Ms. Collins recently got an aquarium that is 3 ft tall, 3 feet wide, and 6 ft. long. She needs to fill her aquarium with water but she already put .5 ft of gravel in the bottom.

How much more room is left for the water?

Hence, the volume of the pyramid is 48 cubic inches.

A pyramid is a geometric shape that consists of a polygonal base (usually a square or a triangle) and triangular faces that meet at a single point at the top, called the apex. Pyramids have been built by many ancient civilizations as monumental structures, including the ancient Egyptians, Aztecs, and Mayans. The most famous of these is the Great Pyramid of Giza in Egypt, which was built over 4,500 years ago and is one of the Seven Wonders of the Ancient World. Pyramids have also been used as symbols in many cultures and can represent strength, stability, and spirituality.

The volume of a square pyramid can be calculated using the formula V = (1/3) * B * h, where B is the area of the base and h is the height.

In this case, the base of the pyramid is a square with a side length of 3 in, so the area of the base is:

[tex]B = s^2 = 3^2 = 9 sq. in.[/tex]

The height of the pyramid is given as 16 in.

Therefore, the volume of the pyramid is:

[tex]V = (1/3) * B * h = (1/3) * 9 * 16 = 48 cubic inches.[/tex]

Hence, the volume of the pyramid is 48 cubic inches.

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The value of XZ is approximately equal to 96.86.

What is inequality ?

An inequality is a mathematical statement that compares two values, expressions, or quantities using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

We can start by using the transitive property of equality to find that XY = YZ = 95 means that XY + YZ = XZ = 190.

Next, we can use the given information about WX and WZ to write an equation for XZ in terms of u. Since WZ = WX + XZ, we can substitute the given expressions to get:

7u = (u + 66) + XZ

Simplifying and solving for XZ, we have:

7u - u - 66 = XZ

6u - 66 = XZ

Now, we can substitute this expression for XZ into our earlier equation to get:

XZ = 190 = 95 + 95 = XY + YZ = (WX - 66) + (6u - 66)

Simplifying and solving for u, we get:

6u - 66 = 190 - WX

6u = 256 - WX

u = (256 - WX)/6

Substituting this value of u back into the expression for XZ, we get:

XZ = 6u - 66 = 6[(256 - WX)/6] - 66 = 190 - WX

Therefore, XZ = 190 - WX, where WX = u + 66 = (256 - WX)/6 + 66. We can solve for WX by multiplying both sides by 6:

6WX = 256 - WX + 396

7WX = 652

WX = 93.14 (rounded to two decimal places)

Substituting this value into our expression for XZ, we have:

XZ = 190 - WX = 190 - 93.14 = 96.86 (rounded to two decimal places)

Therefore, XZ is approximately equal to 96.86.

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The mean of the sampling distribution of the sample means is 55 and the standard deviation is approximately 1.79 (rounded to one decimal place).

Standard deviation is a measure of the amount of variation or dispersion of a set of data values from its mean or expected value. It is a statistic that represents how spread out the data is from the mean.

The standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences of each data point from the mean. The standard deviation is expressed in the same units as the data and is usually denoted by the symbol "σ" (sigma) for a population or "s" for a sample.

In the given question,

We can start by using the properties of the mean and standard deviation of a sampling distribution:

The mean of the sampling distribution of the sample means (Mx) is equal to the population mean (μ), which is given as 55.

The standard deviation of the sampling distribution of the sample means (Ox) is equal to the population standard deviation (σ) divided by the square root of the sample size (n), i.e.,

Ox = σ / sqrt(n)

where n = 5 (the sample size) and σ = 4 (the population standard deviation).

Substituting these values into the formula, we get:

Ox = 4 / sqrt(5) ≈ 1.79

Therefore, the mean of the sampling distribution of the sample means is 55 and the standard deviation is approximately 1.79 (rounded to one decimal place).

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19) Length of AB is a fourth of the circumference of the circle.

C=2πr

Length of AB = [tex]\frac{1}{4} 2\pi r=\frac{1}{2} \pi r[/tex]

=0.5π(12)

Length of AB =1 8.8495559215 in

Area = 1/4*π*r²

Area = 1/4*π*12²

Area = 113.097335529 in²

20) Arc length = θr

[tex]\frac{3 }{4} \pi *10[/tex]

Length = 23.5619449019 in

Area = [tex]\frac{angle}{2\pi } *\pi r^{2}[/tex]

= [tex]\frac{3\pi }{8} *10^2[/tex]

Area = 117.80972451 in²

To solve the problem, we can use trigonometry and create a right triangle with one leg being the height of building B, the other leg being the distance between building A and B, and the hypotenuse being the line of sight from the top of building A to the top of building B.

Let's call the height of building B "h". Using trigonometry, we can determine the length of the other leg:

tan(30°) = h / x => x = h / tan(30°)

tan(60°) = h / (10√3 - x) => x = 10√3 - h / tan(60°)

Setting these two expressions equal to each other and solving for h, we get:

h / tan(30°) = 10√3 - h / tan(60°)

h (1/tan(30°) + 1/tan(60°)) = 10√3

h = 10√3 / (1/tan(30°) + 1/tan(60°)))

Plugging in the values, we get:

h = 10√3 / (1/(1/√3) + 1/√3)

h = 20√3

Answer:

Step-by-step explanation:

Let's call the height of building A "hA" and the height of building B "hB". We can use trigonometry to solve for hB.

First, let's draw a diagram:

   B

  /|

hB/ |

/  |

/ 60°\

-----

|   /

|  /

| /

|/

A

We know that the distance between building A and B is 10√3. Let's call this distance "d".

Using the angle of depression of 30°, we can form a right triangle with a leg of hA and a hypotenuse of d. The opposite angle is 60°, so the adjacent side is hA/tan(60°) = hA/√3.

Using the angle of depression of 60°, we can form another right triangle with a leg of hB and a hypotenuse of d. The opposite angle is 30°, so the adjacent side is hB/tan(30°) = hB√3.

We know that the sum of the heights of building A and B is equal to the distance between them, so hA + hB = d.

Putting all of this together, we can set up an equation:

hA/√3 + hB√3 = 10√3

Multiplying both sides by √3:

hA + 3hB = 30

But we also know that hA + hB = d = 10√3, so we can substitute:

hB = 10√3 - hA

Substituting into the previous equation:

hA + 3(10√3 - hA) = 30

Simplifying:

-2hA + 30√3 = 30

-2hA = 30 - 30√3

hA = (15√3 - 15)/(-1) = 15 - 15√3

Finally, we can use hA + hB = 10√3 to solve for hB:

hB = 10√3 - hA = 10√3 - (15 - 15√3) = 25√3 - 15

Therefore, the height of building B is 25√3 - 15.

The differential equation is [tex]-0.625ln|p-1| + 2.3026ln|p+1.5| - 1.6779ln|p+1| = t + K,[/tex] where K is a constant of integration.

We need to find the solution to the differential equation:

[tex]dp/dt = f(p) = -0.4p^3 - 1.6p + 3.6[/tex]

To find the general solution, we first need to separate the variables p and t, and then integrate both sides:

[tex]dp / ( -0.4p^3 - 1.6p + 3.6 ) = dt[/tex]

We can integrate the left-hand side using partial fractions:

[tex]dp / ( -0.4p^3 - 1.6p + 3.6 ) = dp / ( -0.4(p-1)(p+1.5)(p+1) )[/tex]

[tex]dp / ( -0.4(p-1)(p+1.5)(p+1) ) = (A / (p-1)) + (B / (p+1.5)) + (C / (p+1))[/tex]

where A, B, and C are constants to be determined.

Multiplying both sides by the denominator, we get:

[tex]dp = (A(p+1.5)(p+1) + B(p-1)(p+1) + C(p-1)(p+1.5)) / (-0.4(p-1)(p+1.5)(p+1)) dp[/tex]

Expanding the terms on the right-hand side and equating the coefficients of p², p, and the constant term, we get:

A + B + C = 0

1.5A - 1B + 1.5C = -1.6/(-0.4)

A - 1.5B - C = 3.6/(-0.4)

Solving these equations, we get:

A = 1.4286

B = -3.4524

C = 2.0238

Substituting these values back into the partial fractions equation, we get:

[tex]dp / ( -0.4(p-1)(p+1.5)(p+1) ) = (1.4286 / (p-1)) - (3.4524 / (p+1.5)) + (2.0238 / (p+1))[/tex]

Integrating both sides, we get:

[tex]-0.625ln|p-1| + 2.3026ln|p+1.5| - 1.6779ln|p+1| = t + K[/tex]

where K is a constant of integration.

This is the general solution to the differential equation.

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The sum of the arithmetic series 12 + 22 + ... + 142 is 1078.

The sum of an arithmetic series can be found by multiplying the average of the first and last terms by the number of terms.

The following formula can be used to get the sum of an arithmetic series:

S = (n/2)(a + l)

where S is the sum of the series, n is the number of terms, a is the first term, and l is the last term.

In this case, we can see that a = 12, d = 10 (the common difference), and l = 142. We can find n by using the formula for the nth term of an arithmetic sequence:

an = a + (n-1)d

Setting this equal to l and solving for n, we get:

142 = 12 + (n-1)10

130 = 10(n-1)

n-1 = 13

n = 14

Now that we know n, we can use the formula for the sum of an arithmetic series to find S:

S = (n/2)(a + l)

S = (14/2)(12 + 142)

S = 7(154)

S = 1078

Therefore, the sum of the arithmetic series 12 + 22 + ... + 142 is 1078.

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Answer:

Hery is 3. Jai is 4

Step-by-step explanation:

3×4=12

The statue is about 9.8 - 1.5 = 8.3 meters taller than Kimberly.

What is height?

Height typically refers to the measurement of how tall or high something or someone is, usually measured from the ground or a given baseline. It is often used as a physical descriptor of an object or person, and can be measured in various units such as feet, meters, or inches. Height can also be used to describe the vertical extent or distance of an object or structure, such as the height of a building or the height of a mountain.

We can use the Pythagorean theorem to solve the problem.

Let h be the height of the statue. Then, we have:

h² = 4² + 9²

h² = 16 + 81

h² = 97

h ≈ 9.8

Therefore, the statue is about 9.8 - 1.5 = 8.3 meters taller than Kimberly.

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The diameter of the lens of a particular telescope is approximately 4 feet.

The circumference of a circle is defined as the linear distance around it. In other words, if a circle is opened to form a straight line, then the length of that line will be the circle's circumference.

The circumference of a circle is given by the formula:

C = πd

where C is the circumference, d is the diameter, and π is approximately equal to 3.14.

In this case, we are given that the circumference of the lens is 12.56 feet. So we can plug in the values:

12.56 = 3.14d

To solve for d, we need to isolate it on one side of the equation. We can do this by dividing both sides by 3.14:

d = 12.56/3.14

Simplifying, we get:

d ≈ 4

Therefore, the diameter of the lens is approximately 4 feet

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Answer:

The answer to your problem is, D. [tex]-2, \frac{4}{5}[/tex]

Step-by-step explanation:

Using the a-c method to factor the quadratic

The factors of the product 5 x -8 = -40

Which sum to +6 are + 10 and -4

Split the middle term using these factors:

[tex]5x^{2} + 10x - 4x - 8[/tex]

[tex]= 5x(x + 2 ) -4 ( x + 2 )[/tex]

We will then take out the common factor: ( x + 2 )

= ( x + 2 )( 5x - 4 )

[tex]5x^{2} + 6x - 8 = ( x + 2 )( 5x - 4 )[/tex]

Thus the answer to your problem is, [tex]-2, \frac{4}{5}[/tex]

Answer:

Move terms to the left side

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

Evaluate the exponent

Multiply the numbers

Add the numbers

Evaluate the square root

Multiply the numbers

Answer:

x= 4/5

x= -2

so the answer is A

The length of EC is 8 and the length of CD is 16

How to solve the question?

Pythagoras theorem is a fundamental theorem in mathematics named after the ancient Greek mathematician Pythagoras. It states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).

The theorem can be expressed mathematically as:

c^2 = a^2 + b^2

where c is the length of the hypotenuse and a and b are the lengths of the other two sides. This means that if we know the lengths of any two sides of a right-angled triangle, we can use Pythagoras theorem to find the length of the third side.

The theorem has many practical applications, including in construction, engineering, and physics. It is also a key concept in trigonometry and is used extensively in various fields of science and mathematics.

We can use the Pythagorean theorem to solve this problem. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. In this case, we know that the length of the hypotenuse (c) is 10 and the length of one leg (a) (the base) is 6. We can use this information to find the length of the other leg (b) (the perpendicular) as follows:

c² = a²+ b²

10²= 6² + b²

100 = 36 + b²

b²= 64

b = 8

Therefore, the length of the perpendicular (EC) is 8 units.

for CD it is given in question that EC=ED  there fore

ED=8

CD=EC+ED

CD=8+8

CD=16

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The measure of angle Q is equal to 40°.

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry. In Geοmetry, triangles are the type οf pοlygοns, which have three sides and three vertices.

This is a twο-dimensiοnal figure with three straight sides. A triangle is cοnsidered a 3-sided pοlygοn. The sum οf all the three angles οf a triangle is equal tο 180°. The triangle is cοntained in a single plane. Based οn its sides and angle measurement, the triangle has six types.

Using Cos θ = adjacent/ Hypotenuse

Cos Q = 720/ 940

Cos Q = 36/47

Q = arccos 36/47

Q = 40.007793734°

Thus, The measure of angle Q is equal to 40°.

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Step-by-step explanation:

A   xy = 40   is the same as x = 40/y    an inverse relationship

D   this is the samething as A

Don't know about F...it is truncated

Therefore, the sales tax rate on the washer and dryer set was 5.25%.

Sales tax rates vary depending on the country, state, and even city or municipality where the sale is taking place. Therefore, it's difficult to provide a single answer without more information about the specific location you're asking about.

For example, in the United States, the sales tax rate can range from 0% in some states to as high as 10.25% in certain cities or counties. In Canada, the federal sales tax is 5%, but provinces and territories may also have their own sales tax rates.

To find the sales tax rate, we need to divide the sales tax by the total cost of the washer and dryer set:

Sales tax rate = sales tax / total cost

Total cost = $2900 (cost of washer and dryer set)

Sales tax = $152.25\2900

Sales tax rate = 152.25 / 2900

Sales tax rate = 0.0525 or 5.25%

Therefore, the sales tax rate on the washer and dryer set was 5.25%.

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These notes provide a comprehensive guide to solving linear equations using the substitution method, and would be a helpful resource for students studying this topic.

When note-taking with vocabulary and core concepts, follow these steps:
Identify the core concepts: Before taking notes, skim through the material and identify the main ideas or concepts that will be the focus of your notes.
Create headings or sections for each core concept: Organize your notes into sections with headings for each core concept.

This will help you structure your notes and make it easier to find information later on.
Define and highlight key vocabulary: As you take notes, pay attention to important terms or jargon related to the core concepts.

Define these terms in your notes and highlight or underline them for easy reference.
Use bullet points and abbreviations: Keep your notes concise by using bullet points and abbreviations to summarize information.

This will help you understand and remember the material better.
Incorporate examples or explanations: Include examples or explanations that help illustrate the core concepts and vocabulary.

This will help you better understand the material and provide context for the vocabulary.
Review and revise your notes: After taking notes, review and revise them to ensure they accurately reflect the material and incorporate the key vocabulary and core concepts.

This will help reinforce your understanding and improve retention of the information.

By following these steps, you'll create organized and effective notes that incorporate vocabulary and core concepts, making it easier to study and understand the material.

The notes provide several examples with detailed explanations on how to apply the substitution method to solve linear equations.

The examples include equations with coefficients, constants, and variables, and demonstrate how to rearrange the equations to solve for the variables.

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it depends on the shape. There are yt videos you could watch that would explain how to solve the perimeters of that specific shape

OK what are you wanting to find the perimeter to?

Add up all the sides:

EX:

Square: 3+3+3+3

Rectangle: 4+2+4+2

Triangle [Equilateral]: 2+2+2

You get the gist?

All the items are in the correct order as follows:

Order from least to greatest:

4, 2, 3, 1

The reason for the order from least to greatest is based on the number of possible combinations in each situation.

Neither the letters nor the numbers can be repeated: In this situation, there are 26 choices for the first letter, 25 choices for the second letter (since the first letter has already been chosen and cannot be repeated), 8 choices for the first digit (since it can be any number from 1 to 9), 7 choices for the second digit (since the first digit has already been chosen and cannot be repeated), and 6 choices for the third digit. Therefore, the total number of possible combinations is 26 x 25 x 8 x 7 x 6 = 1,872,000.

The letters can repeat, but the number cannot repeat: In this situation, there are 26 choices for each letter and 9 choices for each digit. Therefore, the total number of possible combinations is 26 x 26 x 9 x 8 x 7 = 328,968.

The number can repeat, but the letters cannot repeat: In this situation, there are 26 choices for the first letter, 25 choices for the second letter, and 9 choices for each digit. Therefore, the total number of possible combinations is 26 x 25 x 9 x 9 x 9 = 5,565,750.

The letter "O" cannot be used but there are no restrictions on repeating the other letters or numbers: In this situation, there are 25 choices for each letter (since "O" cannot be used) and 9 choices for each digit. Therefore, the total number of possible combinations is 25 x 25 x 9 x 9 x 9 = 15,506,250.

Based on the above calculations, the order from least to greatest is 4, 2, 3, 1.

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The text format of the question in the picture:

Use the arrows to move each item into the correct order. Click the up arrow to move the item up, or click the down mow to move the them down. Once all the items are in the correct order, submit your response.

A bike license consists of 2 letters, using any of the 26 letters in the alphabet, followed by 3 digits from 1 to 9. Calculate the number of possible license plates in each situation, then, order them from least to greatest.

The letters can repeat, but the number cannot repeat

The number can repeat, but the letters cannot repeat

Neither the letters nor the numbers can be repeated

The letter "O" cannot be used but there are no restrictions on repeating the other letters or numbers.

Answer:

radius of circle T/smaller circle = 4 units

Diameter of larger circle is 10units

radius of larger circle = D/2

= 10/2 = 5units

CIRCUMFERENCE OF SMALLER CIRCLE =

2πr = 2 × 3.14 × 4

= 25.12 units

Area of smaller Circle =

πr² = 3.14 × 4 × 4

= 50.24 units²

CIRCUMFERENCE OF LARGER CIRCLE =

2πr = 2 × 3.14 × 5

= 31.4 units

Area of larger circle =

πr² = 3.14 × 5 × 5

= 78.5 units²

The given statement "In the unit method of proportioning, the longest dimension of an object is set equal to one unit." is False because the unit method of proportioning does not require the longest dimension.

In the unit method of proportioning, a chosen dimension of an object is set equal to one unit, and then all other dimensions are expressed in terms of that unit, regardless of whether it is the longest dimension or not.

For example, if a rectangle has a width of 4 cm and a length of 6 cm, we could choose to set the length as the unit and express the width as a fraction of the unit: 4/6 or 2/3 of a unit.

Alternatively, we could choose to set the width as the unit and express the length as a fraction of the unit: 6/4. In either case, the longest dimension of the object is not necessarily the unit.

The unit method of proportioning is commonly used in art and design to help maintain consistent proportions between different elements of a composition. It allows for easy scaling and adjustment of proportions while preserving the overall relationships between the different elements.

Rather, any dimension can be chosen as the unit, and the other dimensions are expressed in terms of that unit.

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-68/1 is  in the form of rational number.

What is an example of an integer?

A whole number that can be positive, negative, or zero is called an integer. It is not a fraction. Examples of numbers include: -5, 1, 5, 8, 97, and 3,043. The following numbers are examples of non-integers: -1.43, 1 3/4, 3.14,.09, and 5,643. 1. A positive integer and a negative integer cannot be multiplied.

                            Two positive integers can be multiplied to make a positive number. As an integer is only a collection of numbers, there is no specific formula for it. When doing mathematical operations on numbers, such as addition, subtraction, etc., there are nonetheless specific guidelines that must be followed.

-68 as a quotient of integers

In form of rational number

 - 68 = -68/1

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The value of the technological equipment when it was new according to an exponential decay model is approximately $37,633.52.

It is given to us that the value of a new technological equipment depreciates (decreases) after it is purchased, the value of the technological equipment depreciates according to an exponential decay model.

We know that the value of the equipment is $20000 at the end of 6 years, and its value has been decreasing at the rate of 10% per year.

Let the purchase price of machine be $P

Rate of depreciation = 10% p.a.

Period years.

∴ Present value = $20,000

Depreciated value can be calculated by t(6) ---> [∵ Depriciated value = A]

⇒ $20,000 = P(1−10/100)⁶

⇒ $20,000 = P(9/10)⁶

⇒ P = $20,000 (9/10)⁶ A = P(1-100)t

⇒ P = $20,000 × 10/9 × 10/9 × 10/9 × 10/9 × 10/9 × 10/9

⇒ P = $37,633.528463178 ≈ 37,633.52

The value of the technological equipment when it was new was approximately $37,633.52.

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The group who has the largest percentage of people who prefer to travel by automobile is given as follows:

Adult.

A bar graph, also known as a bar chart, is a type of graph used to represent and compare data. It consists of rectangular bars of equal width and varying heights, where the height of each bar represents the value of the data being graphed.

Automobiles are represented by the green bars, hence we must observe the input for which the green bar has the largest value, which is for adults, hence adults compose the largest percentage of people who prefer to travel by automobile.

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Answer:)

O segment XW

Explanation:)

hope it helps :)

Brainliest pls:)

[tex](2^{2})^{4} *5^{4}[/tex][tex](2^{2})^{4} *5^{4}[/tex]The expression is [tex]4^{4} *5^{4}[/tex] is therefore a single power of [tex]2[/tex] and [tex]5[/tex]

[tex]4^{4} *5^{4} =2^{8} *5^{4}[/tex]

A grouping of numbers, symbols, and mathematical operations (such as addition, subtraction, multiplication, and division) is called an expression, and it is used to represent an amount or relationship. Expressions as basic as "[tex]2+3x[/tex]" or as complex as "[tex]3x^{2} +5x-2[/tex]" are both permissible.

Additionally, they might include variables, which are representations of unknown values represented by symbols, such as "[tex]y+2x[/tex]." In algebra, calculus, and other areas of mathematics, expressions are commonly used to discuss problems and describe mathematical properties.

Since [tex]4[/tex] and[tex]5[/tex] may be stated as [tex]2^{2}[/tex] and [tex]5^{1}[/tex] so the [tex](2^{2})^{4} *5^{4}[/tex]

[tex]4^{4} *5^{4} =2^{8} *5^{4}[/tex] [tex]=(2^{2})^{4} *5^{4}[/tex]

So the expression for [tex]4^{4} *5^{4} =2^{8} *5^{4}[/tex] as there are single power of [tex]2[/tex] and [tex]5[/tex]

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Answer:

Step-by-step explanation:

To find the equation of a circle that passes through three given points, we can use the fact that the perpendicular bisectors of the chords joining the points intersect at the center of the circle.

Let's first find the midpoint and slope of the chords joining the three points:

The midpoint and slope of the chord joining (-1, 2) and (4, 2):

Midpoint: $((4 - 1)/2, (2 + 2)/2) = (3/2, 2)$

Slope: $(2 - 2)/(4 - (-1)) = 0$

The midpoint and slope of the chord joining (-1, 2) and (-3, 4):

Midpoint: $((-3 - 1)/2, (4 + 2)/2) = (-2, 3)$

Slope: $(4 - 2)/(-3 - (-1)) = 1/2$

The midpoint and slope of the chord joining (4, 2) and (-3, 4):

Midpoint: $((-3 + 4)/2, (4 + 2)/2) = (1/2, 3)$

Slope: $(4 - 2)/(-3 - 4) = -1/2$

Now we can find the equations of the perpendicular bisectors of these chords:

The equation of the perpendicular bisector of the chord joining (-1, 2) and (4, 2) is the horizontal line $y=2$.

The equation of the perpendicular bisector of the chord joining (-1, 2) and (-3, 4) is the line passing through the midpoint $(-2, 3)$ with slope $-2$:

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

Simplifying, we get $y = -2x - 1$.

The equation of the perpendicular bisector of the chord joining (4, 2) and (-3, 4) is the line passing through the midpoint $(1/2, 3)$ with slope $2$:

$$y - 3 = 2(x - 1/2)$$

Simplifying, we get $y = 2x + 2$.

The center of the circle is the point where these perpendicular bisectors intersect. Solving the system of equations formed by setting any two of the perpendicular bisectors equal to each other, we get the center of the circle as $(1, 2)$.

Finally, the radius of the circle is the distance from the center to any of the three given points. We can use the distance formula to find that the radius is $\sqrt{10}$.

Putting it all together, the equation of the circle is:

$$(x - 1)^2 + (y - 2)^2 = 10$$

or expanding and simplifying:

$$x^2 + y^2 - 2x - 4y + 5 = 0$$

Therefore, the general equation for the circle that passes through the points (-1, 2), (4, 2), and (-3, 4) is $x^2 + y^2 - 2x - 4y + 5 = 0$.

The total difference between 4 5/6 and 9 1/6 on a number line using shorter jumps to the nearest integers is 4 1/3.

To find the difference between 4 5/6 and 9 1/6 on a number line using shorter jumps to the nearest integers, we can follow these steps:

Step 1: Convert the mixed numbers to improper fractions.

4 5/6 = (6 x 4 + 5) / 6 = 29/6

9 1/6 = (6 x 9 + 1) / 6 = 55/6

Step 2: Find the distance between the two fractions on the number line by taking the absolute value of their difference.

|29/6 - 55/6| = |-26/6| = 26/6

Step 3: Simplify the fraction and convert it back to a mixed number, if necessary.

26/6 can be simplified to 13/3, which is an improper fraction.

To convert 13/3 back to a mixed number, we divide the numerator (13) by the denominator (3) and write the remainder as a fraction:

13 ÷ 3 = 4 with a remainder of 1

So, 13/3 = 4 1/3

Therefore, on a number line with shorter jumps to the nearest integers, the total distance between 4 5/6 and 9 1/6 is 4 1/3.

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The sum of the interior angles of the polygon ABCDEF is 720°.

What is the sum of the interior angles of a polygon with n sides?

Sum of interior angles = (n - 2) x 180°

Since polygon ABCDEF is a hexagon (a polygon with six sides), we can substitute n = 6 into the formula to get:

Sum of interior angles = (6 - 2) x 180°

Sum of interior angles = 4 x 180°

Sum of interior angles = 720°

To use triangles to work out the sum of the interior angles of polygon ABCDEF, we can divide the hexagon into four triangles.

Each triangle in the diagram has an interior angle sum of 180°. So, we can find the sum of the interior angles of polygon ABCDEF by adding up the interior angles of the four triangles.

Sum of interior angles = 180° + 180° + 180° + 180°

Sum of interior angles = 720°

Therefore, we get the same answer whether we use the formula or divide the hexagon into triangles to find the sum of the interior angles of polygon ABCDEF, which is 720°.

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We can solve this problem using trigonometry and the properties of triangles.

Let C be the location of the radio transmitter. Then, ACB is a triangle with sides AC = x (the distance from A to the transmitter), BC = y (the distance from B to the transmitter), and AB = 2.00 mi.

We can use the fact that the sum of the interior angles of a triangle is 180 degrees to find the angle at C:

angle ACB = 180 degrees - angle BCA - angle CAB

From the information given in the problem, we know that:

angle CAB = N 36° 20' E

angle BCA = N 43° 40' W

To add or subtract angles, we need to convert them to a common direction. We can do this by adding or subtracting 180 degrees, or by using the fact that 1 degree = 60 minutes (') and 1 minute = 60 seconds ("). Therefore:

angle CAB = 36 degrees + 20/60 degrees = 36.3333... degrees

angle BCA = 180 degrees - (43 degrees + 40/60 degrees) = 136.6666... degrees

Substituting these values into the equation for angle ACB, we get:

angle ACB = 180 degrees - 136.6666... degrees - 36.3333... degrees = 7.0000... degrees

Now, using the law of sines, we can write:

x / sin(angle CAB) = 2.00 mi / sin(angle ACB)

y / sin(angle BCA) = 2.00 mi / sin(angle ACB)

Solving for x and y, we get:

x = 2.00 mi * sin(angle CAB) / sin(angle ACB) = 2.00 mi * sin(36.3333... degrees) / sin(7.0000... degrees) = 9.0734... mi

y = 2.00 mi * sin(angle BCA) / sin(angle ACB) = 2.00 mi * sin(136.6666... degrees) / sin(7.0000... degrees) = 1.1878... mi

Therefore, the distance of the transmitter from B is y = 1.1878... mi (rounded to 4 decimal places).