PLEASE HELP!!! Simplify (x − 1)(x2 + 5x + 2). (5 points)

We have proved that the Newton-Raphson iteration formula for solving the equation\(x^k e^x = 0\) is given by \(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.\)

To prove that the Newton-Raphson method for solving the equation \(x^k e^x = 0\), where k is a constant, is given by the formula

\(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n,\)

we can start by considering the iterative process of the Newton-Raphson method.

Given an initial guess \(x_n\), we want to find a better approximation \(x_{n+1}\)that is closer to the root of the equation \(x^k e^x = 0.\)

The Newton-Raphson method involves the following steps:

Calculate the function value \(f(x_n) = x_n^k e^x_n\) and its derivative \(f'(x_n) = k x_n^(k-1) e^x_n.\)

Find the next approximation x_{n+1} by using the formula:

\(x_{n+1} = x_n - f(x_n) / f'(x_n)\)

Let's apply these steps to our equation \(x^k e^x = 0\):

Calculate the function value and its derivative:

\(f(x_n) = x_n^k e^x_n\\f'(x_n) = k x_n^(k-1) e^x_n\)

Find the next approximation x_{n+1} using the formula:

\(x_{n+1} = x_n - f(x_n) / f'(x_n)\)

Substituting the function value and its derivative:

\(x_{n+1} = x_n - (x_n^k e^x_n) / (k x_n^(k-1) e^x_n)\\= x_n - (x_n^k / k)\)

Simplifying the expression by combining like terms:

\(x_{n+1} = x_n - (x_n^k / k)\\= x_n - x_n^k / k\\= (k - 1) x_n + x_n^2 / k + x_n\)

Therefore, we have proved that the Newton-Raphson iteration formula for solving the equation\(x^k e^x = 0\) is given by \(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.\)

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Answer:

x = 10.47

Step-by-step explanation:

circumference = 2 * 10 * π = 20π

centre angle of a circle (in radiant) = 2π

x : 20π = π/3 : 2π

x = (20π * π/3)/ 2π

x = 10 * π/3

x = 10π/3

x = 10.466667

x = 10.47

Answer:

Mean = 53.

Step-by-step explanation:

The median is the middle value so the 3 cards are

36, 46, x       where x is to be found.

The range is 41, so:

x - 36 = 41

x = 41 + 36

x = 77.

Therefore, the mean is

(36+46+77) / 3

= 159/3

= 53.

a) The definition of the composite function is: \((f \circ g)(x) = \frac{6}{12 + 2x}\)

b) The domain of the composite function is: (-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

The composite function of f(x) and g(x) is given by the function rule presented as follows:

(f ∘ g)(x) = f(g(x)).

For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).

The functions for this problem are given as follows:

Hence the composite function is obtained as follows:

\((f \circ g)(x) = f(\left\frac{6}{x}\right)\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{6}{x} + 2}\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{12 + 2x}{x}}\)

\((f \circ g)(x) = \frac{6}{12 + 2x}\)

The domain is all real values except x = 0, x = -2 and x = -6, as f(x) is not defined at x = -2 and g(x) is not defined at x = 0 and the composite function is not defined at x = -6, hence the interval notation is:

(-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

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Answer:

D

Step-by-step explanation:

Ed2021

The series 6+2+6/9+6/27 is a required converging geometric series. Option D is correct.

Which geometric series converges is determined from the options below

a. 1/6+1/6+1/6+1/6    b. 1/6+2/6+4/6+8/6   c. 6+12+24+48  d. 6+2+6/9+6/27.

Geometric progression is a sequence of series whose ratio with adjacent values remains the same.

Options A B and C have been omitted because the series given in the corresponding option has the increasing order. Option D has a decreasing order with the common ratio between the preceeding values of the series being 1/3. Thus option D is the correct option.

Thus, the series 6+2+6/9+6/27 is a required converging geometric series. Option D is correct.

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If the cost for maaking 3 cups of lemonade is $0.30, then the cost per lemonade is

The cost per lemonade is $0.10

The equation is that represent exponential decay is:

The rate in the equation of an exponential decay is negative, this would make it reduce expentially, rather than grow.

The best equation that demonstrate this is:

Where the rate is 0.35

Answer:

.6 or 3/5

Step-by-step explanation:

Answer:

3/5

Step-by-step explanation:

1/5 times 3 is the same thing as 1/5 times 3/1.

To multiply, you have to multiply 1 times 3 = 3

and 5 times 1 which = 1.

your answer is 3/5

Answer:

50x50=1000000

Step-by-step explanation:

Answer:

Step-by-step explanation:

\( {x}^{2} + 6x - 14 = 0\)

Roots :- 6 and -14

Sum of the roots :

[6 + (-14)]

= (-8)//

Product of the roots :

[(6)(-14)]

= (-84)//

Answer: It’s A

Step-by-step explanation:

On the interval (3π/2, 2π), both the sine and cosine functions are increasing.

The values of sine and cosine functions at (0, π/2, π, 3π/2, 2π) are as follows:

sin (0) = 0;          cos (0) = 1

sin (π/2) = 1;        cos (π/2) = 0;

sin (π) = 0;          cos (π) = - 1

sin (3π/2) = - 1;   cos (3π/2) = 0

sin (2π) = 0;       cos (2π) = 1

Therefore, it is clear from the above values of sine and cosine that on the interval (3π/2, 2π), both the sine and cosine functions are increasing.

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use a factor tree to get 2x2x5

2²x5

\(\huge\underline{\boxed{\bold{Hello\;there!}}}\)

20 as a product of primes:

2×2×5

Remember, primes have only two factors.

2 is only divisible  by 1 and itself, and it's the only even prime number.

5 is also divisible by 1 and itself.

If we multiply 2 times 2 times 5, we will get 20.

\(\huge\boxed{\mathfrak{Answer:{\boxed{\boxed{2*2*5}}}}}\)

\(\bigstar\) I really hope it helps you!

\(\bold{Have\;a\;wonderful\;day!}\)

\(\rm{FabulousKingdom :-)\)

There is a Weak positive association between the amount of goals scored and the number of wins a hockey team has. Most of the data points fall between 4 goals scored and 5  number of wins. Causation cannot be established because their relationship was not in a controlled setting.

When if a relationship between two variables is said to be  negative, it is one that does not just necessarily mean that the association is weak. Although though both variables tend to increase in reaction to one another, a weak positive correlation depicts that the relationship is not very strong.

Therefore, even though  the data tells us that there is a weak positive relationship that exist between the two variables, it is vital to know that that correlation does not equal causation.

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Answer:

a)

b) 1/3

c) 1/2

d) 1/2

e) 0

Step-by-step explanation:

a) There are 2 different types of dessert and 3 different ice cream flavors.      

   Therefore, there are 6 possible ice cream orders:

b) There are 2 different desserts with apricot ice cream.

⇒ P(apricot ice cream) = 2/6 = 1/3

c) There are 3 combinations of sundae.

⇒ P(sundae) = 3/6 = 1/2

d) P(chocolate) = 2/6 = 1/3

   P(blackberry waffle cone) = 1/6

⇒ P(choc) OR P(BWC) = 1/3 + 1/6 = 1/2

e) P(orange sherbet) = 0

as orange sherbet was not an option!

Answer:

I'll do the first one as an example. The answer of the first one is 6.

Step-by-step explanation:

In the first example, they multiplied the number by 2 to get a common denominator for the two fractions so you can easily add. So, the first box will come 10 (5 times 2) and the second box will become 2 (1 times 2). Then simply add the fractions. The sum of the first question is 2. Because 2 10/12 + 3 2/12 = 6. Remember to add only the whole numbers and fractions. If you want, you can try using mathaway for additional help.

Hope this helps a little more.

Answer: 324

Step-by-step explanation: Firstly,  multiply 9x12. And that is 108. Since in the problem it says "Three times the sum" you would multiply 108 by three and get 324.

Answer:

200

Step-by-step explanation:

\(a^{2}\) + \(b^{2}\) = \(c^{2}\)

\(120^{2}\) + \(160^{2}\) = \(c^{2}\)

14400 + 25600 = \(c^{2}\)

40000 = \(c^{2}\)

\(\sqrt{40000}\) = \(\sqrt{c^{2} }\)

200 = c

Jesus love you.

Answer:

yes for each input there is exactly one output.

Step-by-step explanation:

phone pictures is given by y equals 0.25 x where X is the number of 32 y equals 3x + 2y

The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

Answer:

Step-by-step explanation:

Let \((a,b)\in \mathbb{R}^{2}\), a reflection over the x-axis consists in the following operation:

\((a,b) \rightarrow (a,-b)\)

If we know that \(X = (-4,3)\) and \(Y = (2, 3)\), then the points translated over the x-axis are \(X' = (-4, -3)\) and \(Y' = (2,-3)\), respectively. The most precise description of the shape is a rectangle for the following facts:

1) \(XX' = YY' = 8\) and \(XY = X'Y' = 6\).

2) \(X\) and \(X'\) have the same x-component.

3) \(Y\) and \(Y'\) have the same x-component.

4) \(X\) and \(Y\) have the same y-component.

5) \(X'\) and \(Y'\) have the same y-component.

A representation of the shape is included below as attachment.

Answer:

I have no idea what the other person said, but the answer is square if you want a simple answer.

Nice job on getting the correct answer 144 for the first box. For anyone curious, this is found by multiplying the side lengths of the square. So 12*12 = 144.

======================================

All four sides are decreased by 5 meters. So we go from 12 meter sides to 12-5 = 7 meter sides.

The area of the square is found in the same way as earlier: We multiply the side by itself

area = side*side = 7*7 = 49 square meters

So you'll type 49 into the second box

=======================================

To find the amount of decrease, you subtract the two area values:

144 - 49 = 95 goes in the third box

This indicates that the area has decreased by 95 m^2

Answer:

5.81%

Step-by-step explanation:

Answer:

\(m=\frac{2k}{v^{2} }\)

Step-by-step explanation:

Answer:

2sqr3, the first option

Step-by-step explanation:

Answer:

7/3 then 7/8

Step-by-step explanation:

I got it right on edge 2020