factorise (a-b+c)²-(b-c+a)²​

The line of reflection for the given angle is  corresponding vertices.

1. Identify the original angle and its reflected angle in the diagram.
2. Find the midpoint between the corresponding vertices of the original and reflected angles.
3. Draw a line through the midpoint that is perpendicular to the line connecting the corresponding vertices.

In general, to reflect an angle across a line, you would draw a perpendicular line from the vertex of the angle to the line of reflection, and then extend the sides of the angle to intersect the line of reflection at the same angle. The line of reflection would be the perpendicular bisector of the segment connecting the vertex of the original angle to the corresponding vertex of the reflected angle.

This line is the line of reflection, and the angles are reflected across it. The justification for this method is that the line of reflection is equidistant from the corresponding points of the original and reflected angles

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Answer:

24% increase

Step-by-step explanation:

percent change = (new value - old value)/(old value) × 100%

A positive percent change is a percent increase.

A negative percent change is a percent decrease.

In this problem:

new value = 31

old value = 25

percent change = (31 - 25)/(25) × 100%

percent change = 24%

Since the percent change is positive, the percent change is a

24% increase

The percentage change in the weight of a German Shepherd puppy from 4 months to 5 months is the an 24% increase in the puppy's weight in 1 month.

The percentage change in the weight of a German Shepherd puppy from 4 months to 5 months is the difference between the two values (31 - 25 = 6) divided by the starting weight (25). This gives us 6/25 = 0.24, or a 24% increase in the puppy's weight in 1 month.

To explain this further, let's look at an example. If a puppy weighed 25 pounds at 4 months, and it gained 6 pounds over the course of the following month, it would weigh 31 pounds at 5 months. To calculate the percentage increase, take the difference in weight (6 pounds) and divide it by the starting weight (25 pounds). This gives us 6/25 = 0.24, or a 24% increase in the puppy's weight.

To calculate the percentage decrease, use the same steps as above, but subtract the starting weight from the final weight instead. For example, if a puppy weighed 25 pounds at 4 months and lost 6 pounds over the course of the following month, it would weigh 19 pounds at 5 months. The percentage decrease would be calculated as (25 - 19)/25 = 0.24, or a 24% decrease in the puppy's weight.

In summary, the percentage change in the weight of a German Shepherd puppy from 4 months to 5 months is the difference between the two values (31 - 25 = 6) divided by the starting weight (25). This gives us 6/25 = 0.24, or a 24% increase in the puppy's weight in 1 month.

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The probability that the socks will not be blue would be =11/14.

Probability can be defined as the expression that shows the possibility of the occurrence of an event.

The formula that is used to calculate probability = the chosen events/total number of outcomes.

The total number of black socks = 8

The total number of blue socks = 6

The total number of white socks = 14

The total number of socks (outcomes) = 8+6+14 = 28

The socks that are not blue = 8+14 = 2

Therefore the probability that they socks won't be blue = 22/28 = 11/14.

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The vertices of polygon A'B'C'D' are A′(−0.5, 0.75), B′(−0.25, 0.25), C′(0.5, −0.25), D′(0.5, 0.5).

In geometry, dilation is a transformation that changes the size of a figure but not its shape. It is a type of similarity transformation.

When a figure is dilated, each point of the figure moves away or towards the center of dilation by a certain scale factor.

Here we have

Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), and D(4, 4) is dilated using a scale factor of one-eighth to create polygon A′B′C′D′.

To dilate polygon ABCD using a scale factor of one-eighth i.e 1/8 multiply the coordinates of each vertex by the scale factor of 1/8.

The coordinates of A are (-4, 6), multiply each coordinate by 1/8

A' = (-4/8, 6/8) = (-1/2, 3/4) = (-0.5, 0.75)

The coordinates of B are (-2, 2), multiplying each coordinate by 1/8

B' = (-2/8, 2/8) = (-1/4, 1/4) = (-0.25, 0.25)

The coordinates of C are (4, -2), multiplying each coordinate by 1/8

C' = (4/8, -2/8) = (1/2, -1/4) = (0.5, - 0.25)

The coordinates of D are (4, 4). Multiplying each coordinate by 1/8

D' = (4/8, 4/8) = (1/2, 1/2) = (0.5, 0.5)

Therefore,

The vertices of polygon A'B'C'D' are A′(−0.5, 0.75), B′(−0.25, 0.25), C′(0.5, −0.25), D′(0.5, 0.5).

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Generally, the water table in a swamp is located 2 miles below the surface.

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B. The probability of an outcome is between 0 and 1. C. The sum of the probabilities of all possible outcomes is 1.

Option B is correct because probability values must be between 0 and 1.

Option C is correct because the sum of the probabilities of all possible outcomes must equal 1.

Option A is incorrect because it is not necessary for half of the possible outcomes to have probabilities greater than 0.5.

Option D is incorrect because the distribution does not have to be symmetrical.

Option E is incorrect because the outcomes can have common events and can be dependent.

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the interval where both F(x) and g(x) are increasing is x < 0, which can be represented on the number line as follows:

To find the interval where both functions F(x) and g(x) are increasing, we need to determine where the derivative of each function is positive. A function is increasing when its derivative is positive, which means that the function is becoming larger as x increases.

The derivative of F(x) can be found by applying the derivative rules for absolute value and addition, which gives us:

F'(x) = 3x/|x|

Now, we need to determine where F'(x) is positive. This occurs when either 3x is positive and |x| is positive, or when 3x is negative and |x| is negative. Therefore, F'(x) is positive for x > 0 and x < 0.

Next, we need to find the derivative of g(x) by applying the derivative rules for subtraction and multiplication, which gives us:

g'(x) = -1 + 8

Simplifying the expression, we get:

g'(x) = 7

Since g'(x) is a constant, it is always positive, which means that g(x) is increasing for all values of x.

To find the interval where both F(x) and g(x) are increasing, we need to identify where both F'(x) and g'(x) are positive. This occurs when x < 0, as this satisfies the condition for F'(x) being positive, and g'(x) is always positive.

Therefore, the interval where both F(x) and g(x) are increasing is x < 0, which can be represented on the number line as follows:

     <=====o------------------------>

         x<0                    x>0

In this interval, both functions are increasing as x becomes more negative.

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John's parents deposited 1000 into a savings account as a college fund when he was born. We need to find out how much John will have in this account after 18 years at a yearly simple interest rate of 3.25%.

We can use the formula for simple interest to solve this problem.

The formula for simple interest is:

I = PRT

Where,I = interest

P = principal (the initial amount of money)

R = rate of interest (as a decimal)

T = time (in years)

We are given that John's parents deposited 1000 when he was born. So, P = 1000. The interest rate is 3.25% per year, which is 0.0325 as a decimal. And we are given that the time is 18 years, so T = 18 years.Using the formula for simple interest, we can find the amount of interest earned:

I = PRTI = (1000)(0.0325)(18)I = 585

We can then add the interest earned to the principal to find the total amount of money in the account after 18 years:

A = P + IA = 1000 + 585A = 1585

Therefore, John will have 1585 in this account after 18 years at a yearly simple interest rate of 3.25%.

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t decreased by 29 , Two more than g , Eleven times x , h divided by twelve and Five minus k are the phrase of given expression .

An expression in mathematics is a group of digits, variables, and operations that illustrates a mathematical connection or concept. Symbols, words, or a combination of both can be used to write expressions in a variety of ways. Expressions that are examples include: 3x + 4, 2y - 7z , (a + b) ,x2 + y2 = 2 5sin(x) + 3cos(x). Equations, inequalities, functions, formulae, and many other mathematical ideas can all be represented as expressions. Additionally, they can be altered or simplified using algebraic methods like factoring, combining like terms, and solving for a variable.

given

The sum of m and 83.

Forty-two times s.

Nine divided by d.

t decreased by 29.

Two more than g.

Eleven times x.

h divided by twelve.

Five minus k

t decreased by 29 , Two more than g , Eleven times x , h divided by twelve and Five minus k are the phrase of given expression .

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we can, now  if we look at 0 = x² + 5, that's when the parabola y-value is 0, that is, what's "x" when y = 0? well, if we look at the graph, the graph never touches the x-axis, so that means the graph never has any "real roots", only complex ones or imaginary ones.  We can tell because the graph never touches the x-axis.

There are 243 ways to distribute five unlabeled balls into three labeled boxes.

Since the balls are unlabeled, we only need to consider the number of balls in each box, rather than which specific ball goes where.

We can use a combination approach to solve this problem. Let's think about distributing the balls one at a time. For the first ball, there are three boxes to choose from. For the second ball, there are also three boxes to choose from. We can continue this process until all five balls have been distributed.

So, for each ball, there are three choices of which box to put it in. Therefore, the total number of ways to distribute the five balls into the three labeled boxes is

3 x 3 x 3 x 3 x 3 = 3^5 = 243

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Answer:

1. irrational

2. irrational

3. rational

4. rational

5. irrational

6. rational

Step-by-step explanation:

A rational number includes any whole number, fraction, or decimal that ends or repeats. An irrational number is any number that cannot be turned into a fraction.

1.) pi is a never ending number which means that, according to the definition above, it must be IRRATIONAL

2.) the line above the 46 means that it is repeating, making it IRRATIONAL

3.) the square root of 100 is 10, making it RATIONAL

4.) -16 is an integer (a whole number that can be positive, negative, or zero), making it RATIONAL

5.) the square root of 21 results in a long decimal that cannot be converted into a fraction, by the definition above, it is IRRATIONAL

6.) 10 is a whole number, making it RATIONAL

In conclusion 39 science fiction books were sold on Thursday.

How to solve and what does algebra mean?

Let's use algebra to solve this problem. Let x be the number of science fiction books sold on Thursday. Then we know that:

86 = 8 + 2x

We can solve for x by first subtracting 8 from both sides:

78 = 2x

Then dividing both sides by 2:

x = 39

Therefore, 39 science fiction books were sold on Thursday.

Algebra is a branch of mathematics that deals with the study of symbols and the rules for manipulating those symbols. It involves using letters and other symbols to represent variables and quantities in equations and formulas.

Algebra is used in a wide range of fields, including mathematics, science, engineering, and economics, and it is an essential tool for solving many real-world problems.

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Answer:

A≈28.27mi²

Step-by-step explanation:

[tex]A=\pi r^2[/tex]

[tex]\pi \times 3^2[/tex]

≈ 28.27433mi²

A≈28.27mi²

No, there is not sufficient evidence to substantiate the claim at the 0.10 level. Null Hypothesis (H0): p ≤ 0.69; Alternative Hypothesis (H1): p > 0.69

A newsletter publisher believes that under 69% of their readers own a Rolls Royce.

No, there is not sufficient evidence to substantiate the claim at the 0.10 level. In order to substantiate the claim at the 0.10 level, the publisher would need to collect data from their readers and perform a hypothesis test to compare the observed percentage of readers with the claimed percentage.

Null Hypothesis: The proportion of the newsletter readers that own a Rolls Royce is less than or equal to 69%.

Null Hypothesis (H0): p ≤ 0.69

Alternative Hypothesis: The proportion of the newsletter readers that own a Rolls Royce is greater than 69%.

Alternative Hypothesis (H1): p > 0.69

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The probability that the number of calls between 2:00 pm and 2:10 pm is exactly 200 is 0.000002204.

This can be calculated using the Poisson distribution. The Poisson distribution is used to model the probability of a given number of events occurring in a given time interval.

The Poisson equation is P(x) = (λ^x e^-λ)/x!

where λ is the expected number of occurrences per interval.
For this question, λ = 3/min, since the rate of calls to the computer software help desk is 3 per minute.
Plugging λ = 3/min into the Poisson equation, we get

P(x) = ((3/min)^200 e^-(3/min))/200!.
This simplifies to

P(x) = 0.000002204.

The probability of having exactly 200 phone calls to a computer software help desk in the 10-minute period from 2:00 pm to 2:10 pm is 0.000002204.
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Exact coordinates of the terminal point (x, y) are (-3.40, 4.71).

Let's dive deeper into the details below.

The angle below has a measure of 5.8 radians. The exact coordinates of the terminal point (x, y) can be determined by using trigonometry.
First, we must remember that the formula for the x-coordinate is x = r cos θ, where r is the length of the radius and θ is the measure of the angle. Therefore, we can calculate the x-coordinate by plugging in the radius (which is given) and the measure of the angle (5.8 radians) into the formula:
x = 5.8 cos (5.8) = 5.8 × -0.5806 = -3.40
Now, we must use the formula for the y-coordinate which is y = r sin θ. Plugging in the radius and the measure of the angle, we can calculate the y-coordinate:
y = 5.8 sin (5.8) = 5.8 × 0.8139 = 4.
Therefore, the exact coordinates of the terminal point (x, y) are (-3.40, 4.71).

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The answer that refers to the total number of cases of a disease or a disorder in a specified population at a particular point in time is prevalence.

Prevalence is the total number of cases of a disease or disorder in a population at a given point in time, and does not include cases that have been resolved or previously diagnosed cases. It is an important measure of the health of a population, as it allows researchers to identify patterns in the distribution of a disease or disorder and helps inform public health strategies.

Prevalence is calculated by dividing the total number of cases of a disease or disorder in a population at a given point in time, by the size of the population. For example, if a population of 100,000 people has 500 cases of a particular disease, the prevalence would be 0.005 or 0.5%.

Prevalence is an important metric in epidemiology and public health, and is often used in combination with incidence rates to measure the health of a population. Incidence rates measure the number of new cases of a disease or disorder that occur in a population over a certain time period, whereas prevalence is a snapshot of the total number of cases of a disease or disorder in a population at a given point in time.

Knowing the prevalence of a disease or disorder in a population helps public health practitioners understand the magnitude of a health issue, inform public health strategies, and identify risk factors and trends in the distribution of a disease or disorder.

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Answer:

The equation y = -3x - 5 represents a linear function with a slope of -3 and a y-intercept of -5.

To understand what would happen to the graph if the slope was changed to 1, we need to compare the graphs of y = -3x - 5 and y = x - b, where b is some constant.

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. So, when we change the slope of the equation y = -3x - 5 to 1, we get:

y = x - b

To find the value of b, we can substitute the coordinates of any point on the line. Let's use the y-intercept, which is -5:

-5 = 1(0) - b

b = -(-5)

b = 5

Therefore, the equation y = x - 5 represents the line with a slope of 1 and a y-intercept of 5.

To compare the graphs of y = -3x - 5 and y = x - 5, we can graph both equations on the same coordinate plane. Here's what the two graphs look like:

Graph of y = -3x - 5 (slope = -3, y-intercept = -5):

|

-5| x

| x

| x

| x

| x

| x

x---------------

-3 -2 -1 0 1 2 3

Graph of y = x - 5 (slope = 1, y-intercept = 5):

|

5| x

| x

| x

| x

| x

| x

x---------------

-5 -4 -3 -2 -1 0 1 2 3

As we can see, changing the slope of the equation from -3 to 1 rotates the line counterclockwise and makes it steeper. The y-intercept remains the same at -5.

The equation 24÷4=6 can be thought of as 24 broken into 4 groups of 6 each. This can be shown mathematically as follows: 24/4 = 6.

The division 24 ÷ 4 = 6 can be represented as 24 divided into 4 groups of 6 each. Therefore, each group contains 6 elements.

Another way to represent this division is by using a division box. In this case, 24 is the dividend, 4 is the divisor, and 6 is the quotient. Here's how to write it in the division box format:``` 6|24----4```The divisor is outside the division box, while the dividend is inside the division box. Then, we divide 24 by 4 to obtain 6. Therefore, 24 ÷ 4 = 6.

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The ratio of black and white keys of piano give correct values of A, B, C as 9, 52, 130.

The ratio of black to white keys of Piano of different sizes are as follow,

Black      A      36        63      90

White     13      B          91        C

From the table of black and white keys relation of proportionality is equal to,

( A / 13 ) = ( 36 / B ) = ( 63 / 91 ) = ( 90 / C )

This implies ,

( A / 13 ) = ( 63 / 91 )  

⇒ A = ( 63 / 91 ) × 13

⇒ A = ( 9 / 13 ) × 13

⇒ A = 9

Similarly,

( 36 / B ) = ( 63 / 91 )

⇒ B = 36 × ( 91 / 63 )

⇒ B = 36 × ( 13 / 9 )

⇒ B = 52

And

( 63 / 91 ) = ( 90 / C )

⇒ C = 90 × ( 91 / 63 )

⇒ B = 90 × ( 13 / 9 )

⇒ B = 130

Therefore, the correct values of A , B, C using the ratio of black and white keys of the piano is equal to 9, 52, 130.

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The above question is incomplete, the complete question is:

The table below shows the ratios of black to white keys on pianos of various sizes.

Black A 36 63 90

White 13 B 91 C

Determine which table has the correct values for A, B, and C.

Therefore , the solution of the given problem of equation comes out to be  y=(x-12)³ and y=(x+8)³.

Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Instead of a distinct algorithm that divides 12 into two parts and can be used to assess data received from y + 7, normalization in this case yields b + 7.

Here,

The following two equations show a rightward translation of the parent equation's coordinate plane graph:

=> y=(x-12)³

=> y=(x+8)³

Therefore , the solution of the given problem of equation comes out to be  y=(x-12)³ and y=(x+8)³.

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A burrito costs $2 at Taco Hut. Let's use "b" to represent the cost of a burrito and "t" to represent the cost of a taco.

From the problem, we know that:

4b + 5t = 13 (for Clark)

5b + 3t = 13 (for Bruce)

We want to determine the cost of a burrito, so we can solve for "b" using the second equation:

[tex]5b + 3t = 13\\5b = 13 - 3\\b = (13 - 3t)/5[/tex]

Now we can substitute this expression for "b" into the first equation:

[tex]4b + 5t = 13\\4[(13 - 3t)/5] + 5t = 13\\52/5 - 12t/5 + 5t = 13\\52 - 12t + 25t = 65\\13t = 13\\t = 1[/tex]

So we know that a taco costs $1. Now we can substitute this value into either of the original equations to solve for "b":

[tex]5b + 3t = 13\\5b + 3(1) = 13\\5b = 10\\b = 2[/tex]

Therefore, a burrito costs $2 at Taco Hut.

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The answer is: "helping to make family changes within the dysfunctional system."

Step-by-step explanation:

While family-based therapies can be effective for treating anorexia nervosa, helping to make family changes within the dysfunctional system is not an immediate goal of treatment for individuals with anorexia nervosa.

The immediate goal of treatment for individuals with anorexia nervosa is to restore their physical health, which includes helping them recover from malnourishment, helping them eat normally again, and helping them regain their lost weight.

Once their physical health is stabilized, additional therapies may be recommended to address the psychological, emotional, and social factors that contribute to their eating disorder, which may include family-based therapies.

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Answer:

no the didn't hear the question

Answer:

I am pretty sure the answer is that the question can't be heard

Step-by-step explanation:

Rounded to three decimal places, the probability that the sample mean is between $155 and $160 is 0.072.

To find the probability that the sample mean is between $155 and $160, we will use the Central Limit Theorem. The Central Limit Theorem states that the distribution of the sample mean (with a large enough sample size) will be approximately normally distributed with the same mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Mean of the sample distribution: μ = $150
Standard deviation of the sample distribution: [tex]σ/√n = $25/√52 ≈ $3.46[/tex]
Now, we'll calculate the z-scores for $155 and $160:
[tex]Z1 = (155 - 150) / 3.46 ≈ 1.445[/tex]
[tex]Z2 = (160 - 150) / 3.46 ≈ 2.890[/tex]
Using a z-table or calculator, we can find the probability for each z-score:
[tex]P(Z1) ≈ 0.9259[/tex]
[tex]P(Z2) ≈ 0.9981[/tex]
Now, we can find the probability between the two z-scores:
[tex]P(1.445 < Z < 2.890) = P(Z2) - P(Z1) = 0.9981 - 0.9259 = 0.0722[/tex]

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Answer:

First, we can factor out 5x²y²z from each term:

15x²y³z+25x³y²z+35x²y²z² = 5x²y²z(3y+5xz+7z)

So the fully factorized expression is:

5x²y²z(3y+5xz+7z)

By using the fact that the measures ∠BAE and ∠EAC are equal, we will see that x = 20

Here we know that AE is an angle bisector of ∠BAC, this means that the measures of the two formed angles are the same ones.

Then we can write:

∠BAE = ∠EAC

Now we know that the measures of these angles are:

∠BAE = x + 30

∠EAC = 3x - 10

Replacing that in the equation above we willget:

x + 30 = 3x - 10

solving that for x, we will get:

30 + 10 = 3x - x

40 = 2x

40/2 = x

20 = x

That is the value of x.

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