Determine whether angle-angle-angle (AAA) is a valid means for establishing triangle congruence. If it is a valid criterion, explain why. If it is not valid, use GeoGebra to create a counterexample demonstrating that it doesn’t work and give an explanation. If you construct a counterexample, take a screenshot of your work, save it, and insert the image in the space below.

Using translation concepts, it is found that the function \(f(x) = -3\sqrt{x}\) is the function \(g(x) = \sqrt{x}\) reflected over the x-axis and vertically stretched by a factor of 3.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, from \(g(x) = \sqrt{3}\) to \(f(x) = -3\sqrt{x}\), g(x) was multiplied by -3, that is, it was reflected over the x-axis(due to the multiplication by the negative number) and vertically stretched by a factor of 3.

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Answer:

x = 2\(\sqrt{5}\)

Step-by-step explanation:

The radius of the circle = 4 + 2 = 6

Thus the radius is from the centre to the top of segment x

Using Pythagoras' identity in the right triangle formed, that is

x² + 4² = 6²

x² + 16 = 36 ( subtract 16 from both sides )

x² = 20 ( take square root of both sides )

x = \(\sqrt{20}\) = 2\(\sqrt{5}\)

If 3 is an equilibrium value of a differential equation, it means that all values will remain constant at 3. If the initial value is below 3, the values will approach 3.

In the context of a differential equation, an equilibrium value represents a stable solution where the derivative of the function is zero. In this case, if the equilibrium value is 3, it means that when the initial value of the function is set to 3, the function will remain constant at 3 for all time.

If the initial value is below 3, the values will tend to approach the equilibrium value of 3. As time progresses, the function will evolve, and its values will change. However, due to the nature of the equilibrium at 3, the values will gradually move closer to 3 over time, eventually stabilizing at that value. This behavior is characteristic of stable equilibrium points in differential equations.

On the other hand, if the initial value is above 3, the values will tend to move away from 3, either increasing or decreasing depending on the specific dynamics of the differential equation. The behavior of the system around the equilibrium value is determined by the equation's slope or rate of change

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To find the distance that Scott drove on his trip to North Carolina, we can use the equation: Distance = Speed x Time. Since we know that Scott's average speed was 50 mph, we can substitute this value into the equation and write: Distance = 50t, where t is the time it took Scott to drive to North Carolina.

This equation tells us that the distance Scott drove is directly proportional to the time he spent driving. So, if he drove for 4 hours, the distance he covered would be 50 x 4 = 200 miles. Similarly, if he drove for 6 hours, the distance would be 50 x 6 = 300 miles. Therefore, we can use this equation to calculate the distance Scott drove for any given amount of driving time.
To find the distance Scott drove, you can use the equation "distance = average speed × time." In this case, Scott's average speed while driving is 50 mph, and the time taken is represented by "t." To create the equation using these terms, you can write:

Distance = 50 × t

This equation helps you calculate the distance Scott drove on his trip to North Carolina by multiplying his average driving speed (50 mph) by the time it took him to get there (t).

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Answer:

Solution- x = 5 Equation- x + 4 = 9

Step-by-step explanation:

I hope this helps you understand.

Answer:

uhm... if where doing lettes its BC but the number... maybe 14 or something im not really good at this type of math

Step-by-step explanation:

Answer:

7.5 miles per hour

Step-by-step explanation:

3.75/.5 = 7.5 miles per hour

The probability that the sample proportion is less than 0.27 with population mean 0.25 and sample size 107 is equals to 0.1844.

We have a historical data reports. Here claim is defined as, the manager believes that 25% of the company's orders come from first-time customers.

Sample size of orders, n = 107

We have to determine probability that the sample proportion is less than 0.27, i.e., P( X < 0.27). Now, 0.25 is the population proportion and sample proportion is

\(\hat p = 0.27 \). Calculate the

Standard deviations, σ \( = \sqrt{\frac{0.25 × (1 -0.25) } {107}} \)

= 0.0419

As we see the sample size is > 30, the normal distribution can be used. The Z-Score formula for sample proportion is written as \(Z = \frac{\hat p - p}{\sigma }\) , where, E --> standard error

Now, the required probability, P(p-hat< 0.27) = \(P (\frac{ \hat p - p }{ \sigma} < \frac{0.27 - 0.25}{0.0419})\)

= P ( Z < 0.48)

Using the distribution table value of P(Z< 0.48) is 0.1844. Hence, required probability value, P(p-hat < 0.27) is 0.1844.

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The normal approximation for the distribution of (outcome - point spread is (np(1 - p)0.5

What is Normal Distribution?

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.

Reason:

The number of trials n in the binomial setting and the constant success probability p for each of these trials decide the proper normal distribution to choose. Our binomial variable has a mean of np and a standard deviation of (np(1 - p)0.5, which approximates a normal distribution.

It can be demonstrated using simple mathematics that there are a few circumstances in which we must apply a normal approximation to the binomial distribution. To ensure that both np and n(1 - p) are higher than or equal to 10, the number of observations n must be sufficient, as must the value of p. This is a generalization that is supported by statistical theory. The standard approximation can always be used, however it may not be a very accurate approximation if these requirements are not met.

The normal approximation for the distribution of (outcome - point spread is (np(1 - p)0.5

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The radius of convergence is R = √(1/2).

To find the coefficients a_2n and a_2n+1 in the Taylor series of g(t) about 0, we can express g(t) as a geometric series and use the formula for the sum of a geometric series.

First, let's rewrite g(t) as:

g(t) = 1 / (1 + 2t^2)

This can be expressed as a geometric series with the first term a = 1 and the common ratio r = -2t^2.

Using the formula for the sum of an infinite geometric series, which is given by:

S = a / (1 - r)

we can find the coefficients a_2n and a_2n+1.

For even values of n (n = 0, 1, 2, ...):

a_2n = 1 / (1 - (-2t^2))^2n

= 1 / (1 + 2t^2)^(2n)

For odd values of n (n = 0, 1, 2, ...):

a_2n+1 = 1 / (1 - (-2t^2))^(2n+1)

= 1 / (1 + 2t^2)^(2n+1)

The radius of convergence (R) for the series can be determined by finding the range of values of t for which the series converges. In this case, the series is a geometric series, so it converges when the absolute value of the common ratio is less than 1:

|-2t^2| < 1

2t^2 < 1

t^2 < 1/2

|t| < √(1/2)

Therefore, the radius of convergence (R) for the series is √(1/2).

To summarize:

a_2n = 1 / (1 + 2t^2)^(2n)

a_2n+1 = 1 / (1 + 2t^2)^(2n+1)

The radius of convergence is R = √(1/2).

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56.6 years  is the mean of the modes of the given set of numbers.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode.

                     Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

The mean is calculated by adding together all the values

                 =  (54+54+54+55+56+57+57+58+58+60+60

                  = 623

                  =  56.6 years.

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Answer:

Step-by-step explanation:

To find g[f(2)], we need to evaluate the composite function g[f(2)] by first finding f(2) and then substituting the result into g(x).

Let's start by finding f(2):

f(x) = 2x² - 3x

f(2) = 2(2)² - 3(2)

= 2(4) - 6

= 8 - 6

= 2

Now that we have the value of f(2) as 2, we can substitute it into g(x):

g(x) = 5x - 1

g[f(2)] = g(2)

= 5(2) - 1

= 10 - 1

= 9

Therefore, g[f(2)] is equal to 9.

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The pair in the solution of the equation 2x-3y = 7 is (5,1).

The set of all values that, when substituted for unknowns, make an equation true is known as the solution.

A specific location on the graph is the solution of a linear equation in two variables, where ax+by = c, meaning that when the x-coordinate is multiplied by a and the y-coordinate is multiplied by b, the sum of these two values equals c. There are essentially an endless number of solutions to a linear equation with two variables.

Now in the question,

To find the pair of solutions of equation 2x - 3y = 7, we satisfy all the pairs one by one in the given equation

1. Putting the value of (x, y) as (0,2) in the equation we get-

2*0 - 3*2 = 7 ⇒ -6 =7

Therefore LHS ≠ RHS

Hence it is not the solution to the equation.

2. Putting the value of (x, y) as (2,-3) in the equation we get-

2*2 - 3*-3 = 7 ⇒ 13 =7

Therefore LHS ≠ RHS

Hence it is not the solution to the equation.

3. Putting the value of (x, y) as (5,1) in the equation we get-

2*5 - 3*1 = 7 ⇒ 7 = 7

Therefore LHS = RHS

Hence it is the solution to the equation.

4. Putting the value of (x, y) as (1,5) in the equation we get-

2*1 - 3*5 = 7 ⇒ -13 =7

Therefore LHS ≠ RHS

Hence it is not the solution to the equation.

Thus (5,1) is the solution of the equation.

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Answer:

17 =x

Step-by-step explanation:

These are alternate interior angles and alternate interior angles are equal when the lines are parallel

9x+7 = 10x-10

Subtract 9x from each side

9x+7-9x = 10x-10-9x

7 = x-10

Add 10 to each side

7+10 =x-10+10

17 =x

Answer:

The answer and work is both located in the screenshot provided!

Step-by-step explanation:

Hoped this helped!

Answer: It is 972

Uhm I just used Desmos scientific calculator

The standard matrix of a reflection in ℝ² across the line -2x₁ + 2x₂ = 0 is given by [[0, 1], [1, 0]].

To find the standard matrix of a reflection in ℝ² across a given line, we can use the formula: S =\(I - 2nn^T\)

where S is the standard matrix, I is the identity matrix, and \(nn^T\) is the outer product of the unit normal vector of the line.

In this case, the line is defined by the equation -2x₁ + 2x₂ = 0. By rearranging the equation, we have:

2x₂ = 2x₁

x₂ = x₁

This suggests that the line has a slope of 1, which means the normal vector is orthogonal to the line and has a slope of -1. A unit vector in the direction of the normal vector is\([1/sqrt(2), -1/sqrt(2)].\)

Using this normal vector, we can calculate the outer product \(nn^T\):

\(nn^T = [[1/sqrt(2)], [-1/sqrt(2)]] * [[1/sqrt(2), -1/sqrt(2)]]\)

= [[1/2, -1/2], [-1/2, 1/2]]

Finally, subtracting this outer product from the identity matrix, we obtain the standard matrix of the reflection:

S = I - \(2nn^T\) = [[1, 0], [0, 1]] - 2[[1/2, -1/2], [-1/2, 1/2]] = [[0, 1], [1, 0]]

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Answer:

Hey there!

When we are given what one of our variables is equal to, we can easily solve the system of equations via substitution, which is where we take the variable value, plug it into the other equation, and solve for the other variable.

In this case, we just take our value for y and plug it in for the value for y in the first equation and solve for x.

2(-x+7)=14-2x

-2x+14=14-2x

-2x=-2x

x=x

As we can see, there are infinitely many solutions to this first equation, which means that there is no possible way to solve for y because x has infinitely many solutions, so there are infinitely many solutions to this system of equations, because they are both the same line.

I hope this helps! :D

Answer:

ans of an 1 is option b

Step-by-step explanation:

because x and y both are +ve

The score that could not be your exam score is 70.The correct option is (a).To calculate the standard deviation of a set of data, you take the square root of the average of the squared differences of the values from the mean.

The question is asking which of the given scores could not be your exam score if your exam score is 2.12 standard deviations below the mean. The mean score on the exam is 82, so the score that is 2.12 standard deviations below the mean is: 82 - (2.12 x standard deviation) = 82 - (2.12 x 10) = 70.Therefore, the score that could not be your exam score is 70.

To explain further, standard deviation is a measure of how spread out the numbers in a set of data .The other options (85, 80, and 90) are not correct because they are not 2.12 standard deviations below the mean. To summarize, the score that is 2.12 standard deviations below the mean score of 82 is 70.

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1. The constant term of the polynomial is: 8.

2. The exponent of the third term is 1.

A term of a polynomial can include any of the following:

Any of the above is referred to as a term of a polynomial.

Given the polynomial, -y^4 + 2y² + 3y + 8, the polynomial has 4 terms, -y^4, 2y², 3y, and 8.

Thus:

1. The constant term of the polynomial is: 8.

2. The exponent of the third term is 1.

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Answer:

2:5

Step-by-step explanation:

divide / simplify the ratio

Answer:

2:5     8:20

Because 2:5 is equivalent to 4:10 and so it 8:20

Answer:

706.858347

Step-by-step explanation:

\( \: \Large \mathbb{SOLUTION:}\)

\( \: \: \rm{ {7x}^{2} + 4x - {x}^{2}}\)

\( \: \: \text{Reorder and gather like terms}\)

\( \: \: \rm{( {7x}^{2} - {x}^{2} ) + 4x}\)

\( \: \: \text{Collect coeffiecients of like terms}\)

\( \: \: \rm{(7 - 1) {x}^{2} + 4x}\)

\( \: \: \text{Calculate the sum or difference}\)

\( \: \: \rm{ \underline{ \underline{ {6x}^{2} + 4x}}}\)

\( \rm{6x {}^{2} + 4x}\)

Collect like terms

\( \red{7x {}^{2} } + 4x \red{ - x {}^{2} }\)

\( \red{6x {}^{2} } + 4x \)

Answer:

35

Step-by-step explanation:

Just divide 350 by 10 since it asks, "How many miles per gallon".  

= 35

Answer:

The number of pounds that will fit in each bag is 2/3 pounds of flour

Step-by-step explanation:

Here, we want to know the amount of pounds that will fit in each bag

What we have to do here is to divide the total number of pounds of flour, by the number of bags filled

We have this as;

2 3/4 divided by 4 1/8

This is;

11/4 divided by 33/8

= 11/4 * 8/33 = 2/3 pounds

Step-by-step explanation:

the correct answer is option a 6a-7

To calculate the confidence interval for the population mean, we need to use the sample mean, sample standard deviation, sample size, and degree of confidence. In this case, the sample mean is 6.4 years, the sample standard deviation is 20 years, the sample size is 42, and the degree of confidence is 0.99.

Step 1: Find the critical value (z-score) for the 0.99 degree of confidence. Using a z-table or calculator, the z-score for 0.99 confidence is approximately 2.576.

Step 2: Calculate the margin of error. The formula for margin of error is (z-score * sample standard deviation) / sqrt(sample size). Plug in the values: (2.576 * 20) / sqrt(42) ≈ 8.

Step 3: Calculate the confidence interval. Subtract and add the margin of error to the sample mean: 6.4 - 8 = -1.6 and 6.4 + 8 = 14.4.

The confidence interval for the population mean is approximately between -1.6 and 14.4 years. None of the multiple-choice options provided match this result. Please double-check the numbers given in the problem.

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Answer:

about 2 or 3

Step-by-step explanation:

heres what u do go onlie and put the books up for sale.

Answer:

The book of amber will reach the pool 6.78 seconds before the other

Step-by-step explanation:

common sense