What is K in number theory?

When the number under the root sign has no square factors, a radical is said to be in its simplest form.

In the 14th century, the term radical was first used. It was derived from the Late Latin radicalis, which was derived from the Latin radic-, radix, which meant "root." The definition "of, connected to, or proceeding from a root" underlies the first usage of the word "radical," which are all about actual roots.

Radical: The sign used to represent the square root or nth root. Square-root-containing expressions are known as radical expressions. The radical symbol's "radicand" is a number or phrase. A radical equation is one that uses variables as radicands in radical expressions.

Using the Pythagorean theorem, x = 27:

7² + ?² = 9²\sx² = 81 - 49\x = √32\x = 4√2

For the lower portion:

x² + 2² = (4√2)

²\x² + 4 = 32\x² = 28\x = √28\x = 2√7

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Y-axis divides the line segment joining the given points (-2, -3) and (3, 7) in the ratio is equal to 2 : 3.

As given in the question,

Given points of the line segments are :

( x₁ , y₁ ) = ( -2 , -3 )

( x₂ , y₂) = ( 3, 7 )

When y-axis divides the line segment its coordinate are ( 0, y)

Let the ratio which divides the line segment be m : n

( 0 , y ) = [ ( mx₂ + nx₁) / ( m + n) ,  ( my₂ + ny₁) / ( m + n)]

⇒( 0 , y ) = [ ( 3m -2n) / ( m + n) ,  ( 7m -3n) / ( m + n)]

⇒( 3m -2n) / ( m + n) = 0

⇒ 3m -2n = 0

⇒3m = 2n

⇒ m : n = 2 : 3

Therefore, the y-axis divides the given line segment in the ratio equals to 2 : 3.

The above question is incomplete , the complete question is:

In what ratio is a line segment joining the points (-2, -3) and (3, 7) divided by y-axis?

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The number of weed killer cans needed is 2.4 cans and it will cost $ 47.4

A trapezium is a quadrilateral with at least one pair of parallel lines. The two parallel lines are named a and b. The area of a trapezium is given as:

A = ½( a+b) h

where a and b are the parallel sides and h is the height of the trapezium.

since the lawn takes the shape of a trapezium,

The height of the lawn is calculated as:

h² = 17²- 8²

h² = 289-64

h² = 225

h = √225 = 15m

therefore A = ½(12+20)15

A = ½×32× 15

A = 16×15

A = 240m²

If one can will go for 100m², then the number of can that will be needed for the lawn = 240/100 = 2.4 can of weed killers.

If one weed killer cost $19.75, then

2.4 weed killers will cost 19.75 × 2.4 = $47.4

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Answer:

0

Step-by-step explanation:

1. Review the definition for a real number: Positive or negative, large or small, whole numbers, fractions or decimal numbers are all Real Numbers

2. Review the definition for a non real number: The numbers which are not real and are Imaginary (such as i or a square root)

3. Your question may be missing an answer choice

4. Since all 4 of these numbers are positive, negative, whole, fraction, or decimal numbers, they are all real. Unless you are missing a number in the answer choices, there are no non real numbers.

But, wait! I may have missed something here. '0' is technically both an imaginary and real number, so it may be the answer to your problem!

ln 3x = ln (3x). The derivative of ln (3x) is 1/3x. in this case, f(x) = ln (x) and g(x) = 3x. The derivative of ln (x) is 1/x and the derivative of 3x is 3. Therefore, the derivative of ln (3x) is 1/3x which is equal to 1/(3x).

in this case, f(x) = ln (x) and g(x) = 3x. The derivative of ln (x) is 1/x and the derivative of 3x is 3. Therefore, the derivative of ln (3x) is 1/3x which is equal to 1/(3x). Using the chain rule, the derivative of ln (3x) can be found. The chain rule states that the derivative of a function f(g(x)) is f'(g(x)) * g'(x). In this case, f(x) = ln (x) and g(x) = 3x.ln 3x = ln (3x). The derivative of ln (3x) is 1/3x.

ln 3x = ln (3x). The derivative of ln (3x) is 1/3x.

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The coordinates of S(-7,1) after a reflection over the line y = 3 is given as follows:

(-7,5).

The coordinates of the original point in this problem are given as follows:

S(-7,1).

The reflection line is given as follows:

y = 3.

The reflection line is an horizontal line, meaning that:

The y-coordinate of S is 2 units below of the reflection line, hence after the reflection it will be two units above, as follows:

3 + 2 = 5.

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The mathematical function f/x= 1 x is known as the reciprocal function.

It is a mathematical operation that takes a number and produces its reciprocal, or inverse, as the result.

For example, if you input the number 2 into the reciprocal function, it will return the result of 1/2, or 0.5. The reciprocal function is also known as the multiplicative inverse, since multiplying a number by its reciprocal will always result in the number 1.

The reciprocal function is an important mathematical tool used to calculate the inverse of a given number. It is an essential element of many algebraic equations, and can be used in a variety of ways to simplify complex problems.

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The simplification of the given expression would be = -60

The simplification of an expression is defined as the representation of a large number or sophisticated equation into a simpler one.

The given expression = -50 + 5/13P

where P.= -26

Therefore, -50 + 5/13(-26)

Solve for; 5/13(-26) = 5/13 × -26 = -130/13 = -10

= -50 -10 = -60.

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Solving a formula for a variable means rewriting the formula so that the variable is Isolated to one side.

Solving a formula for a particular variable entails placing that variable alone with a coefficient of 1 on one side of the equals sign. The other side of the equals sign represents all other variables and constants.

A formula is a mathematical representation of how two variables relate to one another. In the sciences, including physics, biology, and chemistry, formulas are also employed. They are employed in medicine to do computations for calculating body mass index or distributing medication. Calculations are done using formulas in spreadsheet systems.

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The graph of y = -2x is a straight line passing through origin with slope -2

Here we have been given an equation.

To graph the equation y = -2x, we find the coordinates of the points satisfying y = -2x

For x = 0,

y = -2(0)

y = 0

For x = 2

y = -2(2)

y = -4

For x = -2,

y = -2(-2)

y = 4

For x = 3,

y = -2(3)

y = -6

So, we get  the coordinates (0, 0), (2, -4), (-2, 4), (3, -6)

Now we draw a line passing through points (0, 0), (2, -4), (-2, 4)

The graph is as shown below.

The slope of the line y = -2x is -2

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Answer: 15

Step-by-step explanation:

1.5/2 = x/20

2x = 30

x = 15

the general term will be a,ar,ar², .... i.e 3, 12, 48..

What is geometric sequence?

The sequence where another varies each word by a common ratio is known as a geometric progression or geometric sequence. When we add a constant (which is not zero) to the term before it, the sequence's subsequent term is created. The following symbols stand in for it: a, ar, ar2, ar3, ar4, etc.

Geometric Progression (GP), a form of sequence in mathematics, is a series in which each subsequent term is created by multiplying each preceding term by a set integer, known as a common ratio. A geometric sequence of integers that follows a pattern is another name for this development.

Given,

a = 3

ar+ar² = 60

r+r² = 20

r(r+1)=20

r = 4

So the general term will be a,ar,ar², .... i.e 3, 12, 48..

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The  value of r is 4 , so the line that passes through the pair of points has the given slope. (r, 2), (6, 3), m=1/2.

The ratio of the change in the y coordinate to the change in the x coordinate is known as the slope of a line. The terms Y and x, respectively, stand for the net change in the y-coordinate and the net change in the x-coordinate. where "m" denotes a line's slope. The outcome is that a line's slope is tan.

Two points along the selected line should have their coordinates determined. The difference between these two places' y-coordinates should be determined (rise).

The difference between these two places' x-coordinates should be determined (run). Divide the y-coordinate difference by the x-coordinate difference (rise/run or slope).

Given Points are (r, 2), (6, 3) , slope m = 1/2

(3 - 2)/(6 - r) = (1/2)

Simplifying the above equation, then we get

6 - r = 2

r = 4

Therefore, (r, 2), (6, 3), m = 1/2 the slope of the line passing through each pair of points is r = 4.

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The triangle that has the coordinates as A(0,-4) B(0,-9) C(-2,-5) is; A scalene Triangle

The formula for the distance between two coordinates is;

D = √[(y₂ - y₁)² + (x₂ - x₁)²]

Thus;

Distance AB = √[(-9 + 4)² + (0 - 0)²]

Distance AB = √25

Distance AB = 5

Distance BC = √[(-5 + 9)² + (-2 - 0)²]

Distance BC = √20

Distance CA = √[(-4 + 5)² + (-2 - 0)²]

Distance CA = √5

Since the three sides all have different lengths, then they the triangle is said to be a scalene triangle.

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The 25th percentile for the given dataset is 5, and the 80th percentile is 16.

What is the percentile?

A percentile is a measure used in statistics that indicates the value below which a given percentage of observations in a group of observations fall. Percentiles divide a set of observations into 100 equal parts, where each part represents 1% of the observations.

To find the 25th percentile (also known as the first quartile) and 80th percentile (also known as the fourth quartile) for a set of data, you can use the following steps:

Arrange the data in increasing order:

1, 3, 5, 9, 10, 11, 14, 15, 16, 18, 20, 22, 24, 25, 27, 29, 31, 37

To find the 25th percentile, use the following formula:

25th percentile = (N+1) x 25%

where N is the number of observations. In this case, N = 18.

Plugging in the values, we get:

25th percentile = (18+1) x 25% = 19 x 25% = 4.75

So, the 25th percentile is the 4.75th value in the ordered list. Rounding up to the nearest whole number, we get 5 as the 25th percentile.

To find the 80th percentile, use the following formula:

80th percentile = (N+1) x 80%

where N is the number of observations. In this case, N = 18.

Plugging in the values, we get:

80th percentile = (18+1) x 80% = 19 x 80% = 15.2

So, the 80th percentile is the 15.2th value in the ordered list. Rounding up to the nearest whole number, we get 16 as the 80th percentile.

Hence, the 25th percentile for the given dataset is 5, and the 80th percentile is 16.

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The equation that shows the situation is; 3.5x + 2y = 42.

We know that sometimes in mathematics, the problem can be given in the form of a sentence and then the first step in the solution of the problem would be to rewrite the sentence into an equation.

In this case, we have that; Francis is at the state fair. A fair concession stand is selling funnel cakes for $3.50 and deep-fried Oreos for $2.00. Given that the total amount spent is $42.00 when  number of funnel cakes x and the number of deep-fried Oreos y. The equation is; 3.5x + 2y = 42.

We now see that;

Total number= 42

Each deep-fried Oreos cost $ 3.5 and we have y number of it

Each funnel cake cost $2.00 and we have x of it.

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The side length of BC in ∠ABC is 11.

Solution:

∠A = 32°

∠C = 39°

∠B = 180°-39°-42°

∠B = 99°

side length of AC = 16

a / sin A = b / sin B = c / sin C

a / sin42° = 16 / sin99°

a = 16 sin42°/ sin99°

a = 10.84

a = 11

The side length of BC = 11

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If the scale for the drawing is 1 inch : 4 feet , then the length of the rug in the drawing  is 2 inches  .

the actual length of the rug in the hallway is = 8 feet ;

the scale factor for the drawing is given as 1 inch : 4 feet  ;

that means 4 feet of actual length is represented by 1 inch in the drawing ,

So , 1 feet in the actual length will be = [tex]\frac{1}{4}[/tex] inch in the drawing ;

that means , 8 feet of the actual length will be = [tex]\frac{8}{4} =2[/tex] inch in drawing .

Therefore , the length of the rug in the drawing is 2 inches .

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The probability that the lightbulb lasts at least one year is: P(T ≥ 365) = 1 - e^(-λ * 365).

To determine the probability that a lightbulb lasts at least one year, we need to know the failure rate of the lightbulb and its distribution. For example, if the lightbulb follows a exponential distribution with parameter λ, the probability that it lasts at least one year (t = 365 days) can be calculated as:

P(T ≥ 365) = 1 - P(T < 365) = 1 - F(365),

where F(365) is the cumulative distribution function (CDF) of the exponential distribution evaluated at t = 365. The CDF of the exponential distribution is given by:

F(t) = 1 - e^(-λt),

so the probability that the lightbulb lasts at least one year is:

P(T ≥ 365) = 1 - e^(-λ * 365)

The value of λ depends on the specific lightbulb and its failure rate, which needs to be determined from data or from the manufacturer. Once the value of λ is known, the above equation can be used to calculate the probability that the lightbulb lasts at least one year.

Therefore, The probability that the lightbulb lasts at least one year is: P(T ≥ 365) = 1 - e^(-λ * 365).

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The probability that the lightbulb lasts at least one year is: P(T ≥ 365) = 1 - e^(-λ * 365).

To determine the probability that a lightbulb lasts at least one year, we need to know the failure rate of the lightbulb and its distribution. For example, if the lightbulb follows a exponential distribution with parameter λ, the probability that it lasts at least one year (t = 365 days) can be calculated as:

P(T ≥ 365) = 1 - P(T < 365) = 1 - F(365),

where F(365) is the cumulative distribution function (CDF) of the exponential distribution evaluated at t = 365. The CDF of the exponential distribution is given by:

F(t) = 1 - e^(-λt),

so the probability that the lightbulb lasts at least one year is:

P(T ≥ 365) = 1 - e^(-λ * 365)

The value of λ depends on the specific lightbulb and its failure rate, which needs to be determined from data or from the manufacturer. Once the value of λ is known, the above equation can be used to calculate the probability that the lightbulb lasts at least one year.

Therefore, The probability that the lightbulb lasts at least one year is: P(T ≥ 365) = 1 - e^(-λ * 365).

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6 will be the Coefficient of the given expression.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, the expression below.

6h²-9

To find the coefficient of this expression:

A coefficient is an integer that is written along with a variable or it is multiplied by the variable. In other words, a coefficient is the numerical factor of a term containing constants and variables.

Thus, in our case,

Coefficient = 6

Constant = 9

therefore, the Coefficient of the given expression will be 6.

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Answer: Slope = 3

Step-by-step explanation:

Answer: hopefully this helps

The relationship between x and y in the table appears to be a linear, proportional relationship. One way to write an equation for this relationship is using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

To find the slope (m), we can use the formula: m = (y2 - y1) / (x2 - x1).

Using any two points from the table, like (x1, y1) = (0.5, 7) and (x2, y2) = (1, 14)

m = (14 - 7) / (1 - 0.5) = 7 / 0.5 = 14

So the slope (m) = 14, which means that y increases by 14 units for every unit increase in x.

Then we can use any point in the table to find the y-intercept (b)

Using the point (1,14)

14 = 14*1 + b

b=0

So the equation for the proportional relationship shown in the table is : y = 14x

Step-by-step explanation:

The required values of slope and y-intercept are 10 and 15.

The formula for these lines is y = mx + b, where m denotes the slope and b the y-intercept. Our line has a slope of 3 and a y-intercept of -5, which we know from the question. By entering these numbers, we obtain the equation of our line as y = 3x - 5.

We have,

y = 10x + 15

On comparing with general equation of line.

Y = mx + c

m is slope of line, c is y-intercept.

Then,

m = 10

And

y-intercept = 15

Thus,the required values of slope and y-intercept are 10 and 15.

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The given system of equations y = -2x + 4 and 7y = -14x + 28 have Infinite solutions.

We have two equations are y = -2x + 4 and 7y = -14x + 28

We have to find the number of solutions for this set of equations

Let us first solve the given equations

y = -2x + 4   eqn 1

7y = -14x + 28   eqn 2

Substitute eqn 1 into eqn 2

7(-2x + 4) = -14x + 28

-14x + 28 = -14x + 28

0 = 0

This means that given equations y = -2x + 4 and 7y = -14x + 28 have infinitely many solutions.

Therefore, The two lines may have an infinite number of intersecting points (infinite solutions).

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Bayes's Theory is an important tool for understanding probability and for determining the likelihood of certain outcomes occurring.

It states that the probability of an event occurring if another event has already occurred is generally different from the probability of the second event occurring if the first one has already occurred. This is a common mistake made by medical professionals, particularly when interpreting test results.

For example, in a study conducted in both Germany and the United States, researchers asked physicians to estimate the probability that an asymptomatic woman between the ages of 40 and 50 who has a positive mammogram actually has breast cancer. The physicians were told that 7 percent of mammograms show cancer when there is none, the actual incidence of cancer is 0.8 percent, and the false-negative rate is about 10 percent. Through the use of Bayes's Theory, it can be determined that a positive mammogram is due to cancer in only about 9 percent of the cases.

However, in the German group, one-third of the physicians concluded that the probability was about 90 percent, and the median estimate was 70 percent. In the American group, 95 out of 100 physicians estimated the probability to be around 75 percent. This example shows how medical professionals can make mistakes when interpreting test results, due to a lack of understanding of Bayes's Theory.

In order to avoid making such mistakes, medical professionals need to be educated on Bayes's Theory and its importance in determining the probability of certain outcomes occurring. By doing so, medical professionals can increase their accuracy in interpreting test results and make better decisions for their patients.

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Answer:

Step-by-step plotttt

Answer:

23.54

Step-by-step explanation:

Due to the fact that the x coordinates of any two points allow us to calculate their separation from the y-axis, we may deduce that the distance between (-5, 6) and the y-axis is 5 units.

Both statistical and qualitative methods can be used to calculate the distance between two items or points.

The word "distance" in physics can refer to an exact measurement or, more frequently, to an estimate based on a number of different factors.

The length of the line segment that connects any two points on a plane provides the distance between those spots.

The following formula can be used to calculate the separation between two points:

d=((((x2 - x1)2 + (y2 - y1)2)

So, the given points are:

(-5, 6)

We may conclude that the gap between (-5, 6) and the y-axis is 5 units because the x coordinates of any two points show us how far apart they are from the y-axis.

Therefore, due to the fact that the x coordinates of any two points allow us to calculate their separation from the y-axis, we may deduce that the distance between (-5, 6) and the y-axis is 5 units.

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Answer: 644.99999

Step-by-step explanation:

6 4/5 = 34/5 = 6.8

6.8 as a percent is 680%

Hope this helps!

Answer: is 5/4

Step-by-step explanation:

Writing as a fraction of the expression 3/4+1/2 with the fraction calculator

To calculate the addition fraction, the fractions are reduced to a common denominator and then added numerators.

We obtain 3/4+1/2=3⋅2+44⋅2

The GCD of the fraction is equal to 2.

By dividing the numerator and denominator by the GCD, we obtain: 10/8=5/4

The result of the calculation is : 3/4+1/2=54

Possible calculations with the fraction: 5/4