divide and find quotient
(a⁴-b⁴) ÷ (a+b)
(step by step explanation)​

The slope of the linear equation is 0, and the solution of the second equation is x = 10.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

slope = (y2 - y1)/(x2 - x1)

So if the line passes through (-12, 6) and (4, 6), the slope is:

slope = (6 - 6)/(4 + 12) = 0

The slope is 0.

2) How to solve the equation for x?

Here we have the equation:

2/8 = 3/(x + 2)

If we move the denominators we get:

2*(x + 2) = 3*8

2x + 4 = 24

2x = 24 - 4

2x = 20

x = 20/2 = 10

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The simplified form of the given inequality is w > -3.

What is inequality?

 When two values are compared, an inequality reveals whether one is bigger than, less than, or simply not equal to the other. The term "inequality" in mathematics refers to a relationship between two expressions or values that is not equal to one another. The occurrence of an unfair distribution of opportunities and resources among individuals of a certain society is referred to as inequality. To different people and in various contexts, the term "inequality" may mean different things.

Here the given inequality is ,

=> -5w<15

=> -5 *w < 15

=> w>15/-5

=> w > -3.

Hence the correct simplified form of the inequality is w >-3.

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2(f-25) = 86 is the equation use to find f, the cost of each drill set at full price.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Given that, Ariana purchased two drill set from a sale, each of them costs $25 less than its original price,

If f is the original price, then she must have purchased it at (f-25) and for two sets it's 2(f-25)

She paid $86 for her purchase, so,

2(f-25) =  $86

Hence, 2(f-25) = 86 is the equation use to find f, the cost of each drill set at full price.

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The equation for the nth term of the arithmetic sequence 4, 7, 10, 13 is aₙ = 3n + 1

Arithmetic sequence can be represented with the formula as follows:

aₙ = a + (n - 1)d

where

Therefore, let's write the equation for the nth term of the arithmetic sequence 4, 7, 10, 13..

a = 4

d = 7 - 4 = 3

Therefore,

aₙ = 4 + (n - 1)3

aₙ = 4 + 3n - 3

aₙ = 3n + 4 - 3

aₙ = 3n + 1

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Answer:

Step-by-step explanation:

18x+15. Step-by-step explanation: 5(4x+3)-2x. Distribute the 5. 20x +15 - 2x. Combine like terms. 20x-2x +15.

The time taken for Wilson to paint the bookcase is 50 minutes.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, Wilson paints 40% of a bookcase in 20 minutes. It should be noted that 40% = 0.4

Therefore, the time taken to paint the whole bookcase will be:

= Number of minutes / Percentage painted

= 20 / 0.4

= 50

He'll use 50 minutes.

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The other leg has its length to be 11.49 units

To calculate the length of the other leg distance, we make use of the Pythagoras theorem

Mathematically, this theorem is represented by:

w² = y² + z²

Such that x = hypotenuse, y = leg and  z = other leg

From the question, we have the following parameters

w = 14, y = 8 and z = the other leg

Substituting these values in w² = y² + z²

14² = 8² + y²

Evaluate the exponents

196 = 64 + y²

Evaluate the like terms

y² = 132

Take the square roots of both sides

y = 11.49

Hence, the length of the other leg is 11.49 units

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Answer: 11 units

Step-by-step explanation: i took the test and got it right

Dennis spent 12 hours practicing.

1.5 hours = 90 mins
90 mins x 8
720 mins = 12 hours

Answer:

1/23

Step-by-step explanation:

Answer: 2

Step-by-step explanation:

This is because it is a scaled copy which means that the smaller has to multiply either by a whole or a fraction and the bigger can be divided by a whole or a fraction in order to be the smaller triangle if that makes sense. so 5*2=10, 12*2=24 thus if you were to divide 10/2=5, 24/2=12.

Answer:

The answer is 2:1

Step-by-step explanation:

This is because it is a 2/1 ratio

The 99% confidence limit will be option B which is (45, 55)

90% confidence limits for the population mean are (46,54)

mean = 46+54 / 2 = 50.

the margin of error E = 54-46/2 = 4

For 90% Confidence Z- Critical value is = 1.645

But the margin of error

E = ZS/√n

4=(1.645)S/√n

S/√n = 4 / 1.645

= 2.4316

For 95% confidence Z-critical value is 1.96

A 95% confidence interval is = mean ± E

(50 ± 1.96) S/√n = (50 ± 1.96)×2.4316

= 50+ 4.7660

= 45.2340, 54.7660

= (45, 55)

Hence the correct option is B which is (45, 55) as the 99% confidence limit.

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Answer:

Step-by-step explanation:

The size of the angle of one whole revolution is 360 degrees. A revolution describes the angle of a circular surrounding sector as it rotates! This means one full revolution is 360 degrees. And half of a revolution is 180 degrees!

0.1717 is Probability that none has ever been married from selected 5 young women in age category at random.

In the question we have,

the number of females age 20 to 24 has never been married = 70.3%

the number of young women in this age category (20 to 24) at random = 5

We shall find out the probability that none has been maaried from selected group of 5 females.

Probability of female age 20 to 24 has never been married = 0.703

So, the probability that none has been married from selected group of 5 females ( p)= 0.703×0.703×0.703×0.73×0.73

= 0.1717

Therefore, The probability that none has ever been married is 0.1717.

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The number written on the board is 2 2/5

A linear equation is an equation in which the highest power of the variable is always 1. The standard form of a linear equation in one variable is of the form Ax + B = 0. where, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. where, x and y are variables, A and B are coefficients and C is a constant.

represent the number on the board by x, the result of the second student by y , therefore the result of the first student is 2y

solving for the first student, 12+x= 2y

for the second student , 3x= y

substituting 3x for y in first equation

12+ x= 2(3x)

12+x= 6x

collecting like terms

5x= 12

divide both side by5

x= 12/5= 2 2/5.

Therefore the number on the board is 2 2/5

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Answer:

x<3

Step-by-step explanation:

4x<5+7

4x < 12

4/4 x < 12/4

x < 3

The distance between the points (5, 7) and (8,-5) is √13.

The length of the path joining two points determines their distance from one another. It's crucial to know how to calculate the distance between two points when working with graphs. This makes it possible for a learner to estimate how long the line is, which is useful in a variety of circumstances. Using the distance formula is the most typical method of determining the distance.

Points (5, 7) and (8,-5)

Formula:

AB² = (x₂ - x₁)² + (y₂ + y₁)²

AB² = (8 - 5)² + (-5+7)²

AB² = (3)² +(2)²

AB² = 9 + 4

AB² = 13

AB = √13

The distance between the points (5, 7) and (8,-5) is √13.

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The solution of x when solving x/2 + 1 = √3 is :

x is 2√3 - 2 .

Here in the question given equation ,

x/2 + 1 = √3

To find solution,

we have to subtract 1 from LHS and RHS of equation,

⇒ x/2 + 1 - 1 = √3 - 1

⇒ x/2 = √3 - 1

Next multiply both sides  by 2

2( x/2) = 2(√3 -1)

By simplifying both sides we get,

x = 2√3 - 2

So the value of x = 2√3 -2.

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A level of confidence of 95% was used in the case above. A table at the back of a statistics textbook can be used to get the value of z* for a certain confidence level. For a 95% confidence level, the value of z* is 1.96.

 An error margin of 3.92 is discovered when the value of z*, the demographic standard error, and the sample size are entered into the equation.

Statistical Estimation's Justification

Where does the confidence interval calculation formula come from?

The population mean's true value is never known; it can only ever be estimated or approximated. The easiest way of doing this is to choose many identical-sized random samples from the population.

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Using the concepts of errors and measurement, we got that by taking a larger sample 95% confidence interval for p and would prefer to have a smaller margin of error without losing any confidence.

In science, experimental errors may be caused due to the human inaccuracies like a wrong experimental setup in the science experiment or choosing the wrong set of people for the social experiment. Systematic error refers to that error which is actually inherent in the   system of experimentation.

Hence, if we have calculated a 95% confidence interval for p and would prefer to have a smaller margin of error without losing any confidence. in order to do this, we can take a larger sample.

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Yes, the two quantities have a proportional relationship because the variables x and y all have the same constant of proportionality.

Mathematically, a proportional relationship can be represented or modeled with the following mathematical expression:

y = kx

Where:

In order for the two quantities to have a proportional relationship, the variables x and y must remain in a constant ratio.

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 2/3

When x = 90 and y = 60, we have:

Constant of proportionality (k) = 60/90

Constant of proportionality (k) = 2/3

When x = 120 and y = 80, we have:

Constant of proportionality (k) = 80/120

Constant of proportionality (k) = 2/3

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The equation of the absolute value graph is f(x) = |x - 3| + 5

The graph represents the given parameter

From the graph, we can see that the graph is an absolute value graph

An absolute value graph is represented as

f(x) = a|x - h| + k

Where h and k are the vertex of the graph

In this case, they are

h = 3 and k = 5

This is because the minimum point of the graph is (3, 5)

Substitute values for h and k in the form of the equation

So, we have the following representation

f(x) = a|x - 3| + 5

A point on the graph is (2, 6)

This gives

a|2 - 3| + 5 = 6

When the value of variable a is solved, we have

a = 1

So, the equation becomes

f(x) = 1 * |x - 3| + 5

Evaluate the products

f(x) = |x - 3| + 5

Hence, the equation of the graph is f(x) = |x - 3| + 5

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Answer:

[tex]y = |x - 3|+ 5[/tex]

y = |x| is the equation that forms the triangular shape. -3 and 5 reflect the shape to that position.

Answer:

[tex]y_{min}=-17[/tex]

[tex]y_{max}=15[/tex]

Step-by-step explanation:

Given function:

[tex]y=2x^2-12x+1[/tex]

The critical points are those values of x which make the derivative of the function zero.  

Differentiate the function:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2 \cdot 2x^{2-1}-12x^{1-0}+0[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=4x-12[/tex]

Set the derivative to zero and solve for x:

[tex]\implies 4x-12=0[/tex]

[tex]\implies 4x=12[/tex]

[tex]\implies x=3[/tex]

To find the y-value of the critical point, substitute the found value of x into the function:

[tex]\implies 2(3)^2-12(3)+1[/tex]

[tex]\implies 2(9)-12(3)+1[/tex]

[tex]\implies 18-36+1[/tex]

[tex]\implies -18+1[/tex]

[tex]\implies -17[/tex]

Therefore, the critical point is (3, -17).

To find the endpoints of the function in the interval [0, 7], substitute x = 0 and x = 7 into the function:

[tex]\begin{aligned} x=0 \implies 2(0)^2-12(0)+1&=0-0+1\\&=1\end{aligned}[/tex]

[tex]\begin{aligned} x=7 \implies 2(7)^2-12(7)+1&=2(49)-12(7)+1\\&=98-84+1\\&=14+1\\&=15\end{aligned}[/tex]

Therefore:

Therefore the minimum y-value is -17 and the maximum y-value is 15 in the given interval [0, 7]

The minimum and maximum y value of the function is -17 and 15 respectively.

This is a basic problem in calculus.

Given function: [tex]y=2x^{2} -12x+1[/tex]

Step 1: First, let's find the derivative of the function

[tex]\frac{dy}{dx} = 2.2x^{2-1} -12x^{1-0} +0\\\frac{dy}{dx} = 4x-12[/tex]

Step 2: Equate the derivative with zero

4x-12=0

x=3

Therefore, x=3 is the critical value for x

Step 3: Find the critical value for y

[tex]y=2x^{2} -12x+1[/tex]

[tex]y=2\times3^{2} -12\times3+1\\y=-17[/tex]

Thus, the critical points for the function [tex]y=2x^{2} -12x+1[/tex] are (3,-17)

Step 4: Find endpoints using the given interval [0,7]

This can be done by substituting x1=0 and x2=7 simultaneously in the given function and finding y1 and y2.

For x1=0,

[tex]y1=2\times0^{2} -12\times0+1\\y1=0+0+1\\y1=1[/tex]

For x2=7,

[tex]y2=2\times7^{2} -12\times7+1\\y2=98-84+1\\y2=15[/tex]

Now, we have both critical points and endpoints.

Therefore, The minimum and maximum y value of the function is -17 and 15 respectively.

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81 of 270 pages in a book is a part of the situation.

A division is a process of splitting a specific amount into equal parts.

Given,

81 of 270 pages in a book.

Eighty one of two hundred seventy pages in a book.

In the given situation, A book has 270 pages in that we have taken 81 pages which are part of the book.

We have taken pat of the book,

In the given situation, book is whole and 81 is the part.

Hence  81 of 270 pages in a book is a part of the situation.

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The equation that represents the cost of the hamburger with additional topping will be c = 0.295t + 3.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A burger consistently cost $6.00 each extra fixing cost $0.59.

Let 'c' be the cost and 't' be the cost of topping. Then the equation is given as,

c = 0.59t + 6

On Monday the expense of the burger just is half off. Then the equation is given as,

c = 0.50(0.59t + 6)

c = 0.295t + 3

The equation that represents the cost of the hamburger with additional topping will be c = 0.295t + 3.

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Answer:

Square root 19 comma, 5,8,30

Answer:5,8,30

Step-by-step explanation: i took a test

There is a 0.33 percent chance that a woman is the owner of each of the firms identified. Therefore, there is a 0.036 percent chance that women own ALL three of the called businesses.

The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.

Here,

The probability that each of the firms called is owned by a woman is 0.33. Therefore, the probability that ALL three of the firms called are owned by women is:

percentage=0.33*0.33*0.33

percentage=0.035937

=0.036

There is a 0.33 percent chance that each of the businesses is run by a woman. As a result, there is a 0.036 percent chance that women own ALL three of the businesses mentioned.

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The license plate combinations with either three letters then three numbers or three numbers then three letters are 35152000.

The license plate combinations to be made are either three number followed by three letter or three letter followed by three number. we are here assuming that the repetition of the number and letter are allowed.

The number can be any three from 0-9. So, the total choices of number are 10.

The letter can be from A-Z. So, the total choices for letter are 26.

The total choices of the numbers possible are,

ΟΟΟ ΟΟΟ

1 2 3  4 5 6

The first three are the choices of letter and the last three are the choice of number. Two combinations are also possible by interchanging the position of the set of numbers and letters.

So, the possible combinations are,

2 x [26x26x26x10x10x10]

Hence,

The possible combinations for the license plate number are 35152000.

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