expand (x-4)^5 using the binomial theorem and pascal’s triangle show all necesssry steps

Answers

Answer 1

The binomial expansion of the [tex](x-4)^5[/tex] is  [tex]x^5+20x^4+160x^3+640x^2+1280x+1024[/tex]

According to the statement

we have given that a equation and we have to expand it by use of the binomial theorem.

So, For this purpose we know that the

A binomial theorem, statement that for any positive integer n, the nth power of the sum of two numbers a and b may be expressed as the sum of n + 1 terms of the form.

And the general formula is

[tex](x+y)^n= ^nC_0x^ny^0+^nC_1x^(n-1)y^1+^nC_2x^(n-2)y^2+...+^nC_nx^0y^n[/tex]

And we have to solve it with the given equation (x-4)^5.

Then

[tex](x-4)^5=x^5+20x^4+(20)/(2)x^3(4^2)+(60)/(6)x^2(4)^3+(120)/(24)x^1(4)^4+(120)/(120)x^0(4)^5[/tex]

Now after solving the equation become

[tex](x-4)^5=x^5+20x^4+160x^3+640x^2+1280x+1024[/tex]

So, The after expanding the given statement with the binomial theorem the result output is

[tex](x-4)^5=x^5+20x^4+160x^3+640x^2+1280x+1024[/tex]

So, The binomial expansion of the [tex](x-4)^5[/tex] is  [tex]x^5+20x^4+160x^3+640x^2+1280x+1024[/tex]

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Related Questions

To graph the inequality t>3, you would put an open circle on 3 and shade to the left

Answers

Answer:

It is an open circle and you would shade to the right on a number line.

Step-by-step explanation:

The circle is open because you are not including 3.  Put numbers in for t and you will see that the numbers greater than 3 are all on the right side of the number line.

Suppose f′(6)=5 and g′(6)=7.
Find h′(6) where h(x)=4f(x)+5g(x)+1.

Answers

The value of the derivative of functions h'(6) as requested in the task content is; 55.

What is the value of h'(6)?

Since it follows from the task content that the function h(x)=4f(x)+5g(x)+1.

Hence, the derivative of h(x) can be evaluated as;

h'(x)=4f'(x)+5g'(x)

On this note, by substitution, it follows that;

h'(6)=4(5)+5(7)

h'(6) = 55.

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A company determines that the revenue, in dollars, for selling a particular model of lamp is given by R(x)=x(−20x+1200), where x is the price of each lamp. At which of the following prices will the company’s revenue be $10,000?

Answers

The price that will maximize company’s revenue of $10,000 is $50.

How to calculate the price?

From the information, the company determines 50that the revenue, in dollars, for selling a particular model of lamp is given by R(x)=x(−20x+1200),

Therefore, this will be:

R(x) = -20x² + 1200x

10000 = -20x² + 1200x

-20x² + 1200x - 10000 = 0

x² - 60x + 500

x² - 50x - 10x + 500

x(x - 50) - 10(x - 50)

(x - 50)(x - 10)

Therefore, x - 50 = 0

x = 0 + 50 = 50

The price is 50.

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Find the slope of the line passing through the points (-4, -9) and (5, -9).

Answers

The slope of the line passing through the points (-4, -9) and (5, -9) is 0

How to determine the slope?

The points are (-4, -9) and (5, -9).

The slope is calculated using:

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

So, we have:

Slope = (-9 + 9)/(5 + 4)

Evaluate

Slope = 0

Hence, the slope of the line passing through the points (-4, -9) and (5, -9) is 0

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23 gram put into milligrams

Answers

Answer:

Step-by-step explanation: 23000 milligrams

23000 milligrams. just multiply by 1000

1. Determine the measure of angle B.
B
30
A
64
51

Answers

Answer: 51.4°

Step-by-step explanation:

Use law of cosines:

(because you are trying to find angle B, you need to use Cos B)

Cos B = c² + a²-b²/ 2ca

Then, plug in your numbers:

 Cos B = 30²+64²-51²/ 2(30)(64)

Simplify:

Cos B = 0.6237

Next, to get rid of Cos B, so that we have just B, you need to do the Arccosine or 0.6237:

B = arccosine (0.6237)

Which gets you: 51.4°    

The measure of angle B is 51.41 degrees after applying the cos law of the triangle.

What is the triangle?

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

We have given a triangle in the figure:

To find the measure of the angle B

We can apply cos law:

c² = a² + b² - 2ab cosB

The a, b, and c represents the side lengths of the triangle and the measures are:

a = 30

b = 64

c = 51

51² = 30² + 64² - 2(30)(64) cosB

3840CosB = 4996 - 2601

3840CosB = 2395

CosB = 2395/3840

CosB = 0.623

B = Cos⁻¹(0.623)

B = 51.41 degrees

Thus, the measure of angle B is 51.41 degrees after applying the cos law of the triangle.

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In science class, the average score on a lab report is 87 points, with all students scoring within 1.8 points of the average. If x represents a student's score, write an equation that represents the
minimum and maximum scores.

Answers

The equations which represents the minimum and maximum scores of the students is; x = 87 ± 1.8.

Which equations represents the minimum and maximum possible scores of each student?

According to the task content, the

Average score of the students in the science class is; 87 points

All students are within 1.8 points of the average,

it therefore follows from the task content that the

minimum score is;

= 87 -1.8

= 85.2

maximum score is;

= 87+1.8

= 88.8 points.

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Answer:

Step-by-step explanation:

A. |x − 87| = 1.8

-hope this helps.

if sinA=4/5 solve sin2A, cos2A and tan2A​

Answers

Step-by-step explanation:

1) if m(∠A)∈[0;90°), then

[tex]cos(A)=\sqrt{1-sin^2A} =\frac{3}{5};[/tex]

[tex]sin2A=2sinAcosA=2*\frac{3}{5} *\frac{4}{5}=\frac{24}{25};[/tex]

[tex]cos2A=cos^2A-sin^2A=\frac{9}{25}-\frac{16}{25}=-\frac{7}{25};[/tex]

[tex]tan2A=\frac{sin2A}{cos2A}=-\frac{\frac{24}{25}}{\frac{7}{25}}=-\frac{24}{7}.[/tex]

2) if m∠A∈[90°;180°), then

cos(A)=-0.6;

sin2A=-0.96;

cos2A=-0.28;

tan2A=-24/7.

Which of the following equations is an example of inverse variation between
the variables x and y?

Answers

Answer:

we need a whole example not just the variables.

Step-by-step explanation:

Which of the following is the largest Y value from the solution set of the giving system round your answer to the nearest hundredth

Answers

The largest y-value from the solution set of the nonlinear system is 3.78. (Correct choice: C)

What is the solution of a non-linear system

In this question we have a system of non-linear equation formed by a radical equation and a quadratic equation, which can be solved both analytically and graphically. By equalizing the two formulas we have the following equation:

√(2 · x + 4) = x² - 5 · x + 3

√(2 · x + 4) + 13 / 4  = x² - 2 · (5 / 2) · x + 25 / 4

√(2 · x + 4) + 13 / 4 = (x - 5 / 2) ²

√(2 · x + 4) = (x - 5 / 2) ² - 13 / 4

Then, we square both sides to eliminate the radical sign:

2 · x + 4 = (x - 5 / 2)⁴ - (13 / 2) · (x - 5 / 2)² + 169 / 16

2 · x + 4 = x⁴ + 4 · x³ · (- 5 / 2) + 6 · x² · (- 5 / 2)² + 4 · x · (- 5 / 2)³ + (- 5 / 2)⁴ - (13 / 2) · [x² + 2 · (- 5 / 2) · x + ( - 5 / 2)²] + 169 / 16

2 · x + 4 = x⁴ - 10 · x³ + (75 / 2) · x² - (125 / 2) · x + 625 /16 - (13 / 2) · x² + (65 / 2) · x - 325 / 8 + 169 / 16

2 · x + 4 = x⁴ - 10 · x³ + 31 · x² - 30 · x + 9

x⁴ - 10 · x³ + 31 · x² - 32 · x + 5 = 0

The real roots of this polynomial are:

x₁ ≈ 5.152, x₂ ≈ 2.862, x₃ ≈ 1.797, x₄ ≈ 0.189

Now we evaluate f(x) at each root:

y₁ ≈ 3.782, y₂ ≈ 3.118, y₃ ≈ 2.756, y₄ ≈ 2.092

The largest y-value from the solution set of the nonlinear system is 3.78. (Correct choice: C)

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Find the area. This is a trapezoid, with bases that measure 5 feet and 10 feet, and a height of 4 feet.

Answers

Answer:

A = 30 ft²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)

where h is the height and b₁, b₂ the parallel bases , then

A = [tex]\frac{1}{2}[/tex] × 4 × (5 + 10) = 2 × 15 = 30 ft²

Match each function with the corresponding function formula when h(x) = 5 - 3x and g(x) = -3x + 5.

Answers

Answer: -5=x

Step-by-step explanation:

kmbtvonpvnp4tnv

what is the ration between 28000 and 14?

Answers

The ratio between 28,000 and 14 is 2000 : 1

How to determine the ratio?

The numbers are given as:

28,000 and 14

Express as ratio

Ratio = 28000 : 14

Divide each number by 14

Ratio = 2000 : 1

Hence, the ratio between 28,000 and 14 is 2000 : 1

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Choose the algebraic description that maps the image ΔABC onto ΔA′B′C′.

Answers

The algebraic description that maps the image ΔABC onto ΔA′B′C′ is (x, y) ⇒ (x + 7, y - 4)

What is transformation?

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

Translation is the movement of a point either up, left, right or down in the coordinate plane.

The algebraic description that maps the image ΔABC onto ΔA′B′C′ is (x, y) ⇒ (x + 7, y - 4)

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find x and y

plssss help

Answers

90 + 6x = 180

-90

6x = 90

÷6

x = 15

5y + 4y + 90 + (6x15) =360

9y + 90 + 90 = 360

9y + 180 = 360

- 180

9y = 180

÷9

y = 20

Hope this helps!

please help asap
thank you very much

Answers

Answer:

x=30 , y=165 & z=10

happy to help { bts army girl }

Answer:

Step-by-step explanation:

Comment

You must solve x and then y in that order. The reason for that is there are 2 x values and they can be equated to each other. The you can go after the y value, since they are supplement with the value you get from the first operation.

Equations

x + 45 = 2x+ 8

<3 + y + 30 = 180

Solution

<1 and <3 are equal             Two vertically opposite angles are always =.

x  +  45 = 2x + 8                    Subtract x from both sides

x-x + 45 = 2x - x + 8              Combine

45 = x + 8                              Subtract 8 from both sides

45 - 8 = x + 8 - 8                   Combine

37 = x

<1 + <2 = 180                        These two angles sit on the same straight line and have a side in common

x + 45 + y + 30 = 180           Substitute for x

37 + 45 + y + 30 = 180         Combine

112 + y = 180                         Subtract 112 from both sides

112-112 + y = 180 - 112           Combine

y = 68

Mal works at a photo gallery. He charges $50 for a large photo and $40 for a large frame. Sales tax is 5%. How much total tax will a customer pay on both?Answer the questions to show how to write and simplify expressions that represent the problem.

2. Use the distributive property to expand 0.05(50 + 40). (2 points)

Answers

Answer:

$4.50

Step-by-step explanation:

We can use the distributive property to solve this problem. 0.05(50+40) is the total sales tax. 0.05 being the percentage and 50 and 40 being the things we need to distribute 0.05 to. This becomes 2.5+2. This is 4.5.

Answer:

$0.45

Step-by-step explanation:

0.05(50 + 40) = 50 x 0.05 + 40 x 0.05 = 0.25 + 0.20 = 0.45

What is the value of x
83
58
50
70.5

Answers

Answer:

58

Step-by-step explanation:

[tex]x = \frac{141 - 25}{2} = 58[/tex]

Part 1:
A. Express the new length of the long side of the note card, once the two corners are removed.
B. Express the new width of the short side of the note card, once the two corners are removed.

Part 2:
Write a function A(x) that defines the area of the bottom of the box, once the corners are removed and the sides are folded up.

Part 3:
A. Suppose you want the bottom of your box to cover a total area of 16 in2. Set up an equation in standard form that will help you find the size (x) of the corner you need to cut in order for your box to have this area.
B. Solve this equation and take note of any extraneous solutions. Explain why the answer is extraneous, and clearly state the correct answer

Answers

The size of the corner you need to cut in order for your box to have this area is 0.5 inches

Part 1: A. Express the new length of the long side of the note card, once the two corners are removed.

The base length is given as:

Length = 7

When the edges are removed, the new length becomes

New length = 7 - x - x

Evaluate

New length = 7 - 2x

Part 1: B. Express the new width of the short side of the note card, once the two corners are removed.

The base width is given as:

Width = 4

When the edges are removed, the new length becomes

New width = 4 - x - x

Evaluate

New width = 4 - 2x

Part 2: Write a function A(x) that defines the area of the bottom of the box, once the corners are removed and the sides are folded up.

The area of the bottom of the box is calculated as:

Area = New length * New width

This gives

Area = (7 - 2x) * (4 - 2x)

Rewrite as:

A(x) = (7 - 2x) * (4 - 2x)

Part 3: Set up an equation in standard form that will help you find the size (x)

The area is given as:

Area = 16

So, we have:

(7 - 2x) * (4 - 2x) = 16

Expand

28 - 14x - 8x + 4x^2 = 16

Rewrite as

4x^2 - 14x - 8x + 28 - 16 = 0

Evaluate the like terms

4x^2 - 22x + 12= 0

Part 3: Solve this equation and take note of any extraneous solutions

We have:

4x^2 - 22x + 12= 0

Expand the equation

4x^2 - 24x - 2x + 12 = 0

Factorize the equation

4x(x - 6) - 2(x - 6) = 0

Factor out x - 6

(4x - 2)(x - 6) = 0

Solve for x

x = 0.5 or x = 6

The value of x = 6 is too big for the dimensions of the box.

So, x = 6 is an extraneous solution for the equation

Hence, the size of the corner you need to cut in order for your box to have this area is 0.5 inches

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The short sides of a rectangle are 2 inches. The long sides of the same rectangle are three less than an unknown number of inches.


Suppose the area of this rectangle is less than 12 square inches. Which of the following numbers could be the value of the unknown number? Select all that apply.

Answers

Answer:

6,4

Step-by-step explanation:

I'm not sure if 4 is correct but 6 definitely is. I hope this helps

Choose the correct simplification of (4x − 3)(3x2 − 4x − 3).

Answers

the expression simplified is:

[tex]12x^3 - 25x^2 + 9[/tex]

How to simplify the given expression?

Here we have the expression:

[tex](4x - 3)*(3x^2 - 4x - 3)[/tex]

We just need to distribute the product, we will get:

[tex](4x - 3)*(3x^2 - 4x - 3)\\\\(4x)*(3x^2 - 4x - 3) - 3*(3x^2 - 4x - 3)\\\\12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9[/tex]

Now we just need to group terms with the same exponent of x:

[tex]12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9\\\\12x^3 + (-16 - 9)x^2 + (-12 + 12)x + 9\\\\12x^3 - 25x^2 + 9[/tex]

That is the expression simplified

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What is the domain of the rational function f of x is equal to the quantity x squared minus x minus 12 end quantity over the quantity x cubed minus 4 times x squared minus 4 times x plus 16 end quantity question mark

{x ∈ ℝ| x ≠ –2, 2, 4}
{x ∈ ℝ| x ≠ –2, 2}
{x ∈ ℝ| x ≠ –3, 4}
{x ∈ ℝ| x ≠ –3, –2, 2, 4}

Answers

The domain of the rational function is:

{x ∈ ℝ| x ≠ –2, 2}

What is the domain of the rational function?

Here we have the rational function:

[tex]f(x) = \frac{x^2 - x - 12}{x^3 - 4x^2 - 4x + 16}[/tex]

We want to get the domain of that function. First, we can rewrite the numerator and denominator as:

[tex]x^2 -x - 12 = (x + 3)*(x - 4)[/tex]

[tex]x^3 - 4x^2 - 4x + 16 = (x - 4)*(x + 2)*(x - 2)[/tex]

Then we can rewrite the rational function as:

[tex]f(x) = \frac{(x + 3)*(x - 4)}{(x - 4)*(x + 2)*(x - 2)}[/tex]

This can be simplified to:

[tex]f(x) = \frac{(x + 3)}{(x + 2)*(x - 2)}[/tex]

Now, the domain will be the set of all real numbers, minus the values of x that generate problems.

In this case, the values:

x = -2 and x = 2 make the denominator to be zero, and we can't divide by zero, so  we conclue that the domain is:

{x ∈ ℝ| x ≠ –2, 2}

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Which of the following inequalities matches the graph?
-8 -0
O x>4
O x<4
O y> 4
O y<4
1

Answers

Answer:

it matches with equation c

will give brainliest

Answers

ax² + bx + c = 0

discriminant = b² - 4ac

----> x² + 7x + 12

---> Discriminant of this equation = 7² - 12.1.4 = 49 - 48 = 1 (Positive discriminant)

x = (-7 + 1)/(2.1) = -6/2 = -3

or

x = (-7 - 1)/(2.1) = -8/2 = -4

Therefore, this equation has two real solutions and has a positive discriminant.

The correct answer is B

Melissa Costouras obtains a $3,000 loan for darkroom equipment. She makes six monthly payments of $511.18. Determine the APR.

Answers

Using the simple interest formula, it is found that the APR for the loan is of 4.472%.

What is the simple interest formula and when it is used?

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

[tex]A(t) = A(0)(1 + rt)[/tex]

In which:

A(0) is the initial amount.r is the interest rate, as a decimal.

The parameters for this problem are:

A(t) = 6 x 511.18 = 3067.08, A(0) = 3000, t = 0.5.

We solve the equation for r to find the APR.

[tex]A(t) = A(0)(1 + rt)[/tex]

[tex]3067.08 = 3000(1 + 0.5r)[/tex]

[tex]1 + 0.5r = \frac{3067.08}{3000}[/tex]

1 + 0.5r = 1.02236

r = (1.02236 - 1)/0.5

r = 0.04472.

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where are the two variables is part A? Tiya earns $7 an hour mowing her neighbor's lawn.

Part A: Create two variables and determine which is dependent and which is independent for this situation. (4 points)

Answers

The two variables are; earnings, y and hours, x in which case, the former is the dependent variable while the latter is the independent variable.

Which is the dependent and which is the independent variable?

It follows from the task content that Tiya earns $7 an hour mowing her neighbor's lawn.

On this note, it follows that the amount of money earned by Tiya is a dependent variable which solely depends on the number of hours spent on the job, which is the independent variable.

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A model house has a scale of 1 in : 2 ft. if the real house is 26 ft wide then how wide is the model house.

Answers

Answer: 13 in.

Step-by-step explanation:

All you need to do is divide 26 by 2 in this case.

solve this pleas i need urgent answer

Answers

Answer:

f(n)={n/2     = if n is even=   n={2/2

       {3n+1                                 {3(2)+1   =7

Step-by-step explanation:

if n is even u can put any even no in that place and u can get odd no or even no.(i think)

The function f(X) =7^x + 1 is transformed to function g through a horizontal compression by a factor of 1/3

Answers

The equation of the function g(x) is g(x) = 7^(3x) + 1

How to determine the function g(x)

The function f(x) is given as:

f(x) = 7^x  1

When compressed horizontally by a factor of 1/3.

We have:

g(x) = f(3x)

This implies that:

g(x) = 7^(3x) + 1

Hence, the equation of the function g(x) is g(x) = 7^(3x) + 1

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Write the positive or negative number that best
represents the given information.
12 ft above sea level

Answers

Answer:

12

Step-by-step explanation:

Usually, above sea level is represented by a positive number and below sea level by a negative number.

12 ft above sea level = 12

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A stock trader can financially benefit the least from trading stocks using inside information when financial markets are:Multiple ChoiceInefficient.Semi strong form efficient.Weak form efficient.Semi weak form efficient.Strong form efficient. define a reduction. show how the input of one problem is transformed into the input of another problem with an example. Calculate the voltage of the following cellsZn|Zn^2+(0.20M)||Cu^2+(0.10M)|Cu define what one might call a multiple off-line turing machine and describe how it can be simulated by a standard turing machine. Help me please ill really appreciate it!! Compute the determinants. (a) (5 pts) Let A and P be 3 x 3 matrices with det A = 5 and det P=2. Compute det (PAPT). (b) (5 pts) Find det C for C= a 006] 0 0 1 0 0 1 0 0 C00d larry puts together a bookshelf he has purchased on amazon. which of these describes larry? explain the origin of the pre colonial igbo society Biology Class work, help please, respiratory system How does the stockholders' equity section in the balance sheet differ from the statement of stockholders' equity? A) The stockholders' equity section shows activity over a period of time, whereas the statement of stockholders' equity at a point in time. B) The stockholders' equity section is more detailed than the statement of stockholders' equity. C) The stockholders' equity section shows balances at a point in time, whereas the statement of stockholders' equity shows activity over a period of time. D) There are no differences between them. Prove that the equation x^2 + y^2 + z^2 = 8006 has no solutions.(HINT: Work Modulo 8.) Demonstrate that there are infinitely many positive integers which cannot be expressed as the sum of three squares. On a Statement of Activities for a not-for-profit entity, what are the broad categories of supporting service costs required to be reported?Multiple ChoiceFundraising expenses and operating expenses.Program services expenses and administrative services expenses.IncorrectFundraising expenses and supporting services expenses.Fundraising expenses and administrative expenses.Operating expenses and administrative expenses. How does meiosis (including crossing over) lead to increased genetic diversity in a population? Identify the electron configuration for each of the following ions: (a) A carbon atom with a negative charge (c) A nitrogen atom with a positive charge (b) A carbon atom with a positive charge (d) An oxygen atom with a negative charge .Complete the following paragraph explaining the inhibition of glycolysis at high levels of glucose-6-phosphate.Glucokinase is inhibited by high levels of its [by-product, product, or substrate], [glucose-6-phosphate, glucose, or ADP]. When glycolysis is inhibited through [glucokinase, pyruvate kinase, or phosphofructokinase], glucose-6-phosphate builds up, shutting down [glucokinase, phosphofructokinase, or pyruvate kinase]. This [activates glucose-6-phosphate metabolism, prevents glucose being metabolized, or activates glucose metabolism] in the liver, when it is needed in the blood and other tissue. This is an example of [competitive inhibition, feedback inhibition, or non-competitive inhibition] Find the work W done by a force of 6 pounds acting in the direction 60\deg to the horizontal in moving an object 6 feet from(0,0) to (6,0) a single-price monopolist is inefficient because mr = mc. p > atc. it creates a deadweight loss. it increases producer surplus. Select the correct answer from each drop-down menu. Read this excerpt from "Porphyria's Lover" by Robert Browning and complete the sentences that follow. The rain set early in to-night, The sullen wind was soon awake, It tore the elm-tops down for spite, And did its worst to vex the lake These lines from the poem have several examples of. The lines express the importance of of nature. The poetic sound device that is most pronounced in the lines is. what trends in musical theatre are Plays Rent and Avenue Q examples of?Musicals based on films Musicals based on the music of former popular stars and groups Revivals of past musical successes Fresh, offbeat musicals indicating the genre remains full of vitality max, jones and waters shared profits and losses 20%, 40%, and 40% respectively and their partnership capital balance is $10,000, $30,000 and $50,000 respectively. max has decided to withdraw from the partnership. an appraisal of the business and its property estimates the fair value to be $200,000. land with a book value of $30,000 has a fair value of $45,000. max has agreed to receive $20,000 in exchange for her partnership interest after revaluation. at what amount should land be recorded on the partnership books?