes through x 2 times and bounces once.  So there are 3 distinct zeroes

3 relative extreme values. This is how many "mini" max and mins you have.  

a. The new technology leads to an increase in the supply of beginner-level violins, resulting in a rightward shift of the supply curve. The demand curve remains unchanged unless otherwise specified.

b. The new technology increases consumer surplus by $2400, as represented by the shaded area between the original demand curve and the new demand curve up to the new equilibrium quantity.

c. The new technology increases producer surplus by $2400, represented by the shaded area between the original supply curve and the new supply curve up to the new equilibrium quantity.

d. The new technology increases total surplus by $4800, which is the sum of the increase in consumer surplus and the increase in producer surplus.

a. To illustrate the effect of the new technology on the supply and demand of beginner-level violins, we need to consider the following:

Supply: The new technology allows beginner-level violin producers to make violins at a substantially lower marginal cost while maintaining the same quality. This means that the supply of beginner-level violins will increase. We can show this on the graph by shifting the supply curve to the right.

Demand: The demand for beginner-level violins will depend on factors other than the new technology. If there is no change in demand, the demand curve will remain the same. However, if there is an increase in demand due to factors such as increased interest in learning the violin, we would see a shift in the demand curve to the right.

By shifting the supply curve to the right or the demand curve to the right, or both, we can represent the effect of the new technology on the market for beginner-level violins.

b. The increase in consumer surplus can be calculated by finding the area of the triangle formed by the original demand curve, the new demand curve, and the new equilibrium quantity of violins. This represents the additional benefit consumers receive from the lower price due to the new technology.

In the given graph, the increase in consumer surplus is represented by the shaded area between the original demand curve and the new demand curve, up to the new equilibrium quantity. The dollar value of this increase can be calculated by multiplying the increase in quantity by the average difference in price between the original and new equilibrium.

c. The increase in producer surplus can be calculated by finding the area of the triangle formed by the original supply curve, the new supply curve, and the new equilibrium quantity of violins. This represents the additional profit that producers receive from the higher quantity sold at the same or slightly reduced price due to the lower marginal cost from the new technology.

In the given graph, the increase in producer surplus is represented by the shaded area between the original supply curve and the new supply curve, up to the new equilibrium quantity. The dollar value of this increase can be calculated by multiplying the increase in quantity by the average difference in price between the original and new equilibrium.

d. The increase in total (or social) surplus is the sum of the increase in consumer surplus and the increase in producer surplus. In this case, the increase in total surplus would be the sum of the increases calculated in parts b and c.

Therefore, the increase in total surplus due to the new technology is represented by the shaded area between the original supply and demand curves and the new supply and demand curves, up to the new equilibrium quantity. The dollar value of this increase can be calculated by adding the dollar values of the increase in consumer surplus and the increase in producer surplus. In this example, the increase in total surplus is $4800.

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Answer:

3

Step-by-step explanation:

3