Hi! I really need help with this problem

The solution of the expression with three terms using binomial theorem can be solved by supposition and resubstituting the value.

Let us consider an example of three terms :

( 1 + x + x² ) ³

Use binomial theorem and expand the given expression:

Standard form of binomial expansion is :

( a + b )ⁿ = ⁿC₀aⁿb⁰ +  ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b² +..............+  ⁿCₙa⁰bⁿ

Let us consider x + x² = y

( 1 + y )³

=³C₀1³y⁰ +  ³C₁1³⁻¹y¹ + ³C₂1³⁻²y² +  ³C₃1⁰y³

= 1 + 3y + 3y² + y³

Resubstitute the value of y = x + x² we get,

= 1 + 3(x + x²) + 3(x + x²)² + (x + x²)³

= 1 + 3x + 3x² + 3( x² + 2x³ + x⁴) + ³C₀x³(x²)⁰ +  ³C₁x³⁻¹(x²)¹ + ³C₂(x)³⁻²(x²)² +  ³C₃x⁰(x²)³

= 1 + 3x + 3x² + 3x² + 6x³ + 3x⁴ + x³ + 3x⁴ + 3x⁵ + x⁶

= 1 + 3x + 6x² + 7x³ + 6x⁴ + 3x⁵ + x⁶

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Answer:

34.064516129

Step-by-step explanation:

[tex]32 \times \frac{33}{31} = \frac{1056}{31} [/tex]

[tex] = 34.064516129[/tex]

i hope this helps

The factorized expression of (2a³ - 8a) ÷ 2a (a - 2) is (a - 4) ÷ (a - 2)

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

(2a^3-8a)÷ 2a (a-2)

Rewrite the above expression properly

So, we have the following representation

(2a³ - 8a) ÷ 2a (a - 2)

Divide the fraction by 21

This gives

(a - 4) ÷ (a - 2)

The above expression cannot be solved further

Hence, the solution is (a - 4) ÷ (a - 2)

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The height of Dubai fountain is 500 feet tall.

The foundational subject in mathematics is arithmetic, which covers operations with numbers. These include multiplication, division, addition, and subtraction. One of the key areas of mathematics, arithmetic serves as the cornerstone for students studying the topic of mathematics. The Greek term "arithmos," which means "numbers," is where the word "arithmetic" originates. Arithmetic is one of the oldest and most basic concepts in mathematics. It deals with numbers and the basic operations (addition, subtraction, multiplication, and division) that can be carried out on them.

Given

The Burj Khalifa in Dubai is the tallest building in the world, at 2,717 feet.

Burj Khalifa is 217 feet taller

Height of Dubai fountain

Subtracting

2717 - 217

2500

5 times the height

Divide by 5,

2500/5

500

The height of Dubai fountain is 500 feet tall.

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The equation 3x² + 5x + 2 = 0 has two solutions, x = -2 and x = -1/3. This means that when the equation is set equal to zero and then solved, the two values of x that will make the equation true are -2 and -1/3.

To solve 3x² + 5x + 2 = 0, we must first find the roots of the equation. To do this, we can use the quadratic formula to solve for the two roots. The quadratic formula is x = [-b ± √(b² - 4ac)]/2a, where a, b, and c are the coefficients of the equation. To apply this to our equation, we have a = 3, b = 5, and c = 2, so the formula becomes x = [-5 ± √(5² - 4(3)(2))]/2(3). Simplifying this equation gives us x = [-5 ± √29]/6. The two solutions of this equation are x = -2 and x = -1/3. This means that when the equation is set equal to zero and then solved, the two values of x that will make the equation true are -2 and -1/3.

x = [-5 ± √29]/6

x = [-5 + √29]/6 = -2

x = [-5 - √29]/6 = -1/3

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Answer:

Step-by-step explanation:

The coeficient of y² in the expression is the number 3

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

In the given expression we have the following:

3y² + 4x

 As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 3.

3 is the coefficient of y²

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Yes, √3x² - 2x is a polynomial.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

√3x² - 2x

This is in the form of ax² - bx

This is a polynomial with degree 2.

Thus,

√3x² - 2x is a polynomial.

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Answer:

You can tell if a function is positive or negative by checking the Y values. If all the Y values are above the x-axis it should be positive, and if the all y values are below the x-axis the function should be negative.

Good luck!

Answer:

Your answer is 2,600.019

Step-by-step explanation:

Very simply to answer it with or without a calculator.

2.6 * 10^3 + 0.19 * 10^-2

Without calculator
First move the decimal points before adding.

2.6 * 10^3 = 2,600.

0.19 * 10^-2 = 0.0019

This equation 2.6 * 10^3 + 0.19 * 10^-2 becomes

2,600 + 0.0019

Then add.

2,600.0019

Step-by-step explanation:

the multiplication result is found by row×column multiplications.

1st row × 1st column = a

2×1 + 1×-1 + 0×0 = 2 - 1 = 1 = a

1st row × 2nd column = b

2×-1 + 1×-2 + 0×1 = -2 + -2 = -4 = b

1st row × 3rd column = c

2×2 + 1×1 + 0×1 = 4 + 1 = 5 = c

Linear equations are one-degree equations. So, the two solutions of the equation is (0,-4)(6,0).

It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0. A linear equation has the following standard form: ax + by + c = 0.

Here, variables are x and y and constants a, b, and c are used. Also, a ≠ 0, and b ≠ 0.

We can find the solution of the linear equation by putting x = 0 and y = 0 so that two points form which are the solution of the linear equation,

Put x = 0 in the linear equation 2x - 3y = 12,

2 × (0) - 3y = 12

or, - 3y = 12

or, y = -4

The points is (0,-4)

Put y = 0 in the linear equation 2x - 3y = 12,

2x - 3 × (0) = 12

or, 2x = 12

or, x = 6

The points is (6,0)

Therefore, the two solutions of the equation is (0,-4)(6,0)

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The complete question is as follows:

What is the answer for 2x - 3y = 12?

Answer:

I would say the length  is near 8

Answer:

In the given right angled triangle,

base(b)=2 mm and perpendicular(p)=7mm

hypotenuse (h)=?

By using Pythagoras theorem,

h²=p²+b²

or,h²=(7)²+(2)²

or,h²=49+4

or,h²=53

or,h=√53

or,h=7.28

The length of unknown side is 7.28 mm and it is not determined exactly.

The length 7.28 mm is between integers 7 and 8 and it is more closer to 7.

The integration is as follow

Finding an antiderivative of a function is the process of integration. If a function can be integrated and its integral across the domain is finite with the given bounds, then the integration is definite.

Given:

first, [tex]\int\limits {e^{4x} / 19 - e^{8x}} \, dx[/tex]

= [tex]\int\limits {e^{4x} / 19 - e^{(4x)}^2} \, dx[/tex]

let [tex]e^{4x}[/tex] = z

4[tex]e^{4x}[/tex] dx = dz

= 1/4 [tex]\int\limits {dz / \sqrt{19} ^2 -z^2} \,[/tex]

= 1/4 x 1/2√19 log|(z+ √19)/(z-√19)| + C

= 1/8√19 log|([tex]e^{4x}[/tex] + √19)/ ([tex]e^{4x}[/tex] - √19)| + C

Second,

[tex]\int\limits {33 sec^5 (x)} \, dx[/tex]

= 33 [ 1/4 tan x sec³x + 3/4 ∫sec³x dx]

= 33/4  tan x sec³x + 99/4[ 1/2 tan x sec x +1/2 ∫sec x dx]

=  33/4  tan x sec³x + 99/8 tan x sec x +99/8 log (sec x+ tan x) + C

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The mean and standard deviation of the distribution of R-S is

The mean is calculated by simply substracting the values

= mean R - means S

= 10 - 7

= 3

standard deviation, SD

standard deviation is solved by the use of radicals and this affects the solution hence it will not be simple subtraction, rather we solve back to remove the radical and hence we get the variance

= (SD, R)² + (SD, S)²

= 4² + 3²

= 16 + 9

= 25

the variance is 25

SD = √variance = √25 = 5

complete question

The distribution of random variable R has mean 10 and standard deviation 4. The distribution of random variable S

has mean 7 and standard deviation 3. If Rand S are independent, what are the mean and standard deviation of the

distribution of R-S?

A Mean 3 and standard deviation 1

B Mean 3 and standard deviation 5

C Mean 3 and standard deviation 7

D Mean 17 and standard deviation 1

E Mean 17 and standard deviation 5

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The value of x + y is 5.

What is linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Given linear equations are

2x + 3y = 12  ....(i)

2x - y = 4    ......(ii)

To solve the give linear equation, using elimination method.

Subtract equation (ii) from equation (i)

2x + 3y = 12

2x - y = 4

(-)  (+)   (-)

________

   4y = 8

Divide both sides by 4:

y = 2

Putting y = 2 in equation (ii)

2x - 2 = 4

Add 2 with both sides:

2x = 6

Divide both sides by 2

x = 3

Putting x = 3 and y =2 in x + y:

x + y = 3 + 2 =5

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The previous population of the city was 32,000.

Percentage is a measurement to find value of given number out of hundred.

Given that,

The current population of the city = 20,800.

Let the previous population was 100%.

Since, The population of the city decreased by 35%,

So, the current population of the city = 100 - 35 = 65%

According to given condition,

65 % = 20800

1 % = 20800 / 65

1 % = 320

100% = 320 x 100

         = 32,000

Hence, the initial population was 32,000.

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Answer:

n - 6

Step-by-step explanation:

Number n is A less than B: n = B - A.

Answer:jkd

Step-by-step explanation:

d

The system of equations that can be used to find the roots of the equation 4x 5 12x is:x = -5/8

1. Set up the equation: 4x - 12x = 5

2. Simplify the equation on the left side: -8x = 5

3. Solve for x: x = -5/8

To find the roots of the equation 4x - 12x = 5, we must first set up the equation. On the left side of the equation, we can simplify it to -8x = 5. Then, we can solve for x by dividing both sides by -8, giving us x = -5/8. This is the solution to the system of equations, and the root of the original equation.

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The relationship between a scalene triangle and the location of its centroid is; A: The centroid will always be inside the scalene

triangle, since the centroid is always inside any type of triangle.

A scalene triangle is a triangle in which all three sides have different lengths. Also the angles of a scalene triangle have different measures.

Some right triangles can be a scalene triangle when the other two angles or the legs are not congruent.

Now, a centroid of a triangle is defined as the point formed by the intersection of the medians of the triangle. Now, the medians of a triangle always lie within a triangle. This means that their intersection point which is the centroid of a triangle always lies inside a triangle.

Thus, the centroid of the scalene triangle can be concluded to always lie inside the triangle.

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The expression 3x+4y represents 3 bags of $3 tomatoes and 4 bags of $4 onions.

What is an expression?

The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs constitutes a mathematical expression.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented using mathematical symbols. They can also be used to indicate other characteristics of logical grammar, such as the operation order.

Given that a basket of tomatoes costs $3, whereas an onion package costs $4. A customer buys y sacks of onions and x baskets of tomatoes.

Three bags of $3 tomatoes and four bags of $4 onions are denoted by the equation 3x+4y.

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Independent and dependent variables are interdependent.

Dependent Variable: The term "dependent variable" refers to the variable that is being measured or tested in an experiment.

The results of the participants' tests, for instance, would be the dependent variable in a study looking at how tutoring affects test scores because that is what is being measured.

If you keep in mind that the dependent variable depends on the independent variable, finding it can be simpler.

This isn't the same as an experiment's independent variable, which is a variable that can stand on its own. The dependent variable (test results), however, may alter depending on the independent variable (tutoring).

The unrelated factor

Because the experimenters are allowed to change the independent variable as necessary, it is called a "independent" variable.

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To find the x-intercept of a rational function we put y=0 in the given and find the corresponding value of x.To find the y-intercept of a  rational function we put x=0 in the function and the value of y.

The x-intercept is the point where a line crosses the x-axis.At this point y=0 and the y-intercepts is the point where a line crosses the y-axis.At this point x=0

It is point where the graph of the rational function intersects the x-axis or y-axis.

For Horzontal asymptotes

The horizontal asmptotes of a rational function can be determined by looking at the degree of the numerator and denominator.if Nis the degree of numerator and Dis the degree of denominator.Then N<D

So horizontal asymtote is y=0

To finding horizontal asymptotes we can just focus on degree of numerator and denominator.

For vertical asymptotes

vertical asymptotes occur where the denominator of a rational function approaches zero.A rational function cannot cross a vertical asymptotes because it would be dividing by zero. we set denomintor to zero and solve value of x.The values of x are vertical asymptotes.

Hence we can find easily horizontal and vertical asymptotes of rational function.

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Answer:

True False True False

Step-by-step explanation:

Answer: [tex]0=\frac{2}{3}(x-3)(x-3)[/tex]

Step-by-step explanation:

I think

h(t)=480t–16t^2

Max height is the vertex of the parabola at t = -b/2a

t = -480/-32 = 15 seconds

--> h(15)

Answer:

2. One inch on the photograph represents 1.6 yards of the real bridge.

Step-by-step explanation:

1 yd = 36 in.

8 yd = 36 in./yd × 8 yd = 288 in

1 ft = 12 in.

5/12 ft × 12 in./ft = 5 in.

5 in. in the picture equals 288 inches real.

1 in. in the picture equals 57.6 inches real.

57.6 in. × (1 yd)/(36 in.) = 1.6 yd

1 in. in the picture equals 1.6 yd real

Answer:

2. One inch on the photograph represents 1.6 yards of the real bridge.