Write each equation in y = mx + b form.


1. x - y = 4







2. 2x + y = 9

Answer:

The coordinates of the point C that minimizes AC + BC are (-20, 0) or (4, 0)

Step-by-step explanation:

The given coordinates of the points A and B are A(1, 6) and B(8, 8)

The location of the point C = The x-axis

Therefore;

The coordinates of the point C = (x, 0)

The length of the segment AC = √((1 - x)² + (6 - 0)²) = √((1 - x)² + 6²)

The length of the segment BC = √((8 - x)² + (8 - 0)²) = √((8 - x)² + 8²)

At minimum distance of AC + BC, we have;

d(√((1 - x)² + 6²) +√((8 - x)² + 8²))/dx = 0 = (1 - x) × 2 × (0.5 - 1)× (√((1 - x)² + 6²)^(0.5 - 1) + (8 - x) × 2 × (0.5 - 1)× √((8 - x)² + 8²)^(0.5 - 1)

∴ d(√((1 - x)² + 6²) +√((8 - x)² + 8²))/dx = 0 = -(1 - x)/√((1 - x)² + 6²) - (8 - x)/√((8 - x)² + 8²)

-(1 - x)/√((1 - x)² + 6²) = (8 - x)/√((8 - x)² + 8²)

(8 - x)·√((1 - x)² + 6²) = -(1 - x)·√((8 - x)² + 8²)

Squaring both sides gives;

(8 - x)²·((1 - x)² + 6²) = (1 - x)²·((8 - x)² + 8²)

Expanding, using an online tool, we get;

x⁴ - 18·x³ + 133·x² -720·x + 2368 = x⁴ - 18·x³ + 161·x² - 272·x + 128

Which gives;

(161 - 133)·x² - (272 - 720)·x + 128 - 2368 = 28·x² + 448·x - 2240 = 0

Dividing by 28 gives;

x² + 16·x - 80 = 0

(x + 20)·(x - 4) = 0

Therefore, x = -20 or x = 4

The coordinates of the point C that minimizes AC + BC are (-20, 0) or (4, 0)

The coordinates of a point is the position of the point, on the coordinate plane.

The point C that minimizes AC + BC are (-20, 0) and (4, 0)

The given parameters are:

\(\mathbf{A = (1,6)}\)

\(\mathbf{B = (8,8)}\)

From the question, we understand that point C is on the x-axis.

This means that:

\(\mathbf{C = (x,0)}\)

Calculate segments AC and BC using the following distance formula

\(\mathbf{d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}\)

So, we have:

\(\mathbf{AC = \sqrt{(1 - x)^2 + (6 - 0)^2}}\)

\(\mathbf{AC = \sqrt{(1 - x)^2 + 6^2}}\)

\(\mathbf{BC = \sqrt{(8 - x)^2 + (8 -0)^2}}\)

\(\mathbf{BC = \sqrt{(8 - x)^2 + 8 ^2}}\)

Add both distance

\(\mathbf{AB + BC = \sqrt{(1 - x)^2 + 6^2} + \sqrt{(8 - x)^2 + 8^2}}\)

Differentiate, to calculate the minimum distance

\(\mathbf{d' = (1 - x) \times 2 \times (0.5 - 1) \times ((1 - x)^2 + 6^2)^({0.5 - 1}) + (8 - x) \times 2 \times (0.5 - 1) \times ((8 - x)^2} + 8^2))}^{(0.5 - 1)} }\)

Simplify

\(\mathbf{d' = -\frac{1 - x}{\sqrt{(1 - x)^2 + 6^2}}- \frac{8 - x}{\sqrt{(8 - x)^2 + 8^2}}}\)

Set to 0

\(\mathbf{ -\frac{1 - x}{\sqrt{(1 - x)^2 + 6^2}} - \frac{8 - x}{\sqrt{(8 - x)^2 + 8^2}} = 0}\)

Rewrite as:

\(\mathbf{ -\frac{1 - x}{\sqrt{(1 - x)^2 + 6^2}} = \frac{8 - x}{\sqrt{(8 - x)^2 + 8^2}} }\)

Cross multiply

\(\mathbf{(8 - x) \times\sqrt{(1 - x)\² + 6\²} = -(1 - x) \times\sqrt{(8 - x)\² + 8\²}}\)

Square both sides

\(\mathbf{(8 - x)^2 \times (1 - x)\² + 6\² = (-(1 - x))^2 \times (8 - x)\² + 8\²}\)

\(\mathbf{(8 - x)^2 \times (1 - x)\² + 6\² = (1 - x)^2 \times (8 - x)\² + 8\²}\)

Expand

\(\mathbf{x^4 - 18x^3 + 133x^2 -720x + 2368 = x^4 - 18x^3 + 161x^2 - 272x + 128}\)

Evaluate like terms

\(\mathbf{133x^2 -720x + 2368 = 161x^2 - 272x + 128}\)

Collect like terms

\(\mahbf{161x^2 - 133x^2 - 272x + 720x + 128 - 2368 = 0}\)

\(\mathbf{28x^2 + 448x - 2240 = 0}\)

Factor out 28

\(\mathbf{28(x^2 + 16x - 80) = 0}\)

Divide through by 28

\(\mathbf{x^2 + 16x - 80 = 0}\)

Expand

\(\mathbf{x^2 + 20x - 4x - 80 = 0}\)

Factorize

\(\mathbf{x(x + 20) + 4(x + 20) = 0}\)

Factor out x + 20

\(\mathbf{(x + 20)(x - 4) = 0}\)

Solve for x

\(\mathbf{x =- 20\ or\ x = 4}\)

Hence, the point C that minimizes AC + BC are (-20, 0) and (4, 0)

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The expanded logarithmic expression is 7log y + log x + 3log z.

The use of a logarithm can be utilised to solve issues that cannot be resolved using the concept of exponents alone. A logarithm is simply another way to describe exponents. Log interpretation is not that tough. It suffices to know that an exponential equation can also be written as a logarithmic equation in order to comprehend logarithms.

Exponent and logarithm are inverses of one another. This is explained in the section below. John Napier, a mathematician, first developed logarithms as a technique to perform computations simply, and other scientists, engineers, etc. immediately embraced this idea.

The given logarithmic equation is:

log (\(y^{7}xz^{3}\))

Now, we can use the properties of logarithms to expand this fully.

Therefore,

log (\(y^{7}xz^{3}\)) = log (\(y^{7}\)) + log (x) + log (\(z^{3}\))

Therefore,

log (y⁷) = 7 log y

log (z³) = 3 log z

Therefore, the expanded logarithmic expression is 7log y + log x + 3log z.

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Answer:

B

Step-by-step explanation:

(hx)(gx)

(2x+5)(3x+2)

6\(x^{2}\)+4x+15x+10

6\(x^{2}\)+19x+10

Answer B

Answer:

it's 65 because if u count the inside of the boxes u get 65

Answer:

34

Step-by-step explanation:

to get the perimeter you add the side-A with Base-B and Side-C.

The base at the bottom is 10 and the two symmetrical sides is 12.

P= a + b + c

34= 12 + 10 + 12

Answer: 3

Step-by-step explanation:

The scale factor is the ratio of corresponding side lengths of the two triangles.

In the given triangles, the length of the corresponding sides of the triangles are:

For the first triangle:

Side A = 15 units

Side B = 15 units

For the second triangle:

Side A = 45/2 units

Side B = 45/2 units

To find the scale factor, we can divide the length of one side of the second triangle by the corresponding length of the first triangle.

For example, we can use Side A:

Scale factor = (length of Side A of the second triangle) / (length of Side A of the first triangle)

Scale factor = (45/2) / 15

Scale factor = (45/2) * (1/15)

Scale factor = 3/2

Since the two triangles are scaled copies of each other, the scale factor should be the same for all corresponding sides.

Thus, the scale factor is 3 (in simplest form).

Answer:

(-9, 8)

Step-by-step explanation:

(14, -1) >> (x1, y1)

(5, 7) >> (x2, y2)

(y2 - y1)           7 - (-1) = 8

----------- >>>

(x2 - x1)           5 - 14 = -9

x always goes first in a coordinate, so

(-9, 8)

Hope this helped ;)

The mass concentration of CO₂ is density × volume 0.716 g/m³. The correct option is a. 0.716 g/m³.

It is given that the concentration of CO₂ in the atmosphere is 391 ppm by volume.

We have to find its mass concentration in g/m³.

The ideal gas law can be used to find the mass concentration of a gas in a mixture.

The ideal gas law is PV = nRT

Where,

P is pressure,

V is volume,

n is the number of moles,

R is the ideal gas constant, and

T is temperature.

The mass of the gas can be calculated from the number of moles, and the volume of the gas can be calculated using the density formula.

The formula for density is given by density = mass / volume.

Therefore, the mass concentration of CO₂ can be calculated as follows:

First, we need to find the number of moles of CO₂.

Number of moles of CO₂ = (391/1,000,000) x 1 mol/24.45

L = 0.00001598 mol

The volume of CO₂ can be calculated using the ideal gas law.

The ideal gas law is PV = nRT.

PV = nRT

V = nRT/P

where P = 1 atm,

n = 0.00001598 mol,

R = 0.08206 L-atm-K-1-mol-1,

and T = 293 K.

V = (0.00001598 × 0.08206 × 293) / 1

V = 0.000391 m³

The density of CO₂ can be calculated using the formula:

density = mass / volume

Therefore, mass concentration of CO₂ is

density × volume = 1.84 g/m³ x 0.000391 m³

= 0.0007164 g/m³

≈ 0.716 g/m³

Hence, the correct option is a. 0.716 g/m³

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The explicit rule for the arithmetic sequence for the sequence is a(n) = 3n + 2.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have given:

\(\rm a_n=3+a_n_-_1\) and

\(\rm a_1=5\)

\(\rm a_n-a_n_-_1= 3\)

The above expression represents the common ratio:

d = 3

First term:

a = 5

The explicit rule for the arithmetic sequence:

a(n) = 5 + (n - 1)3

a(n) = 3n + 2

Thus, the explicit rule for the arithmetic sequence for the sequence is a(n) = 3n + 2.

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To increase usability in a spreadsheet, you can use comments, descriptive labels, and data validation.

To increase usability in a spreadsheet, you can utilize the following techniques:

1. Comments: Comments allow you to add explanatory notes or instructions within cells. They can provide additional context or clarify the purpose of certain data or formulas. Users can view comments by hovering over the respective cell, making it helpful for collaboration and documentation.

2. Descriptive Labels: Instead of relying solely on cell references or generic labels, use descriptive labels that clearly indicate the purpose of each column, row, or range of cells. This approach enhances readability and makes it easier for users to understand the data and navigate through the spreadsheet.

3. Data Validation: Implement data validation rules to ensure the accuracy and integrity of the data entered into the spreadsheet. Data validation allows you to define constraints or conditions for input, such as numeric ranges, predefined lists, or specific text formats. It helps prevent errors and assists users in entering valid data.

4. Formatting: Properly formatting the cells, columns, and rows can greatly enhance usability. Use consistent formatting for similar types of data, apply color schemes or conditional formatting to highlight important information or trends, and adjust the column widths and row heights to optimize readability.

5. Sheet Organization: Organize the spreadsheet by using multiple sheets if needed. Group related information on separate sheets, and provide clear sheet names that reflect the content or purpose of each sheet. This helps users locate and navigate to specific sections or data within the spreadsheet.

6. Clear Instructions or Documentation: Provide clear instructions or documentation either within the spreadsheet or as separate documentation. Explain the purpose of the spreadsheet, any specific procedures or workflows, and how to interpret the data or use any embedded formulas or macros. This helps users understand the spreadsheet's functionality and ensures consistent usage.

7. Error Handling: Implement error handling mechanisms to provide informative error messages or alerts when users input incorrect or incompatible data. Clear error messages guide users in correcting their input and reduce frustration when dealing with potential errors.

By incorporating comments, descriptive labels, data validation, formatting, sheet organization, clear instructions/documentation, and error handling, you can significantly enhance the usability of your spreadsheet and make it more user-friendly for both yourself and others who interact with it.

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The pilot's distance is increasing.

In the graph, we can see distance on y axis and time on x axis. It is clearly visible that at 2 minutes, the distance covered is 0.4 miles. Further, at 4 minutes, the distance covered increases to 0.8 miles. At 6 minutes, the distance covered again increases by 0.4 miles and is 1.2 miles. At 8 minutes, the distance covered in 1.6 miles, which again increases by 0.4.

Now, it is evident that distance is increasing.

We can further calculate the speed using given information -

Speed = distance/time

Total distance = 1.6 - 0.0

Total distance = 1.6 miles

Total time = 8 - 0

Total time = 8 minutes

Speed = 1.6/8

Speed = 0.2 miles per minute.

Hence, the distance of pilot is increasing at constant rate or speed of 0.2 miles per minute.

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The complete question and figure is attached -

The graph below represents the distance a pilot is from the home airport during a period of time. A 2-column table with 5 rows titled Time and Distance Ran by Myra. The first column is labeled Time (minutes) with entries 0, 2, 4, 6, 8. The second column is labeled Distance (miles) with entries 0.0, 0.4, 0.8, 1.2, 1.6. Which describes the pilot’s distance in section I? zero constant decreasing increasing

in that function x would be -2

Answer:

Step-by-step explanation:

3(x-2)

Answer:

CD = 7

Step-by-step explanation:

CD and GI are of same lenghth so

3x - 6 = x + 8

transpose

3x - x = 8+6

2x = 14

x = 14/2

x = 7

Answer:

40.6°

Step-by-step explanation:

The building and the shadow are perpendicular to each other (or intersect at a 90° angle).

Meaning that this is a triangle problem.

We are making a triangle from the building to the shadow and a diagonal line connecting the ends of both.

We need to find the angle at the top of the building. The opposite side of the angle is 84. The adjacent side is 98.

Opposite / Adjacent = Tan X

So if we go to the calculator:

\(tan^{-1} (\frac{84}{98}) = 40.6\)

The answer is 40.6 degrees.

The scale factor was used for each dilation are-

A transformation that changes the size of a figure is called a dilatation. This indicates that the preimage as well as image are similar and have been scaled up or down, respectively.

A dilatation that results in a reduction (imagine shrinking) or an enlargement (think stretching) produces a smaller or larger image, respectively.

Part a: For ΔABC

Length AB = 2 units

Length A'B' = 4 units

A'B' = 2 *AB

Thus,  For ΔABC - scale factor = 2

Part b: For ΔDEF -

Length DF = 2 units

Length D'F' = 1  units

D'F' = 1/2 DF

Thus, For ΔDEF - scale factor = 1/2

Part c: For ΔGHJ -

Length GH = 3 units

Length G'H' = 1  units

G'H' = 1/3 GH

Thus,  For ΔGHJ - scale factor = 1/3

Part d: For ΔKML -

Length KM = 2 units

Length K'M' = 6  units

K'M' = 3*KM

Thus, For ΔKML - scale factor = 3

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The ratios involved in the ROI formula are the net profit and the investment cost.

The ROI (Return on Investment) formula includes the following ratios:

Net Profit: The net profit represents the profit gained from an investment after deducting expenses, costs, and taxes.

Investment Cost: The investment cost refers to the total amount of money invested in a project, including initial capital, expenses, and any additional costs incurred.

The ROI formula is calculated by dividing the net profit by the investment cost and expressing it as a percentage.

ROI = (Net Profit / Investment Cost) * 100%

Therefore, the ratios involved in the ROI formula are the net profit and the investment cost.

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I'm so sorry that I can't give you the answer because I'm not in your grade! But if u need me for other stuff.. I'm here! so ya!

The angle of elevation from Phillip to the space shuttle is 1.64°, calculated using the Pythagorean theorem and the square root of both sides.

Given that Phillip is watching a space shuttle launch from an observation spot 66 miles away and the space shuttle is at a height of 1.9 miles. The angle of elevation from Phillip to the space shuttle can be found using the following formula: tan θ = opposite/adjacent Where θ is the angle of elevation, opposite is the height of the shuttle, and adjacent is the distance between the shuttle and the observation spot. Using the Pythagorean theorem, we can find the hypotenuse as follows:hypotenuse² = opposite² + adjacent²Substituting the given values, we get:hypotenuse² = 1.9² + 66²= 3.61 + 4,356= 4,359.61Taking the square root of both sides, we get: hypotenuse ≈ 66.083 miles Substituting the given values in the first formula to find the angle of elevation, we get: tan θ = 1.9/66.083θ

tan⁻¹(1.9/66.083)θ ≈ 1.64°Therefore, the angle of elevation from Phillip to the space shuttle is approximately 1.64°.

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a) product of function f(x) and g(x) is 2x² - 6x - 8 and b) product of function that is in part a and an (x) is 2x³ - 4x² - 14x - 8.

Here are the three functions given:

f(x) = x -4

g(x) = 2x + 2

c(x) = x + 1

a) The product of function f(x) and g(x)

f(x). g(x) = (x -4). ( 2x + 2)

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

= 2x² + 2x - 8x - 8

= 2x² - 6x -8

b) product of function f(x). g(x) and a(x)

f(x). g(x) . a(x) =( 2x² - 6x - 8 ). ( x + 1)

= x( 2x² - 6x - 8) + 1(2x² -6x - 8)

= 2x³ - 6x² -8x + 2x² - 6x -8

= 2x³ -4x² - 14x - 8

Therefore we get a) 2x² - 6x - 8 and b) 2x³ - 4x² - 14x -8.

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Answer:

B

Step-by-step explanation:

we have to subtract the volume of the biggest one from the volume of the smallest one

for find the volume it is used the radius, not the diameter

The cat ran 3 miles in one hour

A car runs 3/5 of a mile in 2/10

The number of miles ran in one hour can be calculated as follows

3/5= 2/10

x= 1

Cross multiply

2/10x= 3/5

x= 3/5 ÷ 2/10

= 3/5 × 10/2

= 3

Hence the car ran 3 miles in 1 hour

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The range of the function g(x) is given as follows:

[0, ∞).

From the graph of the function given in this problem, y assumes all real non-negative values, hence the interval notation representing the range of the function is given as follows:

[0, ∞).

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A subclass refers to a class that can inherit properties of another class called a superclass. The subclass will have all the characteristics and behavior of the superclass, and it can be modified to meet the unique needs of a specific class. Therefore, if a program uses two classes, airplane, and jumbojet, then the most likely subclass is the jumbojet.

Suppose that the airplane is the superclass that will have all the characteristics and behavior of an airplane. On the other hand, the jumbojet will be the subclass that inherits the features of an airplane. As the subclass, the jumbojet can be modified to have additional features unique to it.

The inheritance concept in programming ensures that there is efficient use of code. It makes it easy to reuse code for creating new classes. When using inheritance, developers avoid copying and pasting code, which can lead to errors and repetition.

Suppose that the airplane and jumbojet are classes representing vehicles in a flight system.

Airplane is the superclass representing all the aircraft, while jumbojet is the subclass representing a specific type of airplane, which is a large passenger aircraft. Therefore, the jumbojet, being a specific type of airplane, is the most likely subclass.

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Based on the calculations, the location of the earthquake’s epicenter is at (-1, 1).

An epicenter can be defined as the point on the surface of planet Earth, which is perpendicular to the hypocenter (focus) and directly above the earthquake’s origin. Also, it indicates where the seismic waves from an earthquake are most intense.

For this exercise, we would set the epicenter at x and y. Using the equation of a circle, we have the following:

At A (2, 1) and 3 miles away;

\((y-1)^2+(x-2)^2=3^2\)   ......equation 1.

At B (-5, 3) and 4 miles away;

\((y-3)^2+(x-(-5))^2=4^2\\\\(y-3)^2+(x+5)^2=4^2\)   ......equation 2.

At C (10, 1) and 5 miles away;

\((y-1)^2+(x-10)^2=5^2\)   ......equation 3.

Subtracting eqn. 2 from eqn. 1, we have:

\((x-2)^2-[(x+5)^2]=3^2-4^2\\\\x^2-2x-2x+4-[(x^2+5x+5x+25)]=9-16\\\\x^2-4x+4-x^2-10x-25=-7\\\\-14x-21=-7\\\\-14x=-7+21\\\\-14x=14\\\\x=\frac{-14}{14}\)

x = -1 when y = 1.

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Answer: i used desmos to graph the circles and from the graph, you can tell that the point of intersection (epicenter) is (5, 1)

Step-by-step explanation:

A ratio shows how many times one number contains another.

Hence, the sand is in the ratio \(\frac{1}{6}\) of the mixture is

\(\frac{1}{6}\)×\(1800=300kg\)

The Gravel is in the ratio \(\frac{2}{6}\)×\(1800=600kg\)

And the cement is in ratio \(\frac{3}{6}\)×\(1800=900kg\)

What is the ratio ?

A ratio is an ordered pair of numbers \(a\) and \(b\), written \(\frac{a}{b}\) where \(b\) does not equal \(0\). A proportion is an equation in which two ratios are set equal to each other.

Here the given ratio is \(1:2:3\).

Here given that,

The dry concrete is   \(1800kg\).

And the multiplication of the ratio is \(1\)×\(2\)×\(3=6\)

Hence, the sand is in the ratio \(\frac{1}{6}\) of the mixture is

\(\frac{1}{6}\)×\(1800=300kg\)

The Gravel is in the ratio \(\frac{2}{6}\)×\(1800=600kg\)

And the cement is in ratio \(\frac{3}{6}\)×\(1800=900kg\)

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

Answer:  \(\textsf{y = -3/4x - 5}\)

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

Given: \(\textsf{Slope = -3/4 and passes through (4, -8)}\)

Find:  \(\textsf{Determine the equation of the line that fits the criteria}\)

Solution:  The first thing that we need to do is plug the information that was provided into the point-slope formula, distribute, and solve for y.

Plug in the values

Distribute and simplify

Solve for y

Therefore, the final equation of the line that passes through the point (4, -8) and has a slope of -3/4 is \(\textsf{y = -3/4x - 5}\)

Answer:

x = 4

Step-by-step explanation:

3x - 20 = -2x

Add 2x to both sides.

5x - 20 = 0

Add 20 to both sides.

5x = 20

Divide both sides by 5.

x = 4

Answer:

X = 4

Step-by-step explanation:

The correct option for the midpoint of the line segment , where (-1,-2) and (4,-2), is  (1.5,-2).

To find the midpoint of a line segment, we use the midpoint formula, which states that the coordinates of the midpoint (M) are the average of the coordinates of the endpoints.

The midpoint formula is given by:

M = ((x1 + x2) / 2, (y1 + y2) / 2)

Let's apply this formula to find the midpoint of the line segment AB:

x1 = -1, y1 = -2 (coordinates of point A)

x2 = 4, y2 = -2 (coordinates of point B)

Using the midpoint formula:

M = ((-1 + 4) / 2, (-2 + (-2)) / 2)

 = (3 / 2, -4 / 2)

 = (1.5, -2)

Therefore, the midpoint of the line segment , with endpoints (-1,-2) and (4,-2), is (1.5, -2).

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60.8π square inches is the area of the label.

The area or region that an object’s surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has. There are numerous shapes and dimensions in geometry, including spheres, cubes, cuboids, cones, cylinders, etc. Each form has its own volume and surface area.

We wish to find the area of the rectangle A= L x W because we know the label is a rectangle that has been folded into a cylinder form.

W is known to be 7.6 inches.

We must determine the length that encircles the can's circumference.

Radius = 4 inches,

circumference = C = 2 πr.

(In terms of π, therefore don't multiply.) C = (2) π (4)

C = 8 pi millimeters

We now have L = 8π

And W is equal to 7.6.

A = L x W

A = 60.8π square inches.

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