let $a 1a 2a 3a 4$ be a square, and let $a 5,a 6,a 7,\ldots,a {34}$ be distinct points inside the square. non-intersecting segments $\overline{a ia j}$ are drawn for various pairs $(i,j)$ with $1\le i,j\le 34$, such that the square is dissected into triangles. assume each $a i$ is an endpoint of at least one of the drawn segments. how many triangles are formed?

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.

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

Answer:)

O segment XW

Explanation:)

hope it helps :)

Brainliest pls:)

Answer:

Hery is 3. Jai is 4

Step-by-step explanation:

3×4=12

Probability that a shipment will be returned if the true sample proportion of defective cartridges in the shipment is 0.06 is equals to the 99.4457%.

We have A manufacturer of computer printers purchases plastic ink cartridges from a vendor.

Sample size for cartridge sample, n

= 238

Sample proportion of defective cartridges is more than 0.02.

true proportion of defective cartridges in the shipment = 0.06

Population Mean, μ = Σ(x) = 0.06 × 238

= 14.28

standard deviations, σ = sqrt(V(x))

= sqrt(238×0.06×0.94) = 3.74

If there are more than 0.02× 238 = 4.76 defective, the sample will be returned. This probability is 1 subtracted by the pvalue of Z when x = 4.8

Using Z- score in normal distribution formula, z = (x - μ) / σ

=> z = (4.8 - 14.3) / 3.74 = -2.54

=> P(Z < -2. 54) = 0.00554

This means that there is a 1 - 0.00554

= 0.994457376556917.

Hence, required probability is 99.4457%.

For more information about sample proportion, visit :

https://brainly.com/question/31265252

#SPJ4

Complete question:

A manufacturer of computer printers purchases plastic ink cartridges from a vendor. When a large shipment is received, a random sample of 230 cartridges is selected, and each cartridge is inspected. If the sample proportion of defective cartridges is more than 0.02, the entire shipment is returned to the vendor. (a) What is the approximate probability that a shipment will be returned if the true proportion of defective cartridges in the shipment is 0.06?

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.

More can be learned about bar graph at https://brainly.com/question/24741444

#SPJ1

-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

Learn more about integers

brainly.com/question/15276410

#SPJ1

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.

To learn more about height, visit the link:

https://brainly.com/question/28122539

#SPJ1

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.

To learn more about Inequality from given link.

https://brainly.com/question/30228778

#SPJ1

If the debt is normally distributed with a population standard deviation of $1100 and 15% of college seniors owe less than the amount of money is equals to the $2121.96.

The area under the standard normal curve represents to probability. The total area under the curve is equals to one. A Standard Normal Cumulative Probability, is a table which provides the cumulative probability of the left tail, as in the values less than the z-score in question. Here,

population mean, μ = $3262

standard deviation, σ = 1100

P- value = 15%

Using the normal distribution table, Z-score value is equals to - 1.0364. Now, we can use Z-scores formula is written [tex]Z = \frac{X - \mu}{\sigma }[/tex]

Substitutes the known values in above formula, - 1.0364 = (X - 3262 )/1100

=> X - 3262 = 1100× ( - 1.0364)

=> X = 3262 - 1140.04

=> X = 2121.96

Hence, required value is $ 2121.96.

For more information about normal distribution, visit :

https://brainly.com/question/4079902

#SPJ4

Since m and k(k+1)/2 are both integers, we can conclude that (k+1)(k+2)(k+3) is an integer multiple of 6. Thus, by the principle of mathematical induction, the formula n(n+1)(n+2) is an integer multiple of 6 for all non-negative integers n

Mathematical induction is a proof technique used to establish a statement for all positive integers by proving it for the base case and showing that if the statement holds for an arbitrary integer, it must also hold for the next integer. It is a powerful method to prove mathematical statements that follow a pattern or recursive structure.

To prove by mathematical induction that n(n+1)(n+2) is an integer multiple of 6 for all non-negative integers n, we will first show that the formula holds true for the base case n=0.

Base case:

When n = 0, we have:

0(0+1)(0+2) = 0 * 1 * 2 = 0, which is an integer multiple of 6 since 0 = 6 * 0.

Induction hypothesis:

Assume that for some k >= 0, k(k+1)(k+2) is an integer multiple of 6.

Induction step:

We need to show that the formula holds true for k+1, assuming that it holds true for k. That is, we need to show that (k+1)(k+2)(k+3) is also an integer multiple of 6.

Expanding the formula, we get:

(k+1)(k+2)(k+3) = (k² + 3k + 2)(k+3) = k³ + 6k² + 11k + 6

Now, we can use the induction hypothesis that k(k+1)(k+2) is an integer multiple of 6 to write k(k+1)(k+2) = 6m, where m is some integer. Substituting this into the above equation, we get:

k³ + 6k² + 11k + 6 = 6m + k³ + 3k² + 2k

Factoring out 3k² + 3k, we get:

k³ + 6k² + 11k + 6 = 6m + 3k(k+1) + 2k

Factoring out 2k from the last two terms, we get:

k³ + 6k² + 11k + 6 = 6m + 3k(k+1) + 2k = 6(m + k(k+1)/2)

Since m and k(k+1)/2 are both integers, we can conclude that (k+1)(k+2)(k+3) is an integer multiple of 6. Thus, by the principle of mathematical induction, the formula n(n+1)(n+2) is an integer multiple of 6 for all non-negative integers n

To learn more about Mathematical Induction from the given link

https://brainly.com/question/29503103

#SPJ1

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.

To learn more about exponential decay model, click here:

brainly.com/question/28596571

#SPJ4

The size of the x in the regular pentagon is 36 degrees.

In a regular pentagon, all the sides are congruent and all the angles are congruent. To find the internal angle of a regular pentagon, we can use the formula:

Interior angle = (n-2) x 180 / n

where n is the number of sides of the polygon.

For a regular pentagon, n = 5, so we can substitute this value into the formula:

Interior angle = (5-2) x 180 / 5

Interior angle = 3 x 180 / 5

Interior angle = 540 / 5

Interior angle = 108 degrees

For the value of x, we have

x = 108 degrees/3

Evaluate

x = 36 degrees

Therefore, the value of x in the regular pentagon is 36 degrees.

Read more about polygon at

https://brainly.com/question/8409681

#SPJ1

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.

Learn more about arithmetic series visit:

https://brainly.com/question/30260520

#SPJ1

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.

For similar question on comprehensive :

https://brainly.com/question/14814430

#SPJ11

Answer:

21

Step-by-step explanation:

Answer:

7x7=59

Step-by-step explanation:

one shakes 7 hands and there is 7 so 7 time 7

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

The sοlutiοn οf the given equatiοn is x=7 and cοrrect.

The equal sign ('=') cοnnects twο expressiοns tο fοrm a mathematical statement. There needs tο be at least οne unknοwable variable fοr the result tο be determined. An example οf an equatiοn is 3x - 8 = 16. When this equatiοn is sοlved, the result is x = 8.

Part A:

Given equatiοn is

3x+2(4+6x)= 113----------(1)

Multiplying the bracket term by 2 we get

3x+8+12x=113

Arranging the similar terms in the left hand side we get,

3x+12x+8=113

Subtracting 8 frοm bοth sides we get,

3x+12x+8-8=113-8

⇒(3x+12x)= 105

Adding the similar terms in the left hand side we get,

15x = 105

Dividing bοth sides by x= 105/15=7

Sο sοlving the equatiοn we get x=7.

Part B:

Checking fοr the sοlutiοn:

If the sοlutiοn is right then putting the value οf x in the left hand side οf the  given equatiοn will prοduce the right hand side.

putting x=7 in the left hand side οf equatiοn (1),

3x+2(4+6x)

= 3×7+2(4+6×7)

= 21+2(4+42)

= 21+ 2×46

= 21+ 92

= 113

Which is the right hand side οf equatiοn (1).

Sο, the sοlutiοn is cοrrect and checked.

Hence, the sοlutiοn οf the given equatiοn is x=7 and cοrrect.

To know more about equations

brainly.com/question/29174899

#SPJ1

Answer:

9x + 6 = 8

Step-by-step explanation:

"Sum" indicates addition problem. 9 times a number can be represented as 9x (with 9 and 'a number' being x). Then you add 6 because it states 'and 6'. Then, you add equals 8 (=8)

So your equation looks like:

9x + 6 = 8

x=-4 or -3 is simplified for x²+12/x²-16. This is because when the numerator and denominator are both set equal to zero, the only value of x that will satisfy both equations is x=-4 or -3.

The Zero Product Property states that if the product of two real numbers is equal to zero, then at least one of the two numbers must be zero.

When solving an equation like x²+12/x²-16 with x=-4, we must use the Zero Product Property, which states that if the product of two factors is equal to zero, then at least one of the two factors must be equal to zero.

In this case, we can set the numerator and denominator of the equation equal to zero and solve:

x²+12=0

x²-16=0

We can solve each of these equations separately by factoring:

x²+12=0

(x+3)(x+4)=0

x+4=0, x+3=0

x=-4 or -3

x²-16=0

(x-4)(x+4)=0

x-4=0

x=4

Therefore, x=-4 or -3 is the correct answer for x²+12/x²-16.

This is because when the numerator and denominator are both set equal to zero, the only value of x that will satisfy both equations is x=-4 or -3.

For more questions related to real numbers

https://brainly.com/question/155227

#SPJ1

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).

To know more about Standard deviation,visit:

https://brainly.com/question/23907081

#SPJ1

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.

To know more about pyramid visit:

https://brainly.com/question/13057463

#SPJ1

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.

learn more about probability: https://brainly.com/question/24756209

#SPJ1

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:

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 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

To know more about Pythagoras theorem visit :-

https://brainly.com/question/343682

#SPJ1

the set of factors that can be used to rewrite the expression is    

{12xy, (y + 2)}.

To rewrite the expression 12xy2 + 24xy in factored form, we need to find the greatest common factor (GCF) of the two terms, which is 12xy. We can then factor out this GCF to obtain:

12xy2 + 24xy = 12xy(y + 2)

Therefore, the set of factors that can be used to rewrite the expression is {12xy, (y + 2)}.

To understand why this set of factors is correct, we need to review some key concepts of factoring. When we factor an expression, we are essentially breaking it down into its constituent parts, which are multiplied together to give the original expression. In other words, we are looking for the factors that, when multiplied, give the original expression.

One common method of factoring is to use the distributive property of multiplication, which states that a(b + c) = ab + ac. This means that we can factor out a common factor from two or more terms by distributing it to each term. For example, if we have the expression 3x + 6, we can factor out the GCF of 3 to obtain:

3x + 6 = 3(x + 2)

Another key concept in factoring is the notion of a perfect square trinomial, which is a quadratic expression of the form a2 + 2ab + b2, where a and b are constants. This expression can be factored as (a + b)2. For example, the expression x2 + 4x + 4 is a perfect square trinomial, which can be factored as (x + 2)2.

Returning to the expression 12xy2 + 24xy, we can see that the GCF of the two terms is 12xy, since this is the largest factor that divides evenly into both terms. We can then use the distributive property to factor out this common factor:

12xy2 + 24xy = 12xy(y + 2)

This expression is now in factored form, since it consists of the product of the GCF 12xy and the binomial (y + 2). Note that the binomial (y + 2) is not a perfect square trinomial, since it is not of the form a2 + 2ab + b2. Therefore, we cannot further factor this expression using the methods of perfect square trinomials or other common factoring techniques.

In summary, to rewrite the expression 12xy2 + 24xy in factored form, we need to identify the GCF of the two terms, which is 12xy. We can then factor out this common factor using the distributive property, resulting in the factored form 12xy(y + 2). The set of factors that can be used to rewrite this expression is {12xy, (y + 2)}.

To know more about greatest common factor click here:

brainly.com/question/11221202

#SPJ1

The p-value for the given mentioned test, with the test static of -2.01  is calculated out to be  0.0456.

To calculate the p-value for this test, we first need to determine the appropriate null and alternative hypotheses.

Null hypothesis: The proportion of customers who wait longer than 5 minutes at the drive-through for this franchise is equal to the national value of 12%.

Alternative hypothesis: The proportion of customers who wait longer than 5 minutes at the drive-through for this franchise differs from the national value of 12%.

We can use a two-tailed Z-test to test this hypothesis, with a significance level of alpha = 0.05.

The test statistic is given as -2.01. Since this is a two-tailed test, we need to find the area in both tails of the standard normal distribution that is at least as extreme as the test statistic.

Using a standard normal distribution table or a calculator, we find that the area to the left of -2.01 is 0.0228. The area to the right of 2.01 is also 0.0228. Therefore, the total p-value is the sum of these two probabilities:

p-value = 0.0228 + 0.0228 = 0.0456

Therefore, the p-value for this test is 0.0456. This means that there is a 4.56% chance of obtaining a test statistic as extreme as -2.01, assuming that the null hypothesis is true. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the proportion of customers who wait longer than 5 minutes at the drive-through for this franchise differs from the national value of 12%.

Learn more about p-value :

https://brainly.com/question/30761573

#SPJ4

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).

[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]

Learn more about expression

https://brainly.com/question/14083225

#SPJ1