Prove that all the solutions to the equation (z+1)7=z7 have equal real parts, and find what this real part is equal to.

There are 5x6=30 one-to-one functions from a set containing 5 elements to a set containing 6 elements.

A one-to-one (or injective) function is a type of mathematical function that maps each element of one set to one, and only one, element of another set. In other words, a one-to-one function is a function that has a unique output for each input. To calculate the number of one-to-one functions from a set containing 5 elements to a set containing 6 elements, we can use the formula f(x)=y, where x is the number of elements in the original set and y is the number of elements in the target set. In this case, x = 5 and y = 6, so f(x) = 6. Since each element in the original set must be mapped to a unique element in the target set, the total number of one-to-one functions is equal to the product of x and y, or 5 x 6 = 30.

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The length of side B'C' is approximately 3.25 units.

To find the length of side B'C' in the dilated triangle, we need to determine the distance between the points B' and C'.

First, let's find the coordinates of B' and C' after the dilation. Since the dilation is about the origin and the scale factor is 1/2, we can multiply the x-coordinates and y-coordinates of B and C by 1/2.

Coordinates of B' = (2.5 * 1/2, 3 * 1/2) = (1.25, 1.5)

Coordinates of C' = (0 * 1/2, -3 * 1/2) = (0, -1.5)

Now we can calculate the distance between B' and C' using the distance formula:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

= sqrt((1.25 - 0)^2 + (1.5 - (-1.5))^2)

= sqrt(1.25^2 + 3^2)

= sqrt(1.5625 + 9)

= sqrt(10.5625)

≈ 3.25

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Answer:

it should be : x²= 15²+8²

x²= 225+64

x²=289

x=√289

x=17

Therefore , the solution of the given problem of function comes out to be  the function is not a simple exponential function. thus, none of the given options are correct.

Integers, their subtypes, and arithmetic are all studied in mathematics, along with the country's anatomy, structures, and both real and hypothetical places. A function describes how various variables, each with its own accurate performance, are related to one another. A function is composed of an array of parts that, when combined, result in a distinct output for each input.

Here,

To write an exponential equation that models the data, we need to find the common ratio between successive terms.

Starting with the second term, we can find the ratio between consecutive terms as:

=> -2 / 26 = -1/13

=> 18 / -2 = -9

=> 12.74 / 18 = 0.707

=> 8.0918 / 12.74 = 0.635

=> 6.2426 / 8.0918 = 0.771

The ratios are not constant, so the function is not a simple exponential function. Therefore, none of the given options are correct.

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The fee charged for the R 2, 500 withdrawal from TownBank would be R 33. 30.

To find the total fee charged to withdraw the sum of R 2, 500 from TownBank, the formula is :

= 3. 30 + R 1, 20 per R 100

The amount withdrawn was R 2, 500 so the total fee charged would be :

= 3. 30 + 1, 20 x ( 2, 500 / 100 )

= 3. 30 + 1. 20 x 25

= 3. 30 + 30

= 33. 30

= R 33. 30

In conclusion, the total fee charged was R 33. 30.

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First part of the question :

The TownBank current account charges R3,30 plus R1,20 per R100 or part thereof for a cash withdrawal from a TownBank ATM. The first five withdrawals in a month are free. Determine the bank charges for a withdrawal of:

Answer:

In explanation.

Step-by-step explanation:

A: (-6, -6)

B: (4, -8)

C: (2, -2)

D: (-3, -1)

Answer:

The answer is "Option A".

Step-by-step explanation:

In this question except for choice "A", all the value is not nearest about the hundred or thousand, that why the correct answer is "1,049".

Answer:39084620

Step-by-step explanation:

New questions in Mathematics

19 ft 4 ft l Find l. l = √ [?] ft

flying against the jet stream, a jet travels 3000 in 3 hours. Flying with the jet stream, the same jet travels 5360 miles in 4 hours. What is the rate…e of the jet in still air and what is the rate of the jet stream?

Please help! Express the area of the region bounded by the x-axis, y = 1/2x - 2, and y equals the cubed root of x, using definite integrals.

Solve the equation 7/4x-2=-5x+1

How to Convert 11010112 to base 10?

Answer the following. (a) A certain solution has a hydrogen ion concentration of 0.00000896 moles per liter. Write this number in scientific notation…. (b) A humpback whale can weigh up to ×1.1105 pounds. Write this number in standard notation.

Evaluate the expression if a=2,b=-3,C=-1, and D=4 -2(b^2-5c)

Evaluate the expression if a=2,b=-3,C=-1, and D=4 -2(b^2-5c)

The set of all triples of real numbers with the standard vector addition but with scalar multiplication defined by k(x, y, z) = (k2 x,k2 y,k2 z)

Evaluate each expression if a=2,b=-3,C=-1, and d=4 5+d(3b-2d)

Required Laplace transform is

\(L{ Cesia 49 ( 3 + 4 \times cos(a) )^3 } \\ = Cesia 49 [ -81/s + (172/3)/(s^2 + 1) + 54/(s^2 + 4) + (128/9)/(s^2 + 9) ]\)

To solve the Laplace transform of the given function, we use the following formula:

\(L{f(t)} = ∫[0,∞) e^{(-st)} f(t) dt\)

where s is the complex frequency parameter.

Using the formula, we have:

\(L{ Cesia 49 ( 3 + 4 \times cos(a) )^3 }\)

\(= ∫[0,∞) e^{(-st)} Cesia 49 ( 3 + 4 \times cos(a) )^3 da\)

\(= Cesia 49 ∫[0,π] e^{(-st)} ( 3 + 4 \times cos(a) )^3 da\) [since cos(a) is an even function]

\(= Cesia 49 ∫[0,π] e^{(-st)} (3^3 + 33^24cos(a) + 334^2cos^2(a) + 4^3*cos^3(a)) da\)

We can simplify the integrand by using the identity,

\(cos^2(a) = (1 + cos(2a))/2 and cos^3(a) = (cos(a) + 2cos(3a))/3\)

which gives:

\(L{ Cesia 49 ( 3 + 4×cos(a) )^3 }\)

\(= Cesia 49 ∫[0,π] e^(-st) [ 3^3 + 33^24cos(a) + 334^2(1 + cos(2a))/2 + 4^3 \times (cos(a) + 2cos(3a))/3 ] da \\ = Cesia 49 ∫[0,π] e^{(-st)} [ 27 + 363cos(a) + 548(1 + cos(2a))/2 + 64 \times (cos(a) + 2cos(3a))/3 ] da \\ = Cesia 49 ∫[0,π] e^{(-st)} [ 27 + 108cos(a) + 216(1 + cos(2a)) + 64 \times (3cos(a) + 2cos(3a))/3 ] da \\ = Cesia 49 ∫[0,π] e^{(-st)} [ 27 + 108cos(a) + 216 + 216cos(2a) + 64cos(a) + 128/3cos(3a) ] da \\ = Cesia 49 ∫[0,π] e^{(-st)} [ 243/3 + (172/3)cos(a) + 216cos(2a) + (128/3) \times cos(3a) ] da \\ = Cesia 49 [ (243/3)/(-s) + (172/3)/(s^2 + 1) + 216/(s^2 + 4) + (128/3)/(s^2 + 9) ] \\ = Cesia 49 [ -81/s + (172/3)/(s^2 + 1) + 54/(s^2 + 4) + (128/9)/(s^2 + 9) ]\)

Therefore, the Laplace transform of the given function is

\(L{ Cesia 49 ( 3 + 4 \times cos(a) )^3 } \\ = Cesia 49 [ -81/s + (172/3)/(s^2 + 1) + 54/(s^2 + 4) + (128/9)/(s^2 + 9) ]\)

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Correct answer is "Solve the Laplace Transforms- for the function Cesia 49 ( 3 +4cosa )³"

The Laplace transform of the given function is (3s + 4) / (s^2 + 1)^3.

To find the Laplace transform of the given function, we apply the properties and formulas of Laplace transforms. The function can be rewritten as (3s + 4) / (s^2 + 1)^3.

The Laplace transform of 3s is 3/S, and the Laplace transform of 4 is 4/S. The Laplace transform of 1 is simply 1/S.

For the term (s^2 + 1)^3, we can use the formula for the Laplace transform of t^n. In this case, n = 3, so the Laplace transform of (s^2 + 1)^3 is 6!/s^6.

Therefore, applying linearity and the Laplace transform properties, the Laplace transform of the given function is (3s + 4) / (s^2 + 1)^3.

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The exact value of tan(105°) is -2 - √3.

Tangent function of an angle in a right angled triangle is defined as the ratio of the opposite side to the adjacent side.

Given that, we have to find the exact value of tan(105°).

We know that,

105° = 60° + 45°

tan(105°) = tan (60° + 45°)

We know,

tan (A + B) = (tan A + tan B) / (1 - tan A tan B)

So,

tan (60° + 45°) = (tan 60 + tan 45) / (1 - tan (60) tan (45))

tan 60 = √3 and tan 45 = 1

tan (60° + 45°) = (√3 + 1) / (1 - √3)

Multiplying both numerator and denominator by (1 - √3),

                        = (√3 + 1)² / (1 - 3)

                        = -(3 + 2√3 + 1) / 2

                        = -(4 + 2√3) / 2

                        = -(2 + √3)

                        = -2 - √3

Hence the value of tan(105°) is -2 - √3.

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Proof of polynomials, multiples, factors, paschal triangles and binomials:

1. Proof of x² - y² = (x - y)(x + y):

Starting with the right-hand side of the equation:

(x - y)(x + y) = x(x) + x(-y) - y(x) - y(y)

= x² - xy - xy + y²

= x² - 2xy + y² + 2xy

= x² - y²

Therefore, (x - y)(x + y) = x² - y², which proves the identity.

2. Proof of x⁴ - y⁴ = (x² + y²)(x + y)(x - y):

Starting with the right-hand side of the equation:

(x² + y²)(x + y)(x - y) = (x² + y²)(x² - y²)

= x⁴ - x²y² + x²y² - y⁴

= x⁴ - y⁴

Therefore, (x² + y²)(x + y)(x - y) = x⁴ - y⁴, which proves the identity.

3. (3x + 9)(3x - 9) = 9x² - 81

4. (-6x² + 7y³)² = 36x⁴ - 84x²y³ + 49y⁶

5. (8x⁴ + 5y³)² = 64x⁸ + 80x⁴y³ + 25y⁶

6. n⁶ - 25m⁴ = (n³ + 5m²)(n³ - 5m²)

7. 16x¹² - 64y⁴ = 16(y²)³ - 64y⁴ = 16y⁴(y² - 4) = 16y⁴(y + 2)(y - 2)

8. b² - 36c⁴ = (b + 6c²)(b - 6c²)

9. 25x⁶ - 100y⁴ = 25(x³)² - 100(y²)² = 25(x³ + 2y²)(x³ - 2y²)

10. 225x⁶ - y¹⁰ = (15x³ + y⁵)(15x³ - y⁵)

11. (x + 0.5)³ = x³ + 1.5x² + 0.75x + 0.125

12. (s + 4t)⁶ = s⁶ + 24s⁵t + 240s⁴t² + 1280s³t³ + 3840s²t⁴ + 6144st⁵ + 4096t⁶

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Answer:

No

Step-by-step explanation:

Parallel lines have equal slopes. Here the slope of first equation is 5 while the slope of the other equation is 0.2 which is not equal so they are not parallel.

The answer should be the SAS postulate

Hope I answered in time!

Finding the matrix associated with Fathey matrix A associated with the linear map F is given by:

\(A

c

where

e1 = (1, 0, 0, 0)

, e2

= (0, 1, 0, 0),

e3 = (0, 0, 1, 0),

e4 = (0, 0, 0, 1).

We have: F(e1)

= (1, 1, 2

)F(e2) = (1, 1, 2)

F(e3) = (1, 0, 2)

F(e4)

= (0, 1, 0)\)

Thus, we have:

\(A =  |   1   1   1   0 | |   1   1   0   1 | |   2   2   2   0 |. 2.\)

Determining the dimension of the kernel of F: The kernel of F is the set of all vectors (x, y, z, w) in R4 such that.

F(x, y, z, w)

= (0, 0, 0).

In other words, the kernel of F is the solution set of the system of linear equations:

x + y + z = 0

x + y + w = 0 2x + 2y

= 0

This system has two free variables (say z and w). Hence, we can write the solution set in the parametric form as:

\(x

= -z-yw

= -yz,\)

y, and w are free variables.

Thus, the kernel of F has dimension 2.

 Answer:

The matrix associated with F is given by

\(|   1   1   1   0 | |   1   1   0   1 | |   2   2   2   0 |2.\)

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Answer:

The ratio is 1/3.

Step-by-step explanation:

Use ratio and proportion

smaller/larger = 3ft/9ft

= 1/3

the ratio of the perimeter of the smaller polygon to the larger polygon is (1)/(3).

The ratio of the perimeter of the smaller polygon to the larger can be found by comparing the corresponding sides of the polygons.

Given:

Length of a side of the smaller polygon = 3 feet

Length of the corresponding side of the larger polygon = 9 feet

To find the ratio of the perimeters, we divide the length of the corresponding sides of the polygons:

Ratio = Length of the corresponding sides of the polygons

In this case, the ratio is:

Ratio = 3 feet / 9 feet

Ratio = 1/3

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Answer:

\(r = \sqrt{ {(6 - 2)}^{2} + {(1 - ( - 3))}^{2} } \)

\(r = \sqrt{ {4}^{2} + {4}^{2} } = \sqrt{16 + 16} = \sqrt{32} \)

So the equation of the circle is

\( {(x - 2)}^{2} + {(y + 3)}^{2} = 32\)

Answer:

Volume of sphere A

= (4/3)π(3^3) = 36π cubic units

Volume of sphere B

= (4/3)π((3/2)^3) = (4/3)π(27/8) = (9/2)π = 4.5π cubic units

The ratio of the volume of sphere A to sphere B is 4.5:36 = 1:8.

Using it's concept, it is found that there is a 0.713 = 71.3% probability that Rachel takes no more than three sweets from the bag.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that:

So:

\(p = \frac{3}{10} + \frac{7}{10} \times \frac{3}{9} + \frac{7}{10} \times \frac{6}{9} \times \frac{3}{8} = 0.713\)

0.713 = 71.3% probability that Rachel takes no more than three sweets from the bag.

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The required arc length of sector VW is 8\(\pi\).

Given that, in a circle U, radius  UV = 9 and  central angle of sector m∠VUW = 160°.

To find the arc length of sector VW, we can use the formula:

Arc length = (central angle / 360) x circumference of the circle.

First,  find the circumference of the circle by the  formula for the circumference of a circle is given by:

Circumference = 2 x \(\pi\) x radius.

Circumference = 2 x \(\pi\) x 9 = 18π.

Now, let's find the arc length of sector VW using the central angle of 160 degrees:

Arc length = (160/360) x 18π

Arc length = (4/9) * 18\(\pi\) = 8\(\pi\).

Therefore, the arc length of sector VW is 8\(\pi\).

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Answer:

a = -3

Step-by-step explanation:

Step 1:  Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:

5^a = 1/125

Step 2:  Take the log of both sides

log(5^a) = log(1/125)

Step 3:  According to the power rule of logs, we can bring a down and multiply it by log(5):

a * log(5) = log (1/125)

Step 4:  Divide both sides by log(5) to solve for a:

(a * log(5) = log(1/125)) / log(5)

a = -3

Optional 5:  We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:

5^-3 = 1/125

1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator

1/125 = 1/125

Answer:

1

Step-by-step explanation:

Just use a calculator like calculatorsoup.com

Answer: b=p/r-z/r

Step-by-step explanation:

make sure the p/r is a fraction and so is z/r. p goes on top r goes on bottom, minus z over r

The equatiοn οf the line οf best fit is ŷ= 0.96x+3.79

The slοpe is 0.96

The y-intercept is 3.79

The heights οf peοple that have arm spans οf 66 inches is 67.15 inches and the heights οf peοple that have arm spans οf 74 inches is 74.83 inches.

When the line tοuches the y-axis, it fοrms a y-intercept. Find the y when x = 0 tο find these. The y-intercept pοint will have the shape οf (0,y) When the line tοuches the x-axis, it fοrms an x-intercept.

We have the fοllοwing cοmputatiοn summary frοm the graphing calculatοr:

Sum οf X = 486

Sum οf Y = 506

Mean X = 44.1818

Mean Y = 46

Sum οf squares (SSX) = 1225.636

Sum οf prοducts (SP) = 1171

Hence, the fοrmula fοr the line οf best fit is ŷ= 0.96x+3.79

A linear regressiοn equatiοn is mentiοned

ŷ=mx+b

Where m is the slοpe, and b is the y-intercept

Sο, the slοpe is 0.96 and the y-intercept is 3.79

The heights οf peοple that have arm spans οf 66 inches and 74 inches

This means that:

x = 66 and x = 74

When x = 66,

y=0.96*66+3.79=67.15

When x = 74,

y=0.96*74+3.79= 74.83

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The expression is equivalent to 2(a  -3) + 4a will be 6a - 6. Then the correct option is A.

The equivalent is the expression that is in different forms but is equal to the same value.

The expression is given below.

⇒ 2(a  -3) + 4a

Simplify the expression, then we have

⇒ 2(a  -3) + 4a

⇒ 2a - 6 + 4a

⇒ 6a - 6

The expression is equivalent to 2(a  -3) + 4a will be 6a - 6. Then the correct option is A.

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The missing options are given below.

A. 6a - 6

B. 6a - 1

C. a - 6

D. None of the above

The first approximation of 537 can be written as a = 536 and b = 1, where the greatest common divisor of a and b is 1.

In number theory, the greatest common divisor (GCD) of two numbers is the largest positive integer that divides both numbers without leaving a remainder. In this case, since a = 536 and b = 1, the GCD of a and b is 1. This means that 536 and 1 have no common factors other than 1.

The first approximation of 537 can be expressed as a product of these two numbers, a and b, where a represents the larger part of the approximation and b represents the smaller part. In this case, a is equal to 536, and b is equal to 1. Since the GCD of a and b is 1, it indicates that 536 and 1 have no common factors other than 1. This approximation may not be the most accurate, but it satisfies the condition of having a GCD of 1.

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A parabola is a figure similar to the following:

In the example given the parabola opens downwards and the vertex acts as a maximum point. We can also have the following:

This parabola opens upwards and the vertex acts as a minimum point.

Now, the range is the values of the y-variable that the function outputs. We notice that in the first case, the range is the values that are smaller than the y-coordinate of the vertex.

In the second case, we notice that the range is the values that are greater than the y-coordinate of the vertex.

Therefore, we can conclude that the range is determined by the vertex, therefore, the right answer would be C.

Answer:

The answer is 9

Step-by-step explanation:

The answer is 9

Answer:

Religion is important because it shapes people’s morals, customs, traditions, beliefs, and, ultimately, behavior. Shared religious beliefs bind people together. References to the story of Noah’s Ark, for example, would be familiar to all members of the Christian religion

Step-by-step explanation: