100 points please help

One figure should be rotated to match the other's alignment. Expand one figure till it is the same size as another.

A figure or object in a coordinate plane can be transformed to create a new figure or object that has been relocated, flipped, or altered in some other way. Translations, rotations, and reflections are the three primary forms of transformations. Moving a figure horizontally or vertically without altering its size or shape is known as translation. Rotation entails angling a figure around a fixed point, often known as the rotational center.

given

The subsequent transformations must be used in order to demonstrate similarity between two figures:

Translation (moving the figures to the same spot) (moving the figures to the same position)

Rotation (rotation one figure to fit the other) (rotating one figure to match the other)

Dilation (resizing the figures such that they have the same shape, but maybe different sizes) (resizing the figures so that they have the same shape, but possibly different sizes)

Consequently, the following set of transformations should be used to demonstrate that the figures abc and def are similar.

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2x + y = -7

y= -7-2x

put this value in 2nd equation

3x=6+4(-7-2x)

3x=6-28-8x

11x= -22

x= -2

y= -7-2(-2)

y= -7+4

y= -3

Here, we will use the method of steepest descent to find the minimiser of the function f(x1, x2, x3). The steepest descent method is an iterative optimization algorithm used to find the local minimum of a function.

Step 1: Initialize the starting point (x1, x2, x3) and set the initial values.
Step 2: Compute the gradient of the function f(x1, x2, x3) with respect to each variable (x1, x2, x3). The gradient is a vector that points in the direction of the steepest increase of the function.
Step 3: Calculate the step size, which determines how far along the descent direction we move. This can be done using various techniques, such as line search or a constant step size.
Step 4: Update the current point by moving in the direction of the negative gradient (steepest descent direction) with the computed step size. The new point will be (x1_new, x2_new, x3_new).
Step 5: Check the convergence criteria. If the change in the function value or the variables is below a certain threshold, stop the iteration process. Otherwise, return to Step 2 with the updated point.
By following these steps, the method of steepest descent will help us find the minimizer of the function f(x1, x2, x3).

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The two numbers in the system of equation is 5 and 13.

A group of multiple-variable equations that must all be solved concurrently make up a system of equations. Finding values for the variables that satisfy every equation in a system of equations is the objective. Each equation in the system reflects a connection between the variables. In order to find a singular solution or a group of solutions, systems of equations can be solved using a variety of methods, such as substitution or elimination. In many disciplines, including mathematics, physics, engineering, and economics, systems of equations can occur.

Let us suppose the two numbers as x and y.

x + y = 18

x - y = -8

The second equation can be written as:

x + 8 = y

Substitute the value of y in equation 1:

x + x + 8 = 18

2x = 10

x = 5

Substitute the value of x to get y:

x + y = 18

5 + y = 18

y = 13

Hence, the two numbers in the system of equation is 5 and 13.

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The number of driving lessons you need to take with a professional instructor before your parents can teach you varies depending on the regulations in your area. In some regions, a specific number of driving lessons is required by law before you can apply for your driver's license. As a result, you should check with your local Department of Motor Vehicles (DMV) or other regulatory agency to learn more about the specific requirements in your area.

In general, however, it is usually beneficial to take as many driving lessons as possible with a professional instructor. Professional driving instructors have been educated in how to teach driving skills safely and effectively. They have also assisted many other people in learning how to drive, and as a result, they have a wealth of knowledge and expertise to draw on.

The more driving lessons you take with a professional instructor, the more chances you'll have to learn and improve your driving abilities. You may be able to practice with your parents after only a few lessons, but it's generally a good idea to take as many as possible with an instructor before doing so. This will give you the best chance of success while you learn to drive safely and confidently.

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The average speed of the total journey is 75 kilometres per hour.

Anil completes the 72 kilometres journey between Bristol and Cardiff for 48 minutes. He then drive 69 kilometres from Cardiff to Swansea at an average speed of 60 kilometres per hour.

Therefore, let's find Anil average speed for the total of his journey as follows:
speed of his first journey = distance / time

speed of his first journey = 72 / 48

speed of his first journey = 1.5 km/minutes = 90 km/hrs

Therefore,

average speed of the total journey = 90 + 60 / 2

average speed of the total journey = 150 / 2

average speed of the total journey = 75 kilometres per hour

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Answer:

11

Step-by-step explanation:

15 - (p + 1)

Let p=3

15 - (3 + 1)

Parentheses first

15 - (4)

11

Answer:

11

Step-by-step explanation:

Given that,

p = 3

So, to find the value of the expression you have to solve it by replacing p with 3.

15 - ( p + 1 )

15 - ( 3 + 1 )

15 - 4

11

By using the formula for the confidence interval and the standard error, we were able to calculate the lower limit of the interval as 7.59.

To construct a 95% CI for the population mean of a normal distribution, we can use the formula:

CI = sample mean ± z* (standard error)

Where z* is the critical value from the standard normal distribution that corresponds to a 95% confidence level (i.e., 1.96), and the standard error is calculated as:

standard error = population standard deviation / √sample size

In this case, we are given that the population variance is 30, so the population standard deviation is √30 = 5.48 (rounded to two decimal places). The sample size is 20, so the standard error is:

standard error = 5.48 / √20 = 1.226

Now, we can use the formula for the CI:

CI = 10 ± 1.96 x 1.22

Simplifying this expression gives us:

CI = (7.59, 12.41)

This means that we are 95% confident that the true population mean lies within the interval from 7.59 to 12.41. The lower limit of the CI is 7.59, rounded to one decimal place.

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Answer:

Step-by-step explanation:

First, we need to calculate the annual interest rate from the given APR.

APR = 2.25%

Daily interest rate = 2.25% / 365 = 0.00616438

Now, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = time in years

In this case, P = $2,000, r = 0.00616438, n = 365 (daily compounding), and t = 4.

A = 2000(1 + 0.00616438/365)^(365*4)

A = 2000(1.00616438)^1460

A = $2,388.34 (rounded to the nearest cent)

Therefore, the answer is option D) $2,388.34.

Answer: slope=4

Step-by-step explanation:

[tex]Slope=\frac{y2-y1}{x2-x1}[/tex]

[tex]Slope=\frac{4- - 4}{3-2}[/tex]

[tex]Slope=\frac{4+4}{3-2}[/tex]

[tex]Slope=4[/tex]

The number of ways to arrange N people with A and B separated is given by expression   N! - 2*(N-1)! .

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, operators, and functions that are grouped together in a meaningful way. Expressions can be as simple as a single number or variable, or they can be complex and include many different elements. They are used to represent mathematical relationships and operations, and can be evaluated or simplified using mathematical rules and techniques. Examples of expressions include:

Now,

Let the two particular people be A and B.

If we place A in a spot, there are N-1 spots left for B to be placed. Once A and B are placed, there are (N-2)! ways to place the remaining people. Therefore, the number of ways to arrange N people with A and B separated is:

(N-1) * (N-2)!

Alternatively, we can find the total number of ways to arrange N people in a line (N!) and subtract the number of ways to arrange them with A and B together.

To find the number of ways to arrange N people with A and B together, we can treat A and B as a single entity, so there are (N-1)! ways to arrange the remaining people with AB together. However, A and B can be arranged in two ways (AB or BA), so we need to multiply (N-1)! by 2.

Therefore, the number of ways to arrange N people with A and B separated is:

N! - 2*(N-1)!

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Answer:

Data Visualization Tools

Step-by-step explanation:

Yes, the number of linearly independent columns in a matrix A is equal to the number of linearly independent rows in A.

This is because the definition of linear independence states that no linear combination of a set of vectors can equal the zero vector, so if one set of vectors is linearly independent, the other set of vectors must also be linearly independent.

To explain further, the number of linearly independent vectors in a matrix A is determined by the rank of the matrix. The rank of a matrix is the number of linearly independent rows and columns in the matrix.

So if the rank of A is n, then the number of linearly independent columns and rows of A must be n. This is because if there are n linearly independent columns in the matrix, the number of linearly independent rows must also be n.

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Answer:

The answer to our problem is, $17.75

Step-by-step explanation:

First we need to find out what is 25% of 71

25% of 71 is 17.75. Or [tex]17\frac{3}{4}[/tex] We would need to stick to the term in decimals because of we are using money. Have you ever heard of a fraction in money my guess is no. So let’s stay with decimals. 17.75

How I got it:

25 percent * 71

= (25:100)* 71

= (25* 71):100

= 1775:100

= 17.75

Percentage solution with steps:

71 = 100% (1)

X = 25% (2)

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of bothequations have the same unit (%); we have

[tex]\frac{71}{x} = \frac{25}{100}[/tex]

X = 17.75

Thus the answer to your problem is, $17.75

Answer:

If you add two positive numbers together you will get a positive.

Step-by-step explanation:

If there are 243 students at the school, then there are 81 students at Rolling Hills Middle School who have pets.

If the ratio of the total number of students to the number of students with pets at Rolling Hills Middle School is 3 to 1, this means that for every 3 students at the school, there is 1 student with a pet.

Let's represent the total number of students at the school as "3x" (since the ratio is 3 to 1, we can use any multiple of 3 as a placeholder for the total number of students), and the number of students with pets as "x". Therefore, we can write the following equation:

3x : x = 3 : 1

To solve for x, we can cross-multiply:

3x * 1 = x * 3

3x = 3x

We can see that the equation is true for any value of x, which means that there are many possible solutions. However, since we know that the total number of students at the school is 243, we can use this information to solve for x:

3x = 243

x = 81

Therefore, there are 81 students at Rolling Hills Middle School who have pets.

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Answer: y = 17x + 114

Step-by-step explanation:

The equation for the slope-intercept form is y = mx + b.

Arrange the equation so that it resembles y = mx + b.

You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.

y + 5 = 17(x + 7)

y + 5 = 17x + 119

y + 5 - 5 = 17x + 119 - 5

y = 17x + 114

Answer:

Y = 17x + 114

Step-by-step explanation:

1. Y + 5 = 17 (x+7)

2. Y + 5 = 17x + 119   [Multiply the numbers in parenthesis by 17.]

3. Y = 17x + 114.     [To keep the balance and move the 5 over, subtract it from 119.]

The solution of the system of equations is (2, 1).

Here we have the system of equations:

y = 2x - 3

y = -x + 3

To solve the system of equations graphically, we need to graph both of these lines in the same coordinate axis and then find the point where the lines intersect.

That point will be the solution of the system.

On the image at the end you can see the graph of the system of equations, there we can see that the solution is (2, 1).

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As per the surface area, the height of the cylindrical gallon tub of ice cream is approximately 2.625 inches. (option d).

In this problem, we have been given the diameter of the tub, which is 8 inches. The radius of the tub can be calculated by dividing the diameter by 2, which gives us a radius of 4 inches.

We have also been given the total surface area of the tub, which is 232.36 square inches. Using the formula for surface area, we can write:

232.36 = 2π(4)² + 2π(4)h

232.36 = 100.48 + 25.12πh

Subtracting 100.48 from both sides, we get:

131.88 = 25.12πh

Dividing both sides by 25.12π, we get:

h = 131.88 / (25.12π)

Using the value of π as 3.14, we can simplify this expression to:

h = 131.88 / 79.104

h ≈ 2.6256 inches

Hence the correct option is (d).

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This equation fits the given data: Oy = -2x + 10. The equation creates a linear relationship between the x and y values, with each x value increasing by 1 resulting in a decrease in the y value by 2.

Linear refers to a type of relationship between two or more variables. It is a straight line relationship where the output is directly proportional to the input. Linear relationships can be observed in the natural world such as in the relationship between distance and time. They can also be observed in mathematical equations and models, where the output is directly related to the input. Linear relationships are also used to represent real-world problems in the form of linear equations and models.

The equation satisfies the data points, as plugging in each x value will result in the corresponding y value. For example, when x = 0, the equation produces y = 10, which is the given data point. Similarly, when x = 2, the equation produces y = 6, which is also the given data point.

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This equation fits the given data: y = 1/3x + 2. The equation creates a linear relationship between the x and y values. Hence the correct option is b.

Linear refers to a type of relationship between two or more variables. It is a straight line relationship where the output is directly proportional to the input. Linear relationships can be observed in the natural world such as in the relationship between distance and time. They can also be observed in mathematical equations and models, where the output is directly related to the input. Linear relationships are also used to represent real-world problems in the form of linear equations and models.

The equation satisfies the data points, as plugging in each x value will result in the corresponding y value. For example, when x = 0, the equation produces y = 10, which is the given data point. Similarly, when x = 2, the equation produces y = 6, which is also the given data point.

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The correct option for the large bag contains marbles:

The given question:

marbles in the bag:

40 blue marbles

8 green marbles

16 yellow marbles

21 white marbles

One marble is selected by Tyra.

Then, the correct option are-

A: There is a two to one chance that the marble she chooses will be yellow rather than green.

16 yellow marbles = 2* 8 green marbles

B: Compared to all the other colors combined, the stone she chooses is more likely to be blue.

40 blue marbles have the highest number.

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The complete question is-

A large bag contains the following marbles: •

40 blue marbles

8 green marbles

16 yellow marbles

21 white marbles

Tyra selects a marble from the bag at random. Based on the information, which statement is true?

A The marble she selects is twice as likely to be yellow as it is to be green.

B.The marble she selects is more likely to be blue than all the other colors combined.

C. The marble she selects is equally likely to be yellow or white

D. The marble she selects is three times as likely to be white as it is to be green.​

Check the picture below.

[tex]x^2=(8+2)(2)\implies x^2=20\implies x=\sqrt{20}\implies x\approx 4.5[/tex]

The value of x is 4.5 rounded to the nearest tenth.

Tangent of a circle is defined as the line which passes through exactly one point on the circle.

Secant of a circle is the line which passes through two points on the circle.

Secant-Tangent Rule states that if a tangent and a secant are drawn to a circle from the same point outside the circle, then the square of the length of the tangent segment is equal to the product of the lengths of secant and the segment of secant outside the circle.

Using the theorem, we can say here that,

(8 + 2) 2 = x²

x² = 10 × 2

x² = 20

x = √20

x = 4.472 ≈ 4.5

Hence the value of x is 4.5.

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Therefore, the amount of heat produced when 52.40 g of methane, CH4, burns in an excess of air is -39568.2 kJ

The amount of heat produced when 52.40 g of methane, CH4, burns in an excess of air can be calculated using the following equation:

[tex]Q = mcΔT[/tex]

Where Q is the amount of heat produced (in kJ), m is the mass of the methane (in g), and ΔT is the change in temperature (in K).

Using the equation, the amount of heat produced can be calculated as follows:

Q = [tex](52.40 g)(-753.15 K) = -39568.2 kJ[/tex]
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The answer to the expression 547 + 233 × 5 - 142 is 1752. To solve the expression, we must follow the order of operations, which is PEMDAS: Parentheses, Exponents, Multiplication, and Division (performed left to right), and Addition and Subtraction (performed left to right).

Since there are no parentheses or exponents in this expression, we start with multiplication and division. In this case, we have to multiply 233 by 5, which gives us 1165. Then, we add 547 to 1165, which gives us 1712. Finally, we subtract 142 from 1712, which gives us the final answer of 1752. Therefore, the result of the expression 547 + 233 × 5 - 142 is 1752, which can be obtained by following the order of operations and performing the arithmetic operations in the correct order.

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By using LCM, we find that the three planets  x, y and z will be in the exact same locations again after $5400$ days.

To find the minimum positive number of days before the planets are all in the exact same locations again, we need to find the least common multiple (LCM) of the three given periods of rotation.

The prime factorization of each of the given periods of rotation is as follows

$360 =[tex]2^3 \cdot 3^2 \cdot 5$[/tex]

$450 =[tex]2 \cdot 3^2 \cdot 5^2$[/tex]

$540 =[tex]2^2 \cdot 3^3 \cdot 5$[/tex]

To find the LCM, we need to take the highest power of each prime factor that appears in any of the three factorizations. So the LCM is:

[tex]$LCM = 2^3 \cdot 3^3 \cdot 5^2 = 2^3 \cdot 27 \cdot 25 = 5400$[/tex]

Therefore, the three planets will be in the exact same locations again after $5400$ days.

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The expression 3x-(4-x) is equivalent to 4x-4

The distributive property is a mathematical property that describes the relationship between multiplication and addition or subtraction. It states that when a number is multiplied by a sum or difference of two or more numbers, the result is the same as if we multiplied the number by each of the individual terms inside the parentheses and then added or subtracted the products.

To simplify the expression 3x-(4-x), we can distribute the negative sign to the second term inside the parentheses, which gives:

3x - (4 - x) = 3x - 4 + x

Now we can combine the like terms (3x and x) to get:

3x - 4 + x = 4x - 4

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The given question is incomplete, the complete question is:

Which expression is equivalent to 3x-(4-x)?

If 10 friends are going to occupy 10 seats in a shuttle on the way to the airport, then they can arrange themselves in the shuttle in 10! or 3,628,800 ways.

Step-by-step explanation: There are 10 friends and 10 seats to be occupied in a shuttle.

Therefore, the number of ways to arrange the 10 friends in 10 seats is given by 10! (10 factorial), which is calculated as follows: 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1= 3,628,800

Therefore, 10 friends can arrange themselves in the shuttle in 3,628,800 ways.

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Rounding to three decimal places, the probability that exactly 7 Americans out of a sample of 15 own an answering machine is approximately 0.170.

To find the probability that exactly 7 of the 15 Americans selected at random own an answering machine, we can use the binomial distribution formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where P(X = k) is the probability of getting exactly k successes, n is the sample size, p is the probability of success, and (n choose k) is the binomial coefficient which represents the number of ways to choose k successes out of n trials.

In this case, n = 15, p = 0.69 (the proportion of Americans who own an answering machine), and k = 7. Thus, the probability of getting exactly 7 Americans who own an answering machine out of a sample of 15 is:

P(X = 7) = (15 choose 7) * 0.69^7 * (1 - 0.69)^(15 - 7)

Using a calculator or statistical software, we can evaluate this expression to find:

P(X = 7) ≈ 0.170

This means that if we were to repeat this survey many times with samples of size 15, we would expect approximately 17% of the samples to have exactly 7 Americans who own an answering machine.

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