PLEASE HELP!! Find the area of the figure.

To use the Integral Test, we need to find an integral that is comparable to the series. We can do this by using a basic comparison test and comparing it to the p-series with p=2.

n^2 / (n^3 + 3) < n^2 / n^3 = 1/n
The series 1/n is a divergent p-series with p=1, so we can conclude that the original series is also divergent.
To find the corresponding integral, we can integrate the function 1/n^2:
∫(n=1 to ∞) 1/n^2 dn = [-1/n] (n=1 to ∞) = 1/1 - 0 = 1
Since the improper integral converges to 1, we can conclude that the infinite series is divergent by the Integral Test.
Hi there! To use the Integral Test to determine whether the given infinite series is convergent, first rewrite the series as a function:
f(x) = x^2 / (x^3 + 3)

Next, we need to check that the function is continuous, positive, and decreasing on the interval [1, ∞). This function satisfies these conditions.
Now, we will calculate the improper integral:
∫(from 1 to ∞) (x^2 / (x^3 + 3)) dx
Let's use substitution: u = x^3 + 3, so du = 3x^2 dx, and x^2 dx = (1/3)du.
Now, the integral becomes:
(1/3) ∫(from 1 to ∞) (1/u) du
This integral is the same as the integral of 1/u from 1 to ∞, which is a well-known improper integral that diverges (ln(u) evaluated from 1 to ∞ results in ∞).

Therefore, by the Integral Test, the infinite series ∑(from n=1 to ∞) (n^2 / (n^3 + 3)) diverges. So the correct answer is B. Diverges.

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The coordinates of the resulting point, R′ are R' = (-9, -2)

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

The point R(-2, 9) is rotated 90° clockwise around the origin.

This means thar

R = (-2, 9)

Rotation rule = 90° clockwise around the origin.

The rotation rule of 90° clockwise around the origin is

(x,y) becomes (y,-x)

So, we have

R' = (y, -x)

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

R' = (-9, -2)

Hence, the coordinates of the resulting point, R′ are R' = (-9, -2)

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Answer:

100π or ≈ 314.1592

Step-by-step explanation:

Area of a circle formula: A = πr²

A = π(10)²

A = π(100)

A = 100π ≈ 314.1592

Answer:

100pi

Step-by-step explanation:

pi*radius^2=area

pi*10^2=100pi

Answer:

BCA

Step-by-step explanation:

The interior angle measures at stages A, B, and C are approximately 71.7 degrees, 133.4 degrees, and 175.0 degrees, respectively. Therefore, the angles in descending order are C, B, and A.

Let's label the stages A, B, and C. To find the interior angles at each stage, we can use the Law of Cosines:

cos(A) = (b^2 + c^2 - a^2) / 2bc

cos(B) = (c^2 + a^2 - b^2) / 2ca

cos(C) = (a^2 + b^2 - c^2) / 2ab

where a, b, and c are the distances between the centers of the stages.

Using the given distances, we have:

a = 100, b = 135, c = 210

cos(A) = (135^2 + 210^2 - 100^2) / (2*135*210) ≈ 0.309

cos(B) = (210^2 + 100^2 - 135^2) / (2*210*100) ≈ -0.692

cos(C) = (100^2 + 135^2 - 210^2) / (2*100*135) ≈ -0.905

To find the interior angles, we can take the inverse cosine (also known as arccosine) of each value:

A ≈ 71.7 degrees

B ≈ 133.4 degrees

C ≈ 175.0 degrees

So the interior angle measures at stages A, B, and C are approximately 71.7 degrees, 133.4 degrees, and 175.0 degrees, respectively. Therefore, the angles in descending order are C, B, and A.

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The total cost of producing 100 bar stools using the left-rectangle approximation with five rectangles is approximately $200.

The marginal cost function for producing the x-th item of a certain brand of bar stool is given by MC(x) = 20 - 0.5x, where 0 ≤ x ≤ 100. To estimate the total cost of producing 100 bar stools using the left-rectangle approximation with five rectangles, we first need to calculate the width of each rectangle.

The width of each rectangle is (100 - 0) / 5 = 20.

Now, we will evaluate the marginal cost function at the left endpoints of each rectangle:
MC(0) = 20 - 0.5(0) = 20
MC(20) = 20 - 0.5(20) = 10
MC(40) = 20 - 0.5(40) = 0
MC(60) = 20 - 0.5(60) = -10
MC(80) = 20 - 0.5(80) = -20

Next, multiply each value by the width (20) and sum the results to approximate the variable cost:
Variable cost ≈ 20(20) + 10(20) + 0(20) + (-10)(20) + (-20)(20) = 400 + 200 - 200 - 400 = 0

Finally, add the fixed cost of $200 to the variable cost:
Total cost ≈ $200 + $0 = $200

So, the total cost of producing 100 bar stools using the left-rectangle approximation with five rectangles is approximately $200.

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The cost of owning and operating the machine for one more year is approximately $11,160.71.

To calculate the cost of owning and operating the machine for one more year, we need to consider both the operating costs and the decrease in salvage value.

The operating costs for one more year will be $3,500.

To calculate the decrease in salvage value, we need to know the salvage value of the machine after 4 years of use. If the salvage value decreased by $4,000 each year, then after 4 years the salvage value will have decreased by $16,000. Therefore, the salvage value of the machine after 4 years is:

Salvage value after 4 years = Initial salvage value - Total decrease in salvage value

Salvage value after 4 years = $40,000 - $16,000

Salvage value after 4 years = $24,000

To calculate the cost of owning and operating the machine for one more year, we need to consider the difference between the salvage value at the end of the additional year and the salvage value after 4 years. Assuming a straight-line depreciation model, the salvage value of the machine after one more year will be:

Salvage value after one more year = Salvage value after 4 years - (4 x $4,000)

Salvage value after one more year = $24,000 - $16,000

Salvage value after one more year = $8,000

To calculate the cost of owning and operating the machine for one more year, we need to calculate the present value of the difference between the salvage values, plus the operating costs for one more year. Assuming an effective annual interest rate of 12%, the present value can be calculated using the formula:

PV = FV / (1 + r[tex])^n[/tex]

where PV is the present value, FV is the future value, r is the effective annual interest rate, and n is the number of years.

The future value of the salvage value difference plus the operating costs for one more year is:

FV = Salvage value after one more year - Salvage value after 4 years + Operating costs for one more year

FV = $8,000 - $24,000 + $3,500

FV = -$12,500

(Note that the negative value indicates a cost.)

Plugging in the values, we get:

PV = -$12,500 / (1 + 0.12[tex])^1[/tex]

PV = -$11,160.71

Therefore, the cost of owning and operating the machine for one more year is approximately $11,160.71.

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If st - sv, m∠sut - w + °10, and m∠suv =3w, the measure of angle SUT is 52.5°.

Given the information provided, we can set up the following equations:

1) m∠SUT + m∠SUV = 180° (since they are supplementary angles)
2) m∠SUT = w + 10°
3) m∠SUV = 3w

Now we can substitute equations (2) and (3) into equation (1):

(w + 10°) + (3w) = 180°

Combining like terms, we get:

4w + 10° = 180°

Now, subtract 10° from both sides:

4w = 170°

Finally, divide both sides by 4:

w = 42.5°

Now we can find m∠SUT by substituting the value of w back into equation (2):

m∠SUT = 42.5° + 10°

m∠SUT = 52.5°

So, the measure of angle SUT is 52.5°.

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The diameter of approximately 3.58.

The circumference of a circle is the distance around its edge or perimeter. The diameter of a circle is the distance across it, passing through the center. These two measurements are related by the mathematical constant pi (π), which is the ratio of the circumference of any circle to its diameter.

The formula to find the diameter of a circle from its circumference is:

diameter = circumference/pi

So, if you know the circumference of a circle, you can simply divide it by pi to find the diameter. In the case of the given circumference of 11.27, dividing it by pi gives us the diameter of approximately 3.58.

It's important to note that the diameter of a circle is twice the length of its radius, which is the distance from the center of the circle to its edge. So, if you know the diameter of a circle, you can find its radius by dividing the diameter by 2:

radius = diameter / 2

In this case, the radius of the circle would be approximately 1.79 (since 3.58 / 2 = 1.79).

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Answer:

1.6 × 10^4

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

In order for it to be a parallelogram, the 2 lines must be equal.

2x=3x-6

2x - 3x = 3x - 3x -6

-1x = -6

x = 6/1

x = 6

The new coordinate of the vertex after dilation is (-5, -3).

To find the new coordinate, you'll need to use the given scale factor of 1/3 and apply it to the original vertex coordinates (-15, -9). Here's a step-by-step explanation:

1. Identify the original vertex coordinates: (-15, -9).
2. Identify the scale factor for dilation: 1/3.
3. Apply the scale factor to the x-coordinate: (-15) * (1/3) = -5.
4. Apply the scale factor to the y-coordinate: (-9) * (1/3) = -3.
5. The new coordinates after dilation are (-5, -3).

By following these steps, you can find the new coordinates of the vertex after dilation at the origin using the given scale factor.

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Answer: So, according to this prediction, a book with 19 chapters would have approximately 950 pages. However, keep in mind that this is just a prediction based on the trend line, and there may be some variability in the actual number of pages for a book with 19 chapters.

Step-by-step explanation:

Unfortunately, I cannot see the scatter plot you are referring to. However, I can explain how to use a trend line to predict the number of pages in a book with 19 chapters.

A trend line is a line that represents the general direction or tendency of the data in a scatter plot. To use a trend line to predict the number of pages in a book with 19 chapters, you would first need to determine the equation of the trend line.

This equation usually takes the form y = mx + b, where y is the dependent variable (in this case, the total number of pages), x is the independent variable (in this case, the number of chapters), m is the slope of the line, and b is the y-intercept (the value of y when x is 0).

Once you have the equation of the trend line, you can plug in the value x = 19 and solve for y to get the predicted number of pages in a book with 19 chapters.

For example, if the equation of the trend line is y = 50x + 200, then the predicted number of pages for a book with 19 chapters would be:

y = 50(19) + 200

y = 950

So, according to this prediction, a book with 19 chapters would have approximately 950 pages. However, keep in mind that this is just a prediction based on the trend line, and there may be some variability in the actual number of pages for a book with 19 chapters.

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The statement about the chances of occurrence of nonmoving violations more on a weekend than on a weekday in past ten years is cannot be answered using only the information in the database. So, option(b) is provide the right answer.

Database: The database is a large collection of data and it is used to store and retrieve the accordingly. It has an organization of a certain amount of data that needs and it contains. We have a database of all traffic tickets that were issued over the past ten years in a city. The informations including are

2) nonmoving violations

We have to recongise the statement which is not answering by the above informations in database. First statement is can be answerable, because we have data of year in which tickets are issued. Similarly, statements third and fourth related to data of tickets issued in month and year in past ten years. So, both are answerable statements. Therefore, the second statement

is cannot be answerable here.

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Complete question:

a city maintains a database of all traffic tickets that were issued over the past ten years. the tickets are divided into the following two categories. moving violations nonmoving violations the data recorded for each ticket include only the following information. the month and year in which the ticket was issued the category of the ticket which of the following questions cannot be answered using only the information in the database? responses

a) have the total number of traffic tickets per year increased each year over the past ten years?

b) in the past ten years, were nonmoving violations more likely to occur on a weekend than on a weekday?

c) in the past ten years, were there any months when moving violations occurred more often than nonmoving violations?

d) in how many of the past ten years were there more than one million moving violations?

The type of transformation shown is a vertical transformation

In mathematics, a vertical translation refers to a transformation of a function or graph that involves moving it up or down along the y-axis without changing its vertical transformation.

From the attached figure, we can see that the polygons are moved up or down to map them to one another

This means that the transformation is a vertical transformation

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Complete question

Use the image to determine the type of transformation shown.

Image of polygon ABCD and a second polygon A prime B prime C prime D prime below.

Vertical translation

Reflection across the x-axis

180° counterclockwise rotation

Horizontal translation

To solve the equation [tex]2^{3-x} + 2^{x+1} = 17[/tex] and the equation log x + log (x+3) = 1, We get the solution to the system of equations is x = 2. To check if x = 2 satisfies the first equation [tex](2^{3-x} + 2^{x+1} = 17).[/tex]

Solve the first equation, [tex]2^{3-x} + 2^{x+1} = 17.[/tex] Rewrite the equation as[tex]2^{3-x} = 17 - 2^{x+1}.[/tex] Take the logarithm of both sides (base 2): [tex]3-x = log2(17 - 2^{x+1})[/tex]. Rewrite the equation as [tex]x = 3 - log2(17 - 2^{x+1}).[/tex]

Solve the second equation, log x + log (x+3) = 1. Combine the logarithms: log(x(x+3)) = 1. Remove the logarithm by taking the exponent of both sides: x(x+3) = 10. The equation: x^2 + 3x = 10. Rearrange to form a quadratic equation:[tex]x^2 + 3x - 10 = 0.[/tex]

Factor the quadratic equation: (x+5)(x-2) = 0. Set each factor to zero: x+5 = 0 or x-2 = 0. Solve for x: x = -5 or x = 2. The solutions. Check if x = -5 satisfies the first equation [tex](2^{3-x} + 2^{x+1} = 17).[/tex]([tex]2^{3-x} + 2^{x+1} = 17)[/tex]. If it does not, discard it.  

The solution to the system of equations is x = 2.

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Answer:

o MDC de 6 e 9 é 3.

O produto de dois números é 54 e o seu MMC é 18. Precisamos encontrar o MDC desses dois números.

Primeiro, encontramos os dois números cujo produto é 54: 6 e 9.

Então, fatoramos cada número em seus fatores primos: 6 = 2 x 3 e 9 = 3 x 3.

O MDC de 6 e 9 é o produto dos fatores primos comuns, elevados à menor potência. Neste caso, o único fator primo comum é 3, elevado à primeira potência.

Portanto, o MDC de 6 e 9 é 3.

The coordinates of each vertex are: P(8,4) Q(10, 4) R(13,-1) S(8,-1) then the length of side PS is 0 units.

Side PS is the bottom base of trapezoid PQRS. To find its length, we need to calculate the horizontal distance between the x-coordinates of points P and S.

The x-coordinate of point P is 8, and the x-coordinate of point S is also 8. Therefore, the horizontal distance between these two points is 0. So, the length of side PS is 0 units.

The answer is (A) 2 is not correct because the length of side PS cannot be negative or less than zero, and the length of the other base of the trapezoid (QR) is 2 units, which is not equal to the length of side PS.

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As a general guideline, the research hypothesis should be stated as the alternative hypothesis, which is the statement that researchers are trying to support or prove.

The research hypothesis is a statement that describes the expected relationship between variables or the expected difference between groups in a research study. It should be based on a clear and specific research question, and it should be testable using appropriate statistical methods.

In other words, the research hypothesis should be a clear and concise statement that proposes a relationship or difference between variables that can be tested through data analysis. It should also be framed in a way that allows for the rejection or acceptance of the hypothesis based on the results of the study.

The null hypothesis, on the other hand, is the statement that there is no significant relationship or difference between variables. It serves as the default assumption until evidence is provided to support the alternative hypothesis.

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A research hypothesis should be stated as the predicted outcome of the study. It's often a declarative sentence that shows the relationship between variables in a study. The research hypothesis is often contrasted with a null hypothesis, which claims no significant relationship between the study's variables.

In general, a research hypothesis should be stated as the predicted outcome of the study. A research hypothesis is usually written in a declarative sentence format and states the relationship between variables in the study. For example, if your research is about studying the impact of amount of study time on test scores, your hypothesis could be: 'Students who spend more time studying will have higher test scores.'

The research hypothesis is often contrasted with a null hypothesis, which states there will be no significant relationship between the study's variables. In our example, the null hypothesis would be: 'The amount of study time will not impact the test scores significantly.' Remember, a research hypothesis should always be testable through research methods.

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Answer:

Solve for these and you'll find it! :D (Surface Area for all)
The answer is:
A: 6(12)^2 (it's a cube)
B: 2(6.4 x 15.2 + 15.2 x 10.5 + 6.4 x 10.5) (it's a rectangular prism)
C: 6(3x - 1)^2 (it's a cube)
D: 2(pi)(radius)(height) + 2(pi)(radius^2) (it's a cylinder)

Answer:

Step-by-step explanation:

(2-5)3=-9. (-9)5 =-45

The estimated volume of the snowpack in the park is approximately 1.94 billion cubic meters.

To estimate the volume of the snowpack in the park, we need to calculate a double integral of the function d(x, y) over the domain D:

V = ∬_D d(x, y) dA

We can evaluate this integral by using iterated integrals. First, we integrate with respect to x over the interval [0, 30] (since the line y = 180 - 2x intersects the x-axis at x = 90):

V = ∫_0^30 (∫_0^(180-2x) (-0.024x + 0.012y + 1.2) dy) dx

Simplifying the inner integral:

V = ∫_0^30 [-0.024xy + 0.006y^2 + 1.2y]_0^(180-2x) dx

V = ∫_0^30 (-0.432x^2 + 21.6x - 5832) dx

Simplifying the integral:

V = [-0.144x^3 + 10.8x^2 - 5832x]_0^30

V = -0.144(30)^3 + 10.8(30)^2 - 5832(30)

V = 1.942592 billion cubic meters (rounded to nine decimal places)

Therefore, the estimated volume of the snowpack in the park is approximately 1.94 billion cubic meters.

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The substitution u = 3x transforms the integral 31 de into: ∫(3/31)du

This is because the substitution u = 3x implies that du/dx = 3, which means dx = (1/3)du. Substituting this expression for dx in the original integral and using the fact that e is a constant, we have:

∫e^(3x) dx = ∫e^(u) (1/3)du = (1/3)∫e^(u)du = (1/3)e^u + C

where C is the constant of integration. So the final answer in terms of x is:

(1/3)e^(3x) + C

which is equivalent to the original integral. This is an example of how the technique of substitution can be used to simplify an integral and make it easier to solve. It is also a common step in many integral transforms.

When performing an integral with substitution, you transform the original integral into a new one with a different variable. In your case, the substitution is given as u = 3x.

To apply substitution, first find the derivative of the substitution equation with respect to x, which is du/dx = 3. Then, solve for dx: dx = du/3.

Now, substitute u = 3x into the original integral and replace dx with du/3. The transformed integral will have the new variable u and a constant factor 1/3.

Without knowing the specific function you're trying to integrate (it seems like "31 de" might be a typo), I cannot provide the exact transformed integral.

However, I hope this explanation of substitution and transforming integrals is helpful. Please feel free to provide more information or clarify your question if you need further assistance!

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The distance between the points (-3, -6) and (5, 0) is 10 units.

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.

To determine the distance between two points in a coordinate plane, you can use the distance formula, which is derived from the Pythagorean theorem.

The distance formula for two points (x₁, y₁) and (x₂, y₂) in a coordinate plane is:

Distance = √{(x₂ - x₁)² + (y₂ - y₁)²}

Given the two points (-3, -6) and (5, 0), we can plug in the values into the distance formula as follows:

x₁ = -3, y₁ = -6 (coordinates of the first point)

x₂ = 5, y₂ = 0 (coordinates of the second point)

Distance = √{(x₂ - x₁)² + (y₂ - y₁)²}

= √{(8)² + (6)²}

= √{(64) + (36)

= √100

= 10

Hence, the distance between the points (-3, -6) and (5, 0) is 10 units.

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The volume of the campfire pyramid is approximately 8,175 cubic centimeters. This is found by using the formula for the volume of a pyramid and plugging in the given values for the height and base area of the pentagonal pyramid.

The formula for the volume of a pyramid is

V = (1/3) * base_area * height

where V is the volume, base_area is the area of the base, and height is the height of the pyramid.

In this case, the height of the pyramid is given as 27 cm, and the base area is given as 965 square cm. To find the volume, we can plug these values into the formula

V = (1/3) * 965 cm² * 27 cm

V = 8,175 cm³

Therefore, the volume of the campfire pyramid is 8,175 cubic centimeters.

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There are 715 five-digit positive integers where the digits are non-increasing from left to right.

Here, we have to find the number of five-digit positive integers where the digits are non-increasing from left to right, you can think of this as selecting five digits (from 0 to 9) with repetition allowed, while ensuring that the selected digits are arranged in a non-increasing order.

This is essentially a combinations with repetition problem.

For each digit, there are 10 choices (0 to 9). Since repetition is allowed, you can use a stars and bars approach, where you place 4 bars among 10 possible positions (one for each digit choice) to separate the digits into groups.

The number of ways to arrange 5 digits with repetition allowed is given by the formula:

Number of arrangements = (n + k - 1) choose k,

where n is the number of digits (10 choices) and k is the number of bars (4). Plugging in the values:

Number of arrangements = (10 + 4 - 1) choose 4 = 13 choose 4 = 715.

So, there are 715 five-digit positive integers where the digits are non-increasing from left to right.

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BD = CA is proved using the Pythagorean theorem.

It is a quadrilateral that has one pair of parallel sides and a height.

The area is calculated as 1/2 x the sum of the parallel sides x height.

Examples:

Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.

Area = 1/2 x (3 + 4) x 5

Area = 1/2 x 7 x 5

Area = 35/2 = 17.5 cm^2

We have,

From the trapezium ABCD,

BA = CD ______(A)

Now,

We can have two triangles:

ΔABD and ΔACD

Using the Pythagorean theorem.

BD² = AB² + AD² _____(1)

And,

CA² = CD² + AD² ______(2)

From (1), (2), and (A).

BD² = BA² + AD²

CA² = BA² + AD²

This means,

BD² = CA²

BD = CA

Proved

Thus,

BD = CA can be Proven as above.

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Answer:

Step-by-step explanation:

The statement "Dilation 2 has a scale factor 2" (option b).

Dilation is a transformation that changes the size of an object but not its shape. It is a type of transformation that enlarges or reduces an object by a certain factor called the scale factor. The scale factor is a ratio of the size of the dilated image to the size of the original image.

Now, let's talk about the scale factor for each dilation you asked about.

For dilation 1, the scale factor is 1. This means that the size of the dilated image is the same as the size of the original image. In other words, there is no change in size. This type of dilation is often referred to as the identity transformation because it doesn't change the shape or size of the original object.

For dilation 2, the scale factor is 2. This means that the size of the dilated image is twice as large as the size of the original image. In mathematical terms, if the original object has a length of 'x', then the length of the dilated image will be '2x'. Similarly, if the original object has a width of 'y', then the width of the dilated image will be '2y'.

For dilation 3, the scale factor is 3. This means that the size of the dilated image is three times as large as the size of the original image. In mathematical terms, if the original object has a length of 'x', then the length of the dilated image will be '3x'. Similarly, if the original object has a width of 'y', then the width of the dilated image will be '3y'.

Hence the correct option is (b).

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Answer:

Dilation 1 has a scale factor between 0 and 1

Dilation 2 has a scale factor greater than 1

Dilation 3 has a scale factor equal to 1

Step-by-step explanation:

The regular membership fee of the Holiday Health Club is $300.

Let the regular membership fee be x. According to the problem, the club has reduced its annual membership by 10%, so the discounted membership fee is 0.9x. We know that Jorge Sanchez has purchased a year's membership for $270, which is the discounted membership fee. Therefore, we can set up an equation as follows:

0.9x = 270

Solving for x, we get:

x = 270/0.9

x = 300

Hence, the regular membership fee of the Holiday Health Club is $300.

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Answer:

f¹(12) = 20

Step-by-step explanation:

f(-2) = 24

f(-1) = 17

f(0) = 12

f(1) = 9

f¹(x) = 2x - 4

f¹(12) = 20

Answer: y=log 3 x

Step-by-step explanation: