How do you find the value of k in a function?

The coefficient of x³y² in the expansion of (2x+y)5 is 80.

Given data :

The coefficients of terms of (p+q)^n can be found by the Pascal's triangle for small values of n.  Pascal's triangle will start with (1,1)  = coefficients of (p,q)^n =1.  For n=2, we add successive terms of the previous value of n.  Thus for n-2, we have (, 1+1,11=(1,2,1), for n=3, we have (1,3,3,1), giving the following pattern:

(1,1)

(1,2,1)

(1,3,3,1)

(1,4,6,4,1)

(1,5,10,10,5,1)

meaning for n=5, the binomial expansion for (P+Q)^5 is

P^5+5P^4Q+10P^3Q^2+10P^2Q^3+5PQ^4+Q^5

Setting P=2x, Q=y in the term 10P^3Q^2, we get a term

10(2x)^3(y)^2

=10(8x^3)(y^2)

=80x^3y^2

So the required coefficient is K=80.

We can also find the coefficient 10 by binomial expansion of

n=5, x=3 in

C(n,x) = n! / (x! (n-x)!) = 5! / (2!3!) = 5*4*3/(1*2*3) = 10

Then again substituting 10(2x)^3(y)^2 = 80x^3y^2

to get the coefficient K=80.

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Answer: bro this ez 1.5 for the first one second should be 22 correct me if im wrong.

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

I factor out the radicand and get 22

Let's test if my answer is correct!

22 times 22 = 484

So, my answer is correct!

All the options that result in (x + 4 ) (x 4 ) = 0 being true are the ultimate answer and x = − 4 , 4.

Here, x²-16=0

rewrite 16 as 4²

then, (x+4)(x-4)

Any factor on the left side of the equation that is equal to 0 will make the entire expression equal to 0.

x+4=0 and find x

Then x=-4

x-4=0 and find x

x=4.

Hence, All the options that result in (x + 4 ) (x 4 ) = 0 being true are the ultimate answer and x = − 4 , 4.

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The total surface area of the cylinder is 10635 cm-square

Given, the length of the toilet paper roll = 16 cm

The radius of the toilet paper roll = 6cm

The diameter of the inside roll = 3cm

So, the radius of inside cylinder = diameter/2 = 3/2 = 1.5 cm

We know that the formula for :

The total surface area of a cylinder = 2πrh (h+r)

Here, h = 16 cm

r1 = 6cm and r2 = 1.5 cm

Since there are two cylinders one cylinder inside another so here total surface area will be equal to :

2πr1h (h+r1) - 2πr2h (h+r2)

On calculating, Total surface area = 10635 cm-square

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Answer:

B. 1 & 1  

C. 5 & 3

D. 2 & 2

E. 4 & 0

Something interesting about these was me having to just use simple and smaller numbers to complete the equations.

Answer:

answers is in attached picture.

Step-by-step explanation:

Answer:

m=102

Step-by-step explanation:

You forgot to attach an image of the lines, but I have it here, so no worries

We know that two parallel lines are crossed by a transversal. m are consecutive interior angles. We know that they add up to 180 degrees.

So, our equation is

78 + m = 180

m = 102

Considering the definition of parallel line, the equation of the line d is y= 3x -7.

A linear equation o line can be expressed in the form y = mx + b

where

Parallel lines are two lines that prolonged towards infinity never touch.

Two lines are parallel if they have the same slope and different y-intercepts.

In this case, the line is y=3x-4

where:

Since two lines are parallel if they have the same slope, the parallel line has a slope of 3.

The line passes through the point (2, -1). Replacing in the expression for a line:

-1= 3× 2 + b

-1= 6 + b

-1 -6= b

- 7= b

Finally, the equation of parallel line is y= 3x -7.

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Arithmetic mean of the data set 4,5,0,10,8and 3  is '5'

What Is the Arithmetic Mean?

The easiest and most popular way to calculate a mean or average is with simple mathematics. It simply entails adding up a collection of numbers, dividing that total by the number of numbers in the series, and adding the result together.

given data set is -

4 , 5 , 0 , 10 , 8 and 3

number of observations in given data set are '6'

arithmetic mean ( AM ) formula is

AM = (sum of all observations in given data set) / (total number of observations)

sum of all observations in given data set = 4 + 5 + 0 + 10 + 8 + 3

= 30

AM = 30 / 6 = 5

arithmetic mean of the data set 4,5,0,10,8and 3  is '5'

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32.3 divided 5.6 is 0.173

What is an estimation number?

Estimation of numbers is the process of estimating/approximating or rounding off the numbers in which the value is used for some other purpose in order to avoid complicated calculations.

Change the divisor 32.3 to a whole number by moving the decimal point 1 places to the right.

Then move the decimal point in the dividend the same, 1 places to the right.

Now we have the equations:

56 ÷ 323 = 0.173

and therefore:

5.6 ÷ 32.3 = 0.173

Both calculated to 3 decimal places.

32.3 divided 5.6 is 0.173

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Answer:

[tex]m=\frac{3}{2}[/tex]

Step-by-step explanation:

The x value of the y-intercept must be 0, so let

[tex](x_1,y_1)=(0,1)[/tex]

and

[tex](x_2,y_2)=(4,7)[/tex]

The slope of a line can be found with the following:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

So,

[tex]m=\frac{(7)-(1)}{(4)-(0)}\\m=\frac{6}{4}\\m=\frac{3}{2}[/tex]

When we put the value of 1 in place of n in the equation, the value obtained will be equal to the largest prime factor that is 61.

A prime number is any whole number that is greater than 1 and cannot be created by combining other whole numbers. Consequently, a prime number's only factors are 1 and the actual number.

As per the given expression in the question,

2(7ⁿ) - 2(7ⁿ⁻¹) + 7ⁿ⁺¹

Use exponent rule:

[tex]a^b.a^c=a^b^+^c[/tex]

Put the values accordingly,

2(7ⁿ) - 2(7ⁿ⁻¹) + 7ⁿ . 7¹

So,

[tex]\frac{a^b}{a^c}= a^b^-^c[/tex]

⇒ 2(7ⁿ) - 2(7ⁿ/7¹) +  7ⁿ . 7¹

Simplify the above equation,

2(7ⁿ) - 2/7(7ⁿ) + (7)7ⁿ

Take out 7ⁿ as common,

(2 - 2/7 + 7)7ⁿ

Therefore,

61/7(7ⁿ)

Put n = 1 to check for the largest prime number,

61/7(7¹)

= 61

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Answer:

8 minutes = 3 songs

Step-by-step explanation:

Time taken for 1 song is,

→ 72/27

→ 2.6667

→ ≈ 2.7 minutes

Then songs played in 8 minutes,

→ Total time ÷ Time for 1 song

→ 8 ÷ 2.7

→ 2.96296

→ ≈ 3 songs

Hence, the answer is 3 songs.

'4 more than a number' implies that there exists a number which is 4 units greater than the original number, using the concept of addition.

Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").

Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.

Now, let us understand the meaning.

Let the original number be x.

'4 more than a number' implies x + 4.

This means that the new number, x + 4, is greater than the original number, x, by 4 units. We also have to keep in mind, [tex]x + 4 > x[/tex].

Hence, the final meaning is 4 units greater than the original number.

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The ratios of win to lose are 13 : 8, 13/8 and 1.625%

From the question, we have the following parameters that can be used in our computation:

Win = 50 more than lose

Win = 130

This means that

Win = 50 + Lose

So, we have

50 + Lose = 130

Evaluate

Lose = 80

The ratio is then represented as

Ratio = win to lose

This gives

Ratio = 130 : 80

So, we have

Ratio = 13 : 8

Express as fraction

Ratio = 13/8

Lastly, we have

Ratio = 1.625%

Hence, the ratio is 1.625%

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Answer:

x = 43.25

Step-by-step explanation:

(x + 2 )+ (x + 2) + (2x + 3) = 180(total angles in a triangle)

x + 2 + x + 2 + 2x + 3 = 180

x + x + 2x + 2 + 2 + 3 = 180

4x + 7= 180

4x = 180 – 7

4x = 173

divide both sides by (4)

[tex] \frac{4x}{4} = \frac{173}{4} [/tex]

x = 43.25

i hope this helps

The equation of line passing through point (-1,0) and slope 4 in slope intercept is  y = 4x + 4   .

The Slope Intercept form of the line is denoted as " y = mx + c " , c in y intercept and m is slope .

the slope of the line is given to be = 4 ;

and the line passes through the point (-1,0) ,

which can be represented as : 0 = (-1)(4) + c ,

0 = -4 + c .

On simplifying further ,

we get ;

c = 4 .

Substituting the values , we get equation as ⇒ y = 4x + 4 .

Therefore , the equation of line is y = 4x + 4  .

The given question is incomplete , the complete question is

How do you write an equation in slope intercept form with one point and slope ? the point is (-1,0) and slope is 4 .

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There are 5 types of line graphs:

1) Simple line graph                                 2) Compound Line Graph

3) Multiple Line Graph                             4)Vertical Line Graph

5) Horizontal Line Graph                         6) Straight Line Graph

1) Simple Line Graph:

A simple line chart is the most basic type of line chart. Only one dependent variable is tracked in this chart, so there is only one line connecting all the data points on the chart. All points in the chart relate to the same element and the sole purpose of the chart is to track changes in these variables over time. Only variables are graphed, so this graph cannot be used to compare one variable to another.

2) Multiple Line Graph:

In a multiple line chart, multiple dependent variables are plotted on a chart and compared against a single independent variable (often time). Different dependent variables are often marked with different colored lines to distinguish each data set. Each row relates only to points in the specified dataset. Lines do not cross between dependent variables.

3) Compound Line Graph:

If information can be subdivided into two or more types of data. This type of line graph is called a compound line graph.  Composite line charts, like multiline charts, use multiple variables. However, variables are often stacked on top of each other to show the sum of all variables. This informs the user not only of the relationship between each variable, but also of how the total is changing.

4) Vertical Line Graph:

A vertical line chart is a chart in which a vertical line extends from each data point to the horizontal axis. A vertical line chart is sometimes called a column chart. A line parallel to the y-axis is called a vertical line.

5) Horizontal Line Graph:

A horizontal line chart is a chart with a horizontal line running parallel to the globe at each data point. Horizontal line charts are sometimes called line charts.

6) Straight Line Graph:

A line parallel to the X axis is called a vertical line. Line charts are often used to solve conditions that change over specific time intervals. The general linear function has the form y = mx + c, where m and c are constants.

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The transformation of the function is y = -1/7(2ˣ ⁺ ⁸)

From the question, we have the following parameters that can be used in our computation:

y = 2°

Rewrite properly

So, we have

y = 2ˣ

The given transformations are

The riles of these transformations are

When they applied, we have

y = 1/7(2ˣ)

Then,  we have

y = 1/7(2ˣ ⁺ ⁸)

Lastly, we have

y = -1/7(2ˣ ⁺ ⁸)

Hence, the transformed equation is y = -1/7(2ˣ ⁺ ⁸)

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Answer:

[tex]y=\frac{3}{5}x+\frac{1}{5}[/tex]

Step-by-step explanation:

Using the points [tex](3,2)[/tex] and [tex](8,5)[/tex],

[tex]m=\frac{5-2}{8-3}=\frac{3}{5} \\ \\ y-2=\frac{3}{5}(x-3) \\ \\ y-2=\frac{3}{5}x-\frac{9}{5} \\ \\ y=\frac{3}{5}x+\frac{1}{5}[/tex]

The balance after 5 years would be near around 5661 dollars.

What is compound interest?

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.

According to the given question:

First, convert R as a percent to r as a decimal

r = R/100

r = 2.5/100

r = 0.025 rate per year,

Then solve the equation for A

A = P(1 + r/n)ⁿˣ

A = 5000(1 + 0.025/2)²ˣ⁵

A = 5661.35

Hence the balance after 5 years would be near around 5661 dollars.

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Answer:

looooookkkkkk at the picture

The inverse of a 3x3 matrix is found by creating an Adjugate Matrix.

Step 1 : For any matrix M find the adjoint matrix.

        [tex]\text{Let a matrix }M= \left[\begin{array}{ccc}1&2&3\\0&1&4\\5&6&0\end{array}\right][/tex]

                         [tex]M^{T}= \left[\begin{array}{ccc}1&0&5\\2&1&6\\3&4&0\end{array}\right][/tex]

                       Adj M = [tex]\left[\begin{array}{ccc}-24&18&5\\20&-15&-4\\-5&4&1\end{array}\right][/tex]

Step 2 :Find Determinant of a 3x3 Matrix

         [tex]M= \left[\begin{array}{ccc}1&2&3\\0&1&4\\5&6&0\end{array}\right][/tex]

       det (M)= 1 (0- 24 ) - 2 (0 - 20 )+3 (0- 5 )

                  = - 24 + 40 -15

                  = 40 - 39

                  = 1

Step 3 : Find inverse matrix [tex]M^{-1}[/tex]

          [tex]M^{-1 } = \frac{1}{det (M)} (Adj M)[/tex]

          [tex]M^{-1 } = \frac{1}{det (M)} (Adj M)\\\\M^{-1 } = \frac{1}{1}\left[\begin{array}{ccc}-24&18&5\\20&-15&-4\\-5&4&1\end{array}\right]\\\\M^{-1 }=\left[\begin{array}{ccc}-24&18&5\\20&-15&-4\\-5&4&1\end{array}\right][/tex]

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On the Formula tab, click AutoSum > Sum. Excel will automatically sense the range to be summed.

Now, According to the question:

How do I add value to an existing cell in Excel?

One quick and easy way to add values in Excel is to use AutoSum. Just select an empty cell directly below a column of data. Then on the Formula tab, click AutoSum > Sum. Excel will automatically sense the range to be summed.

How do I add a digit to an existing number in Excel?

Say you have 50 in the cell in question, and want to add 30 to it. Then the clever part: Right-click on the cell with 50 in it, and select Paste Special. In the box that comes up, select 'Add'.

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The roots of the quadratic equation x² + 2√3 x + 3 = 0 have only one root and it is -√3

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

x² + 2√3 x + 3 = 0   be equation (1)

On factorizing the equation , we get

The roots of the quadratic equations are calculated by

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

Substituting the values in the equation , we get

x = [ -2√3 ± √ ( ( 2√3 )² - 4 ( 3 ) ) ] / 2

On simplifying the equation , we get

x = [ -2√3 ± √ ( 12 - 12 ) ] / 2

The discriminant is zero we get just one real solution

So ,

x = [ -2√3 ± √0 ] / 2

x = ( -2√3 ) / 2

x = -√3

Therefore , the value of x is -√3

Hence , the root of the quadratic equation is -√3

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The cost of 1 oz is $0.10625

From the question, we have the following parameters that can be used in our computation:

If there is $0.85 for 8 oz

This means that

The cost of 8 oz = $0.85

Assume there exist a proportional relationship between the cost and the size i.e. oz

The cost of 1 oz can be calculated using the following equation

The cost of 1 oz = $0.85/8

Evaluate the quotient

The cost of 1 oz = $0.10625

Hence, the cost of 1 oz is $0.10625

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The number of cubes of edge length 1/3 is 27 and the volume of the cube is 1 cubic inches

From the question, we have the following parameters that can be used in our computation:

The volume of a cube is the cube of its edge length

This means that the volumes are

Volume = Edge length³

So, we have

Volume of cube 1 = (1/3 inch)³ = 1/27 cubic inches

Volume of cube 2 = (1 inch)³ = 1 cubic inch

The number of cubes is then calculated as

Number of cubes = Volume of cube 2/Volume of cube 1

This gives

Number of cubes = 1/(1/27)

Number of cubes = 27

Here, we have

Edge length of cube = 1 inch

The volume of a cube is the cube of its edge length

This means that the volumes are

Volume = Edge length³

So, we have

Volume of cube = (1 inch)³ = 1 cubic inch

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How do you find the mean of 4 numbers?

Finding the mean, refers to finding the average. To do this, add the four numbers together and then divide that number by 4.

The standard form of the linear equation can be written as -3x + y = 1

Standard form defines the method of expressing any mathematical concept such as expression, terms, equation or numbers in a systematic form by following a certain rule.

The system of writing an equation that follows particular rules is termed as standard form of equation.

The standard form of a linear equation with two variables x and y can be written as Ax + By = C

where, A and B are coefficient of x and y respectively, C is the constant.

This form of equation is required to solve linear equation.

The above equation is written in the slope intercept form, and we get

By = -Ax+C

y = -A/Bx+C/B

where, -A/B is the slope of equation, C/B is the y intercept

Now we have a linear equation written in the slope intercept form

y-3x-1 = 0

y= 3x+1

3 is the slope, 1 is the y intercept

now, we can write it in a standard form and get,

-3x+y = 1

hence, standard form of equation is -3x + y = 1

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