Kingsley knows that 1 inch is about 2.54 centimeters.He wants to write an equation he can use to convert any given length in inche (I) to centimeters (c)

The value of the exponential equation is A = 5/3

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = [ 2²⁰¹⁴ + 2²⁰¹² ] / [ 2²⁰¹⁴ - 2²⁰¹² ]   be equation (1)

On simplifying the equation , we get

Taking the common factor as 2²⁰¹² , we get

A = 2²⁰¹² [ 2² + 1 ] / 2²⁰¹² [ 2² - 1 ]

On further simplification , we get

A = ( 2² + 1 ) / ( 2² - 1 )

A = ( 4 + 1 ) / ( 4 - 1 )

A = 5/3

Therefore , the value of A is 5/3

Hence , the equation is A = 5/3

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The coordinates of the triangle after the dilation of k = 2 is given by

A' ( 4 , 8 ) , B' ( 6 , 14 ) and C' ( 14 , 8 )

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

Given data ,

Let the triangle be represented as ABC

Now , let the dilated triangle be represented as A'B'C'

And , the coordinates of the triangle ABC are

The coordinate of A = A ( 2 , 4 )

The coordinate of B = B ( 3 , 7 )

The coordinate of C = C ( 7 , 4 )

And , the dilation factor k = 2

So , the new coordinates of the dilated triangle are

The coordinate of A' = A' ( 4 , 8 )

The coordinate of B' = B' ( 6 , 14 )

The coordinate of C' = C' ( 14 , 8 )

Hence , the triangle is dilated by a scale factor of 2

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Answer: The likelihood of randomly selecting a gold coin from the box is "Likely."

When the probability of an event is 50%, it means that there is an equal chance of the event happening or not happening. In this case, the probability of randomly selecting a gold coin from the box is 50%, so it is likely to occur.

Step-by-step explanation:

Answer:

efgdfhncdrt gguhd r g sixtieth sex

Answer: y = mx+b

              y = -1x+1/4

Step-by-step explanation:

Answer: 189

Step-by-step explanation:

for every 45 minnow there will be 27

315 minnow is 7 times 45 minnow 27*7 is 189

The quotient of the division is 3x - 11 with a remainder of 37x + 21

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

Divide 3x³ - 2x² + 4x - 3 by x² + 3x + 3.

Using the long division method of quotient, we have

x² + 3x + 3 | 3x³ - 2x² + 4x - 3

The division steps are as follows

                    3x - 11

x² + 3x + 3 | 3x³ - 2x² + 4x - 3

                    3x³ + 9x² + 9

------------------------------------------------

                               -11x² + 4x - 12

                               -11x² - 33x - 33

------------------------------------------------

                                           37x + 21

Hence, the quotient is 3x - 11

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The median of all possible values of x is 5.

A triangle is a three-sided polygon that consists of three edges and three vertices.

To find the median of all possible values of x, we need to find all the possible values of x first.

By the triangle inequality, we know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, we can write:

2 + 5 > x

2 + x > 5

5 + x > 2

Simplifying each inequality, we get:

7 > x

x > 3

x > -3

The smallest possible integer value for x is 4 and the largest possible integer value for x is 6.

Therefore, the possible integer values for x are 4, 5, and 6.

Since we have an odd number of values, the median is simply the middle value, which is 5.

Therefore, the median of all possible values of x is 5.

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The equation most closely approximates C is C(x) = 22p+ 18.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that function, C calculates the number of calories recommended per day for a dog based on the dog's weight in pounds.

The equation can be written as:-

C(x) = 22p+ 18.

Here the dependent variable is C(x) and the dependent variable is p. So the value of C(x) will always depend upon the variable p.

Therefore, the correct equation will be C(x) = 22p+ 18.

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Step-by-step explanation:

n=5+3p

when p=26,

n=5+3×26=83

The probability of rolling a 5 and then 6 is 1/36

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

Number cube rolled twice

The sample space of each number cube is

Sample space = {1. 2. 3. 4. 5. 6}

From the above entries, we have

P(5) =1/6

P(6) = 1/6

Using the above as a guide, we have the following:

P = 1/6 * 1/6

Evaluate

P = 1/36

Hence, the probability is 1/36

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Answer:

x > 6

Step-by-step explanation:

4(3x+2) < 5(3x-2)

12x+8 < 15x-10

12x-15x < -10-8

-3x < -18

3x > 18

x> 6

An octant's main features are :

An octant is formed by three perpendicular axes, labeled X, Y, and Z. These axes intersect at a common point called the origin. Each octant contains both positive and negative values along the X, Y, and Z axes. The positive region is located on one side of each axis, while the negative region is on the other side.

Each of the three axes divides an octant into two quadrants. These quadrants are numbered from 1 to 8, with quadrant 1 being in the positive X, Y, and Z regions and quadrant 8 being in the negative X, Y, and Z regions.

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Answer: The original price of the lawn mower was $649

Step-by-step explanation:

If Joaquin bought the lawn mower for $519.20 after a 20% discount, it means that he paid only 80% of the original price. We can use this information to calculate the original price of the mower by setting up the following equation:

0.8x = 519.20

where x is the original price of the lawn mower. To solve for x, we can divide both sides of the equation by 0.8:

x = 519.20 / 0.8

x = $649

The formula for Van 't Hoff's law, which is also known as the law of osmotic pressure, is: П = iMRT, where: Π is the osmotic pressure of the solution,

i is the van 't Hoff factor, which is a measure of the number of particles a solute molecule dissociates into in solution, M is the molar concentration of the solute, R is the gas constant, and T is the absolute temperature. Van 't Hoff is a term used to refer to a Dutch chemist named Jacobus Henricus van 't Hoff, who was known for his work on solutions, chemical equilibrium, and the laws of thermodynamics. To find Van 't Hoff, you can do any of the following: Research: You can learn about Van 't Hoff by doing research on his life and work. There are many online and offline resources available that provide information about his contributions to chemistry and his scientific achievements. Education: If you are a student of chemistry, you are likely to encounter Van 't Hoff's name in your coursework. You can learn about his theories and concepts in your chemistry classes or by consulting your textbooks. Application: You can apply Van 't Hoff's laws and principles in solving problems related to chemical equilibrium, colligative properties of solutions, and other thermodynamic concepts. This may involve using mathematical formulas and equations that are based on his work. In summary, Van 't Hoff refers to a Dutch chemist known for his work in thermodynamics, solutions, and chemical equilibrium. You can learn about his contributions to chemistry through research, education, and application of his principles in problem-solving.

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Leo needs to pay back a total of $215 in two weeks.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Leo takes out a payday loan for $200 to cover some of his rent and will pay it back when he gets his paycheck and the lender charges $15 for every $100.

Now, (15/100)×100% = 15%.

Therefore, He has to pay back,

[(100 + 15)/100]×200.

= (115/100)×200.

= 1.15×200.

= $230.

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The requried difference between the perimeters of the two gardens would be, 12x + 20 - 4s.

Perimeter is the measure of the figure on its circumference.

Here,
Let's assume that Shawn's garden is also a square with side lengths. Therefore, the perimeter of Shawn's garden would be 4s.
The perimeter of Charlie's garden would be 4(3x + 5), which simplifies to 12x + 20.

The difference between the perimeters of the two gardens would be,

12x + 20 - 4s

We can't simplify this expression any further without knowing the value of s.

Therefore, we can conclude that the difference between the perimeters of the two gardens depends on the side length of Shawn's garden.

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The value of x the given parallelogram a rhombus is 18

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

The quadrilateral that is a rhombus

The diagonals of rhombus bisect each other

Using the above as a guide, we have the following:

Angle 1 = A

Substitute the known values in the above equation, so, we have the following representation

5x - 30 = 3x + 6

Evaluate

2x = 36

Divide

x = 18

Hence, the value is 18

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Answer:





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Class 11

>>Applied Mathematics

>>Number theory

>>Complex Numbers

>>The complex number z satisfying the equa

Question



The complex number z satisfying the equations ∣z∣−4=∣z−i∣−∣z+5i∣=0, is

This question has multiple correct options

A

3−i

B

23−2i

C

−23−2i

D

0

Medium

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Updated on : 2022-09-05

Solution



Verified by Toppr

Correct options are B) and C)

We have two equation ∣z∣−4=0 and ∣z−i∣−∣z+5i∣=0

Putting z=x+iy i.e x2+y2=16    ....(1)

and ∣x+iy−i∣=∣x+iy+5i∣

⇒x2+(y−1)2=x2+(y+5)2

⇒y=−2   ...(2)

Putting y=−2 in (1), 

x2+4=16⇒x=±2

Step-by-step explanation:

Hence the complex numbers z satisfying the given equation are 

z1=23−2i and z2=−23−2i

Answer: look at the image for the answers and solutions

Step-by-step explanation:

The equations of the lines in slope-intercept form are:

22. y = -1/2x + 3.

23. y = 2x - 3.

24. y = -x

25. y = -2x + 4.

26. y = 3/2x - 2.

27. y = 5/2x - 1/2

28. y = x + 3

29. y = -x + 2

30. y = -1/4x + 9/4

The equation of a line is y = mx + b, in slope-intercept form, where:

m = slope = rise/run = change in y / change in x

b = y-intercept or the point where the graph intercepts the y-axis.

22. Slope (m) = rise/run = -1/2

y-intercept (b) = 3

Substitute m = -1/2 and b = 3 into the equation, y = mx + b:

y = -1/2x + 3.

23. Slope (m) = rise/run = 4/2 = 2

y-intercept (b) = -3

Substitute m = 2 and b = -3 into the equation, y = mx + b:

y = 2x - 3.

24. Slope (m) = rise/run = -2/2 = -1

y-intercept (b) = 0

Substitute m = -1 and b = 0 into the equation, y = mx + b:

y = -x + 0

y = -x

25. Slope (m) = rise/run = -2/1 = -2

y-intercept (b) = 4

Substitute m = -2 and b = 4 into the equation, y = mx + b:

y = -2x + 4.

26. Slope (m) = rise/run = 3/2

y-intercept (b) = -2

Substitute m = 3/2 and b = -2 into the equation, y = mx + b:

y = 3/2x - 2.

27. Slope (m) = rise/run = 5/2

y-intercept (b) = -0.5 = -1/2

Substitute m = 5/2 and b = -1/2 into the equation, y = mx + b:

y = 5/2x - 1/2

28. Slope (m) = change in y / change in x = (5 - 3) / (2 - 0) = 2/2 = 1

y-intercept (b) = 3

Equation is, y = x + 3

29. Slope (m) = change in y / change in x = (-1 - 4) / (3 -(-2)) = -5/5 = -1

Substitute (x, y) = (3, -1) and m = -1 into y = mx + b, to find b:

-1 = -1(3) + b

-1 = -3 + b

-1 + 3 = b

2 = b

b = 2

The equation would be: y = -x + 2

30. Slope (m) = change in y / change in x = (3 - 2) / (-3 - 1) = 1/-4 = -1/4

Substitute (x, y) = (1, 2) and m = -1/4 into y = mx + b, to find b:

2 = -1/4(1) + b

2 = -1/4 + b

b = 2 + 1/4

b = 9/4

The equation would be: y = -1/4x + 9/4

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The inverse function is  v⁻¹ = ( v/T)^1/3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that the formula of the volume of the sphere is,

⇒ v = 4/3 πr³

T = 4/3π

Now,

To determine the inverse function we can solve the formula for the term r as;

⇒ v = 4/3 πr³

Multiply by 3/4 we get;

⇒ 3v/4 = πr³

Divide by π both side, we get;

⇒ 3v/4π = r³

Substitute r = v⁻¹ in above equation, we get;

⇒  v⁻¹ = ( v/T)^1/3

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Using division, we know that Leo replaces 6 new strings from 3 guitars which are a total of 18 strings.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.

The other operations are multiplication, addition, and subtraction.

On a fundamental level, counting the instances in which one number is included within another is one interpretation of the division of two natural numbers.

When no more full chunks of the size of the second number can be allocated during the computation of the quotient, the division with a remainder or Euclidean division of two natural numbers yields an integer quotient, which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that remains.

So, we know that:

6 new strings are put on each guitar.

He uses 18 strings.

Then, the number of guitars:

⇒ 18/6 = 3

Therefore, using division, we know that Leo replaces 6 new strings from 3 guitars which are a total of 18 strings.

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Answer: Rational functions are defined as the ratio of two polynomials. A rational function has the most solutions in common with the function y = 2x + 6 if their graphs intersect at the most points.

If a rational function has the same degree as the polynomial function y = 2x + 6, which is degree 1, and has a leading coefficient that is the same sign as the leading coefficient of y = 2x + 6, then their graphs will intersect at the most points.

One such rational function that has the same degree as y = 2x + 6 and has a leading coefficient that is the same sign is:

y = (2x + 6) / 1

So the rational function y = (2x + 6) / 1 has the most solutions in common with the function y = 2x + 6.

Step-by-step explanation:

Answer:

32.4

Step-by-step explanation:

8% of 30 is 2.4. So, 2.4 + 30 is 32.4.

Answer:

125 children play tennis and golf

don't forget to follow me ,

The prime factorization of 51 is 3 * 17.

Answer:

$5155

Step-by-step explanation:

We know

A car salesman earns 5% on the sale of a BMW sold for $103,100.

5% = 0.05

What is his take-home pay that day?

We take

103,100 times 0.05 = $5155

SO he takes home $5155.

Step-by-step explanation:

Looks like we're trying to find out what 5% of 103,100 is. We first need to convert the percent into a decimal and then multiply.

[tex]5\% = 0.05[/tex]

Now we can multiply

[tex](0.05)(103100) = 5155[/tex]

P-value of a hypothesis test is an important measure of the strength of evidence against the null hypothesis and helps us make informed decisions about rejecting or failing to reject the null hypothesis.

A hypothesis test is a statistical method used to test the validity of an assumption or a hypothesis about a population based on a sample data.

The correct answer is b. The P-value of a hypothesis test is the probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true.

In hypothesis testing, we start with a null hypothesis, which is usually denoted as H_0, that represents the status quo or the default assumption. The alternative hypothesis, denoted as H_a, represents the opposite of the null hypothesis.

The P-value is the probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true. A low P-value indicates that the sample data provides strong evidence against the null hypothesis, and we reject the null hypothesis.

A high P-value indicates that the sample data does not provide strong evidence against the null hypothesis, and we fail to reject the null hypothesis.

In mathematical terms, the P-value is calculated as the probability of observing a test statistic Z that is more extreme than the one actually obtained, assuming the null hypothesis is true.

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