My algebra 2 teacher wants me to simplify this but i dont know how

If the gradient of AB is 0, the coordinates of point A and B are (-4, 2) and (6, 2) respectively.

If the gradient of line AB is 0, it means that the line is horizontal. In this case, we can determine the coordinates of points A and B using the information given.

Since the midpoint of line AB is (1,2), we can infer that the average of the x-coordinates of A and B is 1, and the average of the y-coordinates is 2.

Let's assume that point A has coordinates (x₁, y₁) and point B has coordinates (x₂, y₂).

Since the midpoint of line AB is (1,2), we can write the following equations:

(x₁ + x₂) / 2 = 1 (1)

(y₁ + y₂) / 2 = 2 (2)

We also know that the length of line AB is 10 units.

Using the distance formula, we can express this as:

√((x₂ - x₁)² + (y₂ - y₁)²) = 10 (3)

Since the gradient of line AB is 0, the y-coordinates of points A and B must be the same. Therefore, y₁ = y₂. We can substitute this into equations (1) and (2):

(x₁ + x₂) / 2 = 1 (1')

y₁ = y₂ = 2 (2')

Now, let's substitute y₁ = y₂ = 2 into equation (3):

√((x₂ - x₁)² + (2 - 2)²) = 10

√((x₂ - x₁)²) = 10

(x₂ - x₁)² = 100

Taking the square root of both sides, we get:

x₂ - x₁ = ±10

Now, we have two cases to consider:

Case 1: x₂ - x₁ = 10

From equation (1'), we have:

(x₁ + x₁ + 10) / 2 = 1

2x₁ + 10 = 2

2x₁ = -8

x₁ = -4.

Substituting x₁ = -4 into equation (1), we find:

(-4 + x₂) / 2 = 1

-4 + x₂ = 2

x₂ = 6

Therefore, in this case, point A has coordinates (-4, 2), and point B has coordinates (6, 2).

Case 2: x₂ - x₁ = -10

From equation (1'), we have:

(x₁ + x₁ - 10) / 2 = 1

2x₁ - 10 = 2

2x₁ = 12

x₁ = 6

Substituting x₁ = 6 into equation (1), we find:

(6 + x₂) / 2 = 1

6 + x₂ = 2

x₂ = -4

Therefore, in this case, point A has coordinates (6, 2), and point B has coordinates (-4, 2).

To summarize, if the gradient of AB is 0, there are two possible solutions:

A(-4, 2) and B(6, 2)

A(6, 2) and B(-4, 2).

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Answer:

x² + 34x + 104 = 0

x² + 34x = -104

x² + 34x + ((1/2)(34))² = -104 + ((1/2)(34))²

x² + 34x + 17² = -104 + 17²

x² + 34x + 289 = 185

(x + 17)² = 185

x + 17 = +√185

x = -17 + √185

When the consumption schedule lies below the 45-degree reference line, it means that at every level of income, people are consuming less than their income.

The consumption schedule represents the relationship between income and consumption in an economy, while the 45-degree reference line represents the line where income and consumption are equal.

In this scenario, saving occurs because people are not spending all of their income. The difference between their income and consumption is their savings. Thus, the amount of saving in the economy will increase as the consumption schedule moves further below the 45-degree reference line.

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When the consumption schedule lies below the 45-degree reference line, saving what does it means?

The expression √180 * 2√30 is equivalent to the expression 60√6

An equation is an expression that shows the relationship between two numbers and variables.

The square root is a factor of a number that, when multiplied by itself, gives the original number.

Given the expression √180 * 2√30

Collecting like terms give:

= 2√(180 * 30)

Simplifying:

= 60√6

The expression √180 * 2√30 is equivalent to the expression 60√6

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Let's assume the cost of a hamburger is represented by 'h' and the cost of an order of fries is represented by 'f'. The values of 'h' will be $1 and 'f' will be $1.20.

From the information provided, we can set up a system of equations based on the total cost of hamburgers and fries purchased by each student:

2h + 3f = 5.60 (Equation 1)

4h + f = 5.20 (Equation 2)

To solve this system, we can use various methods such as substitution or elimination. Let's use the elimination method to eliminate 'f'.

By multiplying Equation 2 by 3, we can get:

12h + 3f = 15.60 (Equation 3)

Now, subtracting Equation 1 from Equation 3, we obtain:

12h + 3f - (2h + 3f) = 15.60 - 5.60

10h = 10

h = 1

Substituting the value of h = 1 into Equation 2, we find:

4(1) + f = 5.20

4 + f = 5.20

f = 1.20

Therefore, a hamburger costs $1 and an order of fries costs $1.20.

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The expression (15x - 6) / (7x - 6), where no denominator equals zero, is equivalent to (15x - 6) / (7x - 6).

To simplify the expression (15x - 6) / (7x - 6), we can start by factoring the numerator and the denominator if possible. However, since no denominator can equal zero, we need to ensure that the expression 7x - 6 is not equal to zero. Let's solve the equation 7x - 6 = 0 to find the value of x that makes the denominator zero.

7x - 6 = 0

7x = 6

x = 6/7

Since x = 6/7 is the value that makes the denominator zero, we cannot use this value in our simplified expression. Therefore, we need to exclude x = 6/7 from the domain of the expression.

Now, let's consider the remaining values of x that do not make the denominator zero. We can simplify the expression by dividing both the numerator and the denominator by their greatest common divisor. In this case, the greatest common divisor of 15x - 6 and 7x - 6 is 1 since there are no common factors other than 1.

Dividing both the numerator and the denominator by 1 yields:

(15x - 6) / (7x - 6)

Since we cannot further simplify the expression due to the restriction on the domain, the simplified form of the expression, where no denominator equals zero, is:

(15x - 6) / (7x - 6)

In summary, the expression (15x - 6) / (7x - 6), where no denominator equals zero, is equivalent to (15x - 6) / (7x - 6).

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Answer:

See photo #7

Step-by-step explanation:

Perimeter = 2 (l + b)

2x² + 4x - 4y = 2 {(2x - 3y) + b}

2x² + 4x - 4y = (4x - 6y) + 2b

2x² + 4x - 4y - (4x - 6y) = 2b

2x² + 4x - 4y - 4x + 6y = 2b

2x² + 2y = 2b

(2x² + 2y)/2 = b

x² + y = b

Breadth = x² + y

Answer:

By scoring 240 in the sixth game, Marlon can maintain this exact average

Step-by-step explanation:

The first thing to do here is to calculate the average for the first 5 games.

Mathematically, the average can be calculated by adding all the scores in the games and dividing by 5;

= (210 + 225 + 254 + 231 + 280)/5 = 1200/5 = 240

Now to maintain this average score of 240, we want to know the score she must have in the 6th game.

Let the score be x;

By adding x to the previous total of 1200 before and dividing by the new count of 6, we can work our way to get x.

Mathematically, what we are saying is;

(1200 + x)/6 = 240

6 * 240 = 1200 + x

1440 = 1200 + x

x = 1440 -1200

x = 240

False. A Pert chart, also known as a Program Evaluation and Review Technique chart, is a project management tool used to represent a project's timeline. It is not a pie chart but rather a flowchart that illustrates the tasks involved in completing a project, the order in which they need to be done, the estimated duration of each task, and the dependencies between them.

Pert charts are used to help project managers plan, schedule, and monitor the progress of a project. They allow project managers to identify critical paths, which are the series of tasks that must be completed on time for the project to meet its deadline. Pert charts also help managers to identify the earliest and latest possible start and end times for each task, as well as slack time, which is the amount of time that a task can be delayed without affecting the overall project timeline. Overall, Pert charts are a valuable tool for project management, but they are not related to pie charts.

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Factoring integers with sublinear resources on a superconducting quantum processor can be achieved using quantum approximate optimization algorithm" (QAOA) or quantum phase estimation algorithm (QPE) approach.

Factoring large integers is a problem of significant importance in the field of cryptography.

Classical computers have limited efficiency in solving this problem, and their performance is expected to decline further as the size of the integers to be factored increases.

In contrast, quantum computers are expected to have exponential speedup in factoring large integers, thanks to Shor's algorithm.

Recently, researchers have been exploring the possibility of using superconducting quantum processors to factor integers with sublinear resources.

One approach is to use a so-called "quantum approximate optimization algorithm" (QAOA), which maps the problem of factoring integers to a problem of finding the ground state of a certain Hamiltonian.

The QAOA can be implemented using a superconducting quantum processor, with the problem Hamiltonian implemented by a set of two-qubit gates.

Another approach is to use the quantum phase estimation algorithm (QPE) to estimate the eigenvalues of the problem Hamiltonian.

This can be used to factor integers by finding the period of a certain function using the quantum Fourier transform, as in Shor's algorithm. QPE can be implemented on a superconducting quantum processor using phase estimation circuits, which require only polynomial resources.

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The probability that the artist chosen will be a painter or a photographer is 3/4

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

To solve this exercise the formula and the procedure that we have to use for probability is:

probability= (achieving success / possible outcomes)

Achieving success = 7 painters + 5 photographer = 12

Possible outcomes = 7 painters + 5 photographer + 4 sculptors = 16

Applying the formula to calculate the probability we get:

probability= (achieving success / possible outcomes)

probability= 12/16

Simplifying:

probability= 3/4

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Answer:aaaa

Step-by-step explanation:because

Answer:

P=26

Step-by-step explanation:

Answer:

Step-by-step explanation:

Begin with the fact that the area of a rectangle is A = L * W.  We know that the area is 42 and the length is 7, therefore, we can sub those values into the area formula to solve for the width.

42 = 7 * W so

w = 6 mm.

The perimeter formula is P = 2L + 2W, and now we know L and W. So

P = 2(7) + 2(6)

P = 14 + 12

P = 26

Answer:c

Step-by-step explanation:

4 % = 4/100

Simplify the fraction.

4/100 = 1/25

21 inch²

we splitthe two shapes, find the areas by multiplying the two sides and we add both of the answers, 15+6

Answer:

2(3) + 2(6) = 6 + 12 = 18 square feet

Answer: Choice C

The interquartile range (IQR) for brand A, $10, is less than the IQR for brand B, $20.

===========================================================

Explanation:

Let's go through the answer choices one by one to see which is true and which is false. Also, we'll see which is helpful when it comes to the spread.

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

Choice A

The IQR is found by subtracting the values of Q1 and Q3, which are the left and right edges of the box in that order.

For boxplot A, we have an IQR = Q3-Q1 = 80-70 = 10.

So we can immediately rule out choice A because the IQR for boxplot A is not 20, but instead it's 10.

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

Choice B

The statement made in choice B is true, since the center vertical lines represent the median, but it's not useful to determine the spread. The median only tells us the center of the distribution. It doesn't tell us how spread out the distribution is.

Imagine you didn't have access to the graph. Now if you're told that the median for brand A is larger than brand B's median, then you'd probably think boxplot A is more spread out; however, the boxplot diagram shows the opposite is the case.

So again the median isn't used here. We can rule out choice B.

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

Choice C

This statement is true. We subtract the box edge values to get the IQR values for each boxplot

For brand A we have IQR = Q3-Q1 = 80-70 = 10

For brand B we have IQR = Q3-Q1 = 70-50 = 20

This is the answer we're after.

The IQR is one tool we can use to measure the spread. The range is another option. We could also use the variance or the standard deviation (two slightly similar ideas) to measure the spread.

As you can see from the diagram, the larger the IQR, the more spread out the data will be.

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

Choice D

This is false because earlier we've shown 10 is the IQR for brand A.

The lac curve, also known as the envelope curve, is a curve that shows the maximum amount of work that can be done in a given period of time.

It is defined by the equation: W = min {W1 + W2, W3, W4, ..., Wn}, where W1, W2, W3, W4, ..., and Wn are the individual work tasks. The envelope curve is called such because it forms an envelope that encompasses all of the individual tasks on the graph, visually representing the maximum amount of work that can be done within the given timeline. This curve can be used to assess the efficiency of a task or project, as well as to analyze the impact of changes in the workload, deadlines, and resources.

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Step-by-step explanation:

hear is your answer in attachment

Answer:

Step-by-step explanation:

You need to use the quadratic equation

x =  \(\frac{-b +/- \sqrt{b^2 - 4ac} }{2a}\)

Givens

x = \(\frac{5 +/- \sqrt{5^2 - 4a*1*3} }{2} \\\)

x =( 5 +/- sqrt(25 - 12) ) / 2

x = (5 +/- sqrt(13) )/2

x = (5 + sqrt(13) / 2

x = 4.303  rounded

x = (5 - sqrt(13) ) /2

x = .6972

Answer:

There is not enough information for me to answer this question. However, since the area is not shown, the missing side length can be any positive number. AKA, infinity.

Answer:

pattern

Step-by-step explanation:

hope it helps............:)

Answer:

A

A

5

Step-by-step explanation:

Rectangular Prism A

volume = length * width * height = 7 cm * 7 cm * 5 cm = 245 cm^3

Rectangular Prism B

volume = length * width * height = 8 cm * 6 cm * 5 cm = 240 cm^3

Answers:

A

A

5

Answer:

36 Quarters and 3 dimes

Step-by-step explanation:

4 x 9 = 36

10 x 3 + 30

Answer:

28 quarters and 23 dimes

Step-by-step explanation:

q = d + 5

.25a +.1d = 9.30

.25(d+5) +.1d = 9.30

.25d + 1.25 +.1d = 9.30

.35d = 8.05

d = 23

23 + 5 = 28

q = 28

Measures of central tendency, measures of variation, and crosstabulation are all types of descriptive statistics.

Descriptive statistics summarize and describe the main features of a data set, including the typical or central values (measures of central tendency) and the spread or variability of the data (measures of variation). Crosstabulation, also known as contingency tables, is a way to summarize the relationship between two variables by displaying their frequency distributions in a table format.
Measures of central tendency, measures of variation, and crosstabulation are types of descriptive statistics. Descriptive statistics are used to summarize and describe the main features of a dataset in a simple and meaningful way.

Central tendency refers to the measures that help identify the center or typical value of a dataset, such as mean, median, and mode. Variation measures describe the spread or dispersion of data, including range, variance, and standard deviation. Crosstabulation is a method of organizing data into a table format to show the relationship between two categorical variables.

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The approximate probability that at least 26 loans will result in default, out of 100 loans with a historical default rate of 20 percent, is 0.0846.

To solve this problem, we can use the binomial distribution formula, which is P(X ≥ k) = 1 - P(X < k), where X is a binomial random variable, k is the minimum number of successes we want to achieve (in this case, 26 defaults), and P is the probability of success on each trial (in this case, 0.2, or 20 percent).

Using this formula, we can find the probability of having less than 26 defaults as follows:

P(X < 26) = Σ(k=0 to 25) (100 choose k) * 0.2^k * (0.8)^(100-k) = 0.9154

(Note: the symbol "choose" represents the binomial coefficient, which can be calculated using the formula n choose k = n!/(k!(n-k)!)

Therefore, the probability of having at least 26 defaults is:

P(X ≥ 26) = 1 - P(X < 26) = 1 - 0.9154 = 0.0846

Therefore, the approximate probability that at least 26 loans will result in default is 0.0846.

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Answer:

∡3 = 142°

Step-by-step explanation:

28° + 10° + ∡3 = 180° (Sum of angles in a triangle)

38° + ∡3 = 180°

∡3 = 180° - 38°

∡3 = 142°

Alternate method:

38° + ∡3 = 180° (Sum of angles on a straight line)

∡3 = 180° - 38°

∡3 = 142°

Answer:

38 degree + 180 degree = [ sum of angle on a straight line]

3= 180 degree - 38 degree

3= 142 degree.

·

answer: 19.5°

Given that the production function of a firm is f(x1, x2) = x1^(1/3) * x2^(2/3), where price of x1 = 1 and price of x2 = 2. Let's derive the conditional demand for x1 and cost function c(y).

Conditional demand for x1 can be derived as:

∂f(x1, x2)/ ∂x1 = (∂/∂x1) (x1^(1/3) * x2^(2/3))= (1/3) * x1^(-2/3) * x2^(2/3)

Now, put the value of x2 = (y/ x1^(1/3))^3 in the above equation.

∂f(x1, x2)/ ∂x1 = (1/3) * x1^(-2/3) * (y/ x1^(1/3))^2 = (1/3) * y^2 * x1^(-4/3)

Since price of x1 = 1, the cost function can be written as c(y) = w1 * x1 + w2 * x2 = x1 + 2x2 = x1 + 4(y/ x1^(1/3))

The cost function of the firm is

c(y) = x1 + 4y^(1/3) * x1^(-1/3) = x1 + 4y^(1/3)/x1^(1/3)

In order to maximize the profit, we need to differentiate the cost function with respect to x1 and equate it to zero.

(c(y))/d(x1) = 1 - 4/3 * y^(1/3) * x1^(-4/3) = 0

x1 = (3/4) * y^(1/3)

On substituting the value of x1 in the cost function, we get:  

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