Given the equation 4x + 7 = 3(2x − 5), solve for the variable. need step by step struggling to understand

The volume of the solid obtained by rotating the region about the y-axis is 3036π cubic units.

How to find the volume by rotating the region?

To find the volume of the solid obtained by rotating the region enclosed by the graphs of y=27-x, y=3x-9, and x=0 about the y-axis, we need to use the method of cylindrical shells.

Here the region is bounded by the graphs of y=27-x, y=3x-9, and x=0. We can see that the region is a trapezoid with vertices at (0, -9), (6, 9), (18, 9), and (27, 0).

Next, we need to determine the height and radius of each cylindrical shell. The height of each shell is the difference between the y-coordinates of the top and bottom of the shell. The radius of each shell is the x-coordinate of the shell.Let's consider a shell with x-coordinate x. The height of the shell is given by (27 - x) - (3x - 9) = 36 - 4x. The radius of the shell is x. The volume of the shell is given by 2πrhΔx, where Δx is the thickness of the shell.

Therefore, the total volume of the solid is given by:

\(V = \int0^6 2πx(36 - 4x)dx + \int6^18 2πx(9)dx + \int18^27 2πx(27 - x - 9)dx\)

Simplifying and evaluating the integral, we get:

V = 2π(216) + 2π(243) + 2π(243/2) = 3036π

Therefore, the volume of the solid obtained by rotating the region about the y-axis is 3036π cubic units.

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Rotating the area about the y-axis yields a solid with a volume of 3036 cubic units.

The cylindrical shell method must be used to determine the solid's volume after rotating the region enclosed by the graphs of

y=27-x, y=3x-9, and x=0 about the y-axis.

In this case, the graphs of y=27-x, y=3x-9, and x=0 define the region's boundaries. The region is a trapezium, as can be seen, with vertices at (0, -9), (6, 9), (18, 9), and (27, 0).

The height and radius of each cylindrical shell must then be determined. Each shell's height is determined by the difference between its top and bottom y-coordinates.

Each shell's x-coordinate corresponds to its radius.Consider a shell with the coordinates x and y. (27 - x) - (3x - 9) = 36 - 4x gives the height of the shell. The shell has a radius of x. 2rhx, where x is the shell's thickness, gives the volume of the shell.

As a result, the solid's entire volume can be calculated using:

When we simplify and assess the integral, we obtain:

V = 2π(216) + 2π(243) + 2π(243/2)

  = 3036π

As a result, the region's volume after being rotated about the y-axis is 3036 cubic units.

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Answer:

So first, we figure out the maximum the patient could be taking each day: 2 tabs every 4 hours = 12 tabs per day at the most.

\(-5x = 78 + 25 <=> -5x = 103 <=> x = -103/5\)

After 10 years, the Certificate of Deposit (CD) will be worth $2,960.49.

To calculate the value of the Certificate of Deposit (CD) after 10 years, we can use the formula for compound interest: A = P\((1+r)^{t}\).

Given:

Principal amount (P) = $2000

Annual Percentage Rate (r) = 4% = 0.04 (expressed as a decimal)

Time period (t) = 10 years

Plugging these values into the formula, we get:

A = 2000\((1+0.04)^{10}\)

Calculating the expression within the parentheses first:

1 + 0.04 = 1.04

Now, we can substitute this back into the formula:

A = 2000\((1.04)^{10}\)

Using a calculator, we find that \((1.04)^{10}\) ≈ 1.48024459.

Substituting this value into the formula:

A ≈ 2000 * 1.48024459

Calculating the result:

A ≈ $2,960.49

Therefore, after 10 years, the Certificate of Deposit (CD) will be worth approximately $2,960.49.

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Answer:

19

Step-by-step explanation:

If the number of skits is x we can write:

9x + 5 = 176

9x = 171

x = 19

To completely cover the rectangular wall that measures 290 square feet, Leah will require a minimum of 10 sheets of wallpaper.

To find the least number of sheets of wallpaper Leah will need, we first need to calculate the total area of the rectangular wall. We are given that the area of the wall is 290 ft².

Next, we need to find out how many 2 ft by 15 ft sheets of wallpaper Leah will need to cover this area.

We can start by figuring out the area that one sheet of wallpaper can cover.

Each sheet of wallpaper has an area of 2 ft x 15 ft = 30 ft².

To cover the entire rectangular wall, Leah will need to divide the total area of the wall by the area of each sheet of wallpaper:

290 ft² ÷ 30 ft² = 9.67

Since Leah cannot use a partial sheet of wallpaper, she will need to round up to the nearest whole number. Therefore, Leah will need at least 10 sheets of wallpaper to cover the rectangular wall with an area of 290 ft².

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Answer:

hope this helps!!

Step-by-step explanation:

Answer:

0, 6

Step-by-step explanation:

Answer:

8*3=23

180-24=156

Step-by-step explanation:

hope this helps.

Answer:

D

Step-by-step explanation:

first find the perimeter of both triangles

Original perimeter: 72 in

scaled perimeter: 24 in

A is wrong since the scaled perimeter is actually smaller.

B is wrong because its not 6 times smaller

C is wrong since it's not 1/9 of the original

D is correct since the scaled is a 1/3 of the original perimeter (72*1/3 = 24)

The surface area of the pyramid is given by the equation A = 170.4 inches²

The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid

Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Given data ,

Let the surface area of the pyramid be represented as A

Now , the equation will be

The slant height of the pyramid h = 6 inches

The side of the equilateral triangle = 12 inches

So , the perimeter of the triangle = 3 x side length

Substituting the values in the equation , we get

The perimeter of the triangle = 36 inches

The area of the base = 62.4 inches²

So , Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Substituting the values in the equation , we get

Surface Area of Pyramid = 62.4 + ( 1/2 ) ( 36 x 6 )

On simplifying the equation , we get

Surface Area of Pyramid = 62.4 + ( 108 )

Surface Area of Pyramid = 170.4 inches²

Hence , the surface area of pyramid is 170.4 inches²

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Answer:

Dependent

Step-by-step explanation:

The output of a function is the y value. This is also the dependent variable.

The factor of independent variable that were in the study will be 2.

It should be noted that an independent variable is the variable that the experimenter changes in order to test the dependent variable.

In this case, if a 2 x 3 factorial design with between subjects variables was carried out with 8 subjects per cell, the independent variable factor is 2.

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Answer:

14 red crayons

Step-by-step explanation:

since we already know the ratios of the crayons we are going to use ratio and proportion to solve our question B:R is 32:28 and they are directly proportional meaning we can scale the quantities by multiplying.32:28 and 16:R , r is the unknown quantity ,then we cross multiply  the 2 ratios to get 32R= 448, then we divide by32 both sides so we can remain with the value of R which is 14

Answer:

If we divide 5 by any other integer, then the remainder will be a non-zero positive integer.

Step-by-step explanation:

The average wattage supplied during a 24 hour time interval is 24 Watts. This is equal to the total energy supplied divided by the time interval, which is 24 hours.

To calculate the total energy supplied, we need to integrate the power function over the 24 hour time interval:

where P(t) is the power function in megawatts.

Alternatively, if we have a table of values of the power function at regular intervals (e.g. every hour), we can estimate the average wattage supplied by taking the average of those values.

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divide 9.75 by 15 equals sixty ixty five cent's

polynomial multiplication.

(A×B)×C = (-2√3 + 3k) × (4√3 - 3k)

A×(B×C) = (√3 + k) × (-8√3 + 6k)

To find (A×B)×C, we first expand A and B:

A = √3 + k

B = 2√3 - 3k

Then we can multiply A and B to get (A×B):

(A×B) = (√3 + k) × (2√3 - 3k)

      = 2√3√3 + 2√3k - 3k√3 - 3k^2

      = 6 + 2√3k - 3√3k - 3k^2

Next, we multiply (A×B) by C:

(A×B)×C = (6 + 2√3k - 3√3k - 3k^2) × (4√3 - 3k)

        = 24√3 + 8√3k - 12√3k - 12k^2 - 12√3k + 9k^2

        = 24√3 - 16√3k - 3k^2

For A×(B×C), we first find (B×C):

(B×C) = (2√3 - 3k) × (4√3 - 3k)

      = 8√3 - 6k - 12k√3 + 9k^2

      = 8√3 - 6k - 12k√3 + 9k^2

Then we multiply A by (B×C):

A×(B×C) = (√3 + k) × (8√3 - 6k - 12k√3 + 9k^2)

        = 8√3 + 8k - 6k√3 - 6k^2 - 12√3k - 12k^2 + 9k^2

        = 8√3 - 6k√3 - 12√3k + 8k - 6k^2 - 12k^2 + 9k^2

        = 8√3 - 6k√3 - 12√3k - 9k^2

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The correct size of the distance matrix for a multivariate data set with 25 subjects and 7 variables is 25 x 25.

Understanding the many objectives and histories of the various types of multivariate analysis, as well as how they connect to one another, is the focus of multivariate statistics.

The distance matrix contains the pairwise distances between all pairs of subjects in the dataset, and therefore has the same number of rows and columns as the number of subjects in the dataset. Since there are 25 subjects in this dataset, the distance matrix will have 25 rows and 25 columns.

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Answer:

16

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

We are given a right triangle. We can use PT to solve for the missing length.

Step 2: Identify Variables

Leg a = 12

Leg b = x

Hypotenuse c = 20

Step 3: Solve for x

Answer:

hi

Step-by-step explanation:hi

hi

k = 13The smallest zero or root is x = -10

===============================

Steps:

note: you can write "x^2" to mean "x squared"

f(x) = x^2+3x-10

f(x+5) = (x+5)^2+3(x+5)-10 ... replace every x with x+5

f(x+5) = (x^2+10x+25)+3(x+5)-10

f(x+5) = x^2+10x+25+3x+15-10

f(x+5) = x^2+13x+30

Compare this with x^2+kx+30 and we see that k = 13

Factor and solve the equation below

x^2+13x+30 = 0

(x+10)(x+3) = 0

x+1 = 0 or x+3 = 0

x = -10 or x = -3

The smallest zero is x = -10 as its the left-most value on a number line.

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The volume of the cylinder after the prism is cut out is 593 cm^3.

To calculate the volume of the cylinder after the prism is cut out, we need to first determine the volume of the prism that will be removed. This can be found by multiplying the length, width, and height of the prism. Once we have this value, we can subtract it from the original volume of the cylinder.

For example, if the cylinder has a radius of 5 cm and a height of 10 cm, and the prism to be removed has a length of 6 cm, a width of 4 cm, and a height of 8 cm, we can calculate the volume of the prism as follows:

Volume of prism = length x width x height
Volume of prism = 6 cm x 4 cm x 8 cm
Volume of prism = 192 cm^3

To find the volume of the cylinder after the prism is cut out, we simply subtract the volume of the prism from the original volume of the cylinder:

Volume of cylinder = pi x radius^2 x height
Volume of cylinder = 3.14 x 5^2 x 10
Volume of cylinder = 785 cm^3

Volume of cylinder after prism is cut out = 785 cm^3 - 192 cm^3
Volume of cylinder after prism is cut out = 593 cm^3

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Answer:

The quadrilateral formed is a trapezoid

Step-by-step explanation:

In this case, it is necessary to know what points A, B, C, and D.

If the points are equal to the following coordinate points

A (-2, 1)

B (2, 1)

C (3, -2)

D (-3, -2)

As shown in the image the answer would be a trapezoid.

________________________________

The figure cannot be a square, a rhombus or a rectangle since by definition these are:

A square has all sides of equal length and all its right angles.

A rhombus is a parallelogram that has all sides of equal length and all its angles different from right angles.

A rectangle is a parallelogram that has all its right angles.

The figure that we obtain is neither a parallelogram nor does it have all its right angles.

False. A trigonometric equation with an infinite number of solutions is not necessarily an identity.

A trigonometric identity is an equation that holds true for all values of the variables involved. It is a fundamental property of trigonometric functions. On the other hand, a trigonometric equation with an infinite number of solutions means that there are multiple values of the variables that satisfy the equation, but it doesn't imply that the equation is true for all values.

For example, the equation sin(x) = 0 has an infinite number of solutions, which are x = 0, π, 2π, 3π, and so on. However, this equation is not an identity because it is not true for all values of x. It is only true when x is an integer multiple of π.

Therefore, it is important to distinguish between trigonometric identities that hold true for all values and trigonometric equations that have an infinite number of solutions but may not be true for all values.

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The ideal way to organize electronically the raw data for a study is to create a structured database or spreadsheet that can easily and efficiently store, sort, and analyze the data.

This will allow for easy retrieval and manipulation of the data, as well as the ability to perform statistical analysis and generate reports. It is important to ensure that the data is accurately recorded and labeled to prevent errors and ensure consistency. Additionally, proper data security measures should be in place to protect the confidentiality and integrity of the data.

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The ideal way to organize electronically the raw data for a study is to use a standardized format, such as a spreadsheet or database, with clear and consistent labeling for each variable.

It is important to ensure that the data is accurate, complete, and easily accessible, and to maintain appropriate security and privacy measures to protect the confidentiality of study participants. Additionally, it is recommended to create a data management plan outlining the procedures for data collection, storage, and sharing throughout the study. This plan should be reviewed and updated regularly to ensure that it remains effective and compliant with relevant regulations and ethical standards. The ideal way to organize electronically the raw data for a study is to use a structured and systematic approach, such as creating a well-designed database or spreadsheet. This allows for efficient data management, easy access, and accurate analysis.

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The positive difference is 10,000. The old format had 26^3 = 17,576 possible combinations, while the new format has 26^4 = 456,976 possible combinations. The difference is 456,976 - 17,576 = 439,400, or 10,000 times the original amount.

The old format for license plates used three letters followed by three digits, which provided 26^3 = 17,576 possible combinations. The state changed the format to four letters followed by two digits, offering 26^4 = 456,976 possible combinations. This gives us a positive difference of 10,000 times the original amount, or 456,976 - 17,576 = 439,400. This increase in the number of combinations greatly increases the number of license plates available in the state.

The old license plate format of three letters followed by three digits provided an initial total of 17,576 combinations. This limits the amount of license plates available, as well as the individuality of the plates. In order to increase the number of plates and provide more individuality, the state changed the format to four letters followed by two digits. This new format increases the total number of combinations to 456,976, which is a positive difference of 439,400, or 10,000 times the original amount. This allows for more license plates to be available, as well as more individuality, as there are now 456,976 unique combinations to choose from.

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Answer:

40

Step-by-step explanation:

It takes 10 apples to make a gram of fat. Multiply the 10 apples by 4 grams of fat to find that it takes 40 apples to make 4 grams of fat.

The answer is 40 apples.

Answer:

n=3

Step-by-step explanation:

Answer:

3 + 2n = 9

-3            -3

=0            =6

2n=6

Since the 2 is being times by n we divide by the answer

6/2 = 3

3 is the Answer.

Step-by-step explanation:

Answer:

(Hope this helps can I pls have brainlist (crown)☺️)

Step-by-step explanation:

Graph in pic

(Credits: Symbolab)