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The complex number in rectangular form is z = √2 - i√2

The rectangular form of of a complex number is given by z = a + ib where

where

Given the complex number

z = 2[cos(- π/4) + isin(- π/4)] , we desire to find the rectangular form of the complex number. We proceed as follows.

z = 2[cos(- π/4) + isin(- π/4)]

z = 2cos(- π/4) + i2sin(- π/4)]

z = 2cos(π/4) - i2sin(-π/4)]

Since cos(π/4) = sin(π/4) = 1/√2, we have that

z = 2cos(π/4) - i2sin(-π/4)]

z = 2 × 1/√2 - i2 × 1/√2

z = 2/√2 - i2/√2

Rationalizing the denominators, we have that

z = 2/√2 × √2/√2 - i2/√2 × √2/√2

z = 2√2/2 - i2√2/√2

z = √2 - i√2

So, we have the number in rectangular form as z = √2 - i√2

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A scale drawing is a representation of an object or space that is reduced or enlarged in proportion to the actual object or space. In this case, the scale of the drawing is 1 unit = 1 foot. To find the dimensions of the scale drawing, we need to divide the actual dimensions of the room by the scale of the drawing.

The actual dimensions of the floor are 450 feet by 20 feet.

So, the dimensions of the scale drawing are:

450 feet / 1 unit = 450 units (length)

20 feet / 1 unit = 20 units (width)

Therefore, the dimensions of the scale drawing are 450 units by 20 units. So, the scale drawing is 450 by 20.

The slope intercept equation of the line that is perpendicular to 4x+2y+18=0 and has a y-intercept of the line 3x-y+8=0 is x-2y+16=0.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

4x+2y+18=0

y=-2x-9

m=-2

m1=1/2

3x-y+8=0

y=3x+8

y-intercept=(0,8)

y=mx+c

y=1/2x+8

2y=x+16

x-2y+16=0

The equation of the line, in slope intercept form, that is perpendicular to 4x+2y+18=0 and has a y-intercept of the line 3x-y+8=0 is x-2y+16=0.

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The graph does not represent a function, because is is possible to draw a vertical line that intersects the graph more than once.

An infinite number of nodes or vertices and the connecting edges make up a graph, which is a type of non-linear data structure. When dealing with real-world issues, graphs in data structures are used because they model the issue as a network, similar to social networks, telephone networks, and circuit networks.

In a telephone network, for instance, it might depict a single user as nodes or vertices, with the telephone line connecting them as edges.

The non-linear type of data structure known as a graph is composed of nodes, also known as vertices and edges. In a graph, the nodes, which are also referred to as vertices, are connected by edges.

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N'O' is a transformation of NO. The measurement of  N'O' is 30.

What is a line segment?

A line segment is a section of a straight line that is bounded by two distinct end points and contains every point on the line between them. The Euclidean distance between the endpoints of a line segment determines its length.

A scale factor is defined as the ratio of the scale of a given original object to the scale of a new object that is its representation but of a different size (bigger or smaller). For example, we can enlarge a rectangle with sides of 2 cm and 4 cm by multiplying each side by a number, say 2.

Given that NO is dilated by a scale factor of 3/4 to form N'O'.

The length of NO is 40.

To find the length of N'O', multiply the scale factor by the length of NO.

Thus the length of N'O is 3/4 ×40 =30

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N'O' is a transformation of NO. The measurement of  N'O' is 30.

What is a line segment?

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Explore all similar answers

Answer:

2× radius of the circle

Step-by-step explanation:

The line segment joining two points on the circle and passing through the centre is the diameter.

Answer:

ttgshffs is the first thing that I want you to you sis and you can tell you what you can tell you what is going to be done in your life and I hope that your time ⌚ will not a better world of us for your birthday Babu we will win the temple Changu and I hope that

The square roots of 144 are:

A. 24

D.144 ^1/2

F.12

144 is a perfect square, so the square root of 144 is a positive and negative value of 12, 24 and 144^1/2.

Option B 6 and C -12 are not square roots of 144 because 6^2 = 36 and -12^2 = 144 .

Option E -144^1/2 is not a real number, because the square root of a non-negative number is always non-negative.

Answer:

1) Quadrilateral ABCD is translated 5 units and 4 units down, then reflected in the y-axis. This will result in congruent figures. Translation only moves the figure without changing the size or shape, and reflection in the y-axis will mirror the figure across the y-axis without altering its size or shape. Since both operations preserve the size and shape of the figure, the resulting figure will be congruent to the original.

2) ΔJKL is dilated by a scale factor of 2 and then rotated 180° about the origin. This will result in congruent figures. Dilation by a scale factor of 2 will double the size of the triangle while maintaining its shape, and rotation by 180° about the origin will flip the triangle over the origin while maintaining its shape. Since both operations preserve the size and shape of the figure, the resulting figure will be congruent to the original.

3) Line segment XY is rotated 90° about the origin, dilated by a scale factor of -1/2, and then reflected in the line x = 5. This will result in similar figures. Rotation by 90° about the origin will rotate the line segment by 90 degrees, dilated by a scale factor of -1/2 will shrink the size by half but with a change in direction and reflection in the line x = 5 will mirror the figure across the x=5 line without altering its size or shape. Since all the operations maintain the shape of the figure but the size changes, the resulting figure will be similar to the original one.

Translation and reflection doesn't change the shape or size of the figure, therefore the resulting figure is congruent to the initial one.

Rotation doesn't change the shape of the figure, but dilation changes the size, therefore the resulting figure is similar to the initial one.

Rotation and reflection don't change, but dilation changes the size, therefore the resulting segment is similar to the initial one.

Given:

Graph them and transform as described.

1. A(1, 2), B(1, 5), C(5, 5)

Reflection: in the x-axis

2. A(4, -3), B(-1, -1), C(1,3)

Reflection: in the y-axis

3. A(2, 1), B(2, -3), C(4, -2)

Reflection: in the line y = 1

See attached for each. It should be self-explanatory.

Answer:

Question 1:

Question 2:

Question 3:

Step-by-step explanation:

Given vertices of the pre-image:

If the pre-image is reflected in the x-axis, the transformation rule is:

Therefore the vertices of the image are:

Given vertices of the pre-image:

If the pre-image is reflected in the y-axis, the transformation rule is:

Therefore the vertices of the image are:

Given vertices of the pre-image:

If the pre-image is reflected in the line y = 1, the transformation rule is:

Therefore the vertices of the image are:

Answer:

Step-by-step explanation:

?

|z|^2 = |z|*|z| = (|z|)^2

Since the argument of z is pi/4, z can be written as z=r*(cos(pi/4)+i*sin(pi/4)) where r is the magnitude of z.

We also know that |x-w| =sqrt(5).

This means that |z-w| = sqrt(5).

Substituting the expression for z, we get:

|r*(cos(pi/4)+i*sin(pi/4))-w| = sqrt(5)

Simplifying this equation, we get:

|r-2-i| = sqrt(5)

Squaring both sides, we get:

(r-2-i)(r-2+i) = 5

Simplifying, we get:

r^2-4+i(2r-2)=5

Equating the real and the imaginary parts, we get:

r^2-4 = 5

and

2r-2=0

Solving these equations simultaneously, we get:

r = sqrt(9)

Therefore,

|z| = sqrt(9)

Hence,

|z|^2 = (sqrt(9))^2 = 9

The equation of the line that passes through the points ( − 1 , − 5 ) and (1, 3) is y = 4x - 1

The slope, m of the linear function is calculated using the points on the graph (-1, -5) and  (1, 3)

m = (y₀ - y₁) / (x₀ - x₁)

m = (-5 - 3) / (-1 - 1)

m = (-8) / (-2)

m = 4

equation passing through point (1, 3)

(y - y₁) = m (x - x₁)

plugging in the points

y - 3 = 4 * (x - 1)

y - 3 = 4x - 4

y = 4x - 4 + 3

y = 4x - 1

The equation of the line passing through points  (-1, -5) and  (1, 3) is written as y = 4x - 1

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The division of the given polynomial would be (x^4) + 81.

What is the synthetic division?

Synthetic division is a method for dividing polynomials that allows you to divide a polynomial by a linear factor (a factor in the form of (x-c) where c is a constant) without actually performing the long division process. It is a short cut method that simplifies the process of dividing polynomials.

To divide the polynomials using synthetic division, we will use the following steps:

Write the polynomials in descending order of exponents. In this case, the given polynomials are already in descending order:

(x^4+ 81) / (x + 3)

Create a grid with the dividend on the left and the divisor on the right.

x^4 81

x 3

Bring down the leading coefficient of the dividend, which is x^4 in this case. Write it in the next row of the grid.

x^4 81

x^4 x 3

Multiply the divisor (x + 3) by the leading coefficient (x^4) and write the result in the next row.

x^4 81

x^4 x 3

x^5 x^5 3x^4

Subtract the second row from the third row and write the result in the next row.

x^4 81

x^4 x 3

x^5 x^5 3x^4

0 81-3x^4

Bring down the next coefficient of the dividend (81) and write it in the next row of the grid.

x^4 81

x^4 x 3

x^5 x^5 3x^4

0 81-3x^4

81

Now we repeat the steps 4-6 for the rest of the coefficients of the dividend, but there is no more coefficients in this example.

The quotient is x^4 and the remainder is 81

So the final answer is:

(x^4)+(81)

Hence, the division of the given polynomial would be (x^4) + 81.

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Answer:

the police tactic of charging a crowd with lathis or batons in order to disperse it

The equation of a circle in general form is (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is the radius.

To put the equation of circle in standard form x2+y2−4x+5y−3=0 you need to complete the square and

bring the equation to the form (x-a)^2 + (y-b)^2 = r^2

so the center of the circle is (-2,2) and the radius is 3

Answer:

To the nearest dollar, Savannah would have $8,007 more in her account than Lincoln.

Step-by-step explanation:

To find out how much more money Savannah would have in her account than Lincoln after 20 years, we need to calculate the future value of both investments using the appropriate interest rate and compounding period.

For Lincoln's investment:

Future value = $6,500 * (1 + (3^3/4/100) / 4)^(4*20) = $6,500 * (1 + 0.046875)^80 = $6,500 * 2.611 = $16,917.50

For Savannah's investment:

Future value = $6,500 * e^(0.041875*20) = $6,500 * 3.843 = $24,924.50

To find the difference between the two investments, we can subtract Lincoln's future value from Savannah's:

$24,924.50 - $16,917.50 = $8,007

To the nearest dollar, Savannah would have $8,007 more in her account than Lincoln.

[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_{3}(y+5)+\log_3(6)~~ = ~~\log_3(66) \\\\[-0.35em] ~\dotfill\\\\ \log_3[(y+5)\cdot 6]=\log_3(66)\implies (y+5)6=66 \\\\\\ y+5=\cfrac{66}{6}\implies y+5=11\implies \boxed{y=6}[/tex]

Answer: Tina has read 16 pages and reads 22 pages per day until the book is finished.

Zuri has read 24 pages and reads 18 pages per day until the book is finished.

We can use this information to set up an equation to represent the number of pages read by each student over a certain number of days.

Let's call the page number they are on when they read the same amount of the book "p"

We can set up the equation as follows:

16 + 22d = 24 + 18d = p

Now we can solve for p by combining like terms:

16 + 22d = 24 + 18d

4d = 8

d = 2

Now we know that it takes 2 days for Tina and Zuri to read the same amount of the book.

Now we can use this value of d to find out what page they are on when they read the same amount of the book.

p = 16 + 22*2 = 16 + 44 = 60

So Tina and Zuri are on page 60 when they have read the same amount of the book.

Step-by-step explanation:

Answers:

(a)    $1092.03

(b)    $1093.08

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

Work shown for part (a)

A = P*(1+r/n)^(n*t)

A = 1000*(1+0.09/2)^(2*1)

A = 1000*(1+0.045)^(2)

A = 1000*(1.045)^(2)

A = 1000*1.092025

A = 1092.025

A = 1092.03

Don't forget to round to the nearest penny, aka nearest hundredth.

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

Work shown for part (b)

A = P*(1+r/n)^(n*t)

A = 1000*(1+0.09/4)^(4*1)

A = 1000*(1+0.0225)^(4)

A = 1000*(1.0225)^(4)

A = 1000*1.09308331878906

A = 1093.08331878906

A = 1093.08

The probability that -2 < x < 2 is given as follows:

P(-2 < x < 2) = 0.16.

From the table given in this problem, the probability distribution is defined as follows:

The desired interval in this problem is given as follows:

-2< x <2.

It is an open interval, meaning that the only outcome that satisfies this interval is X = 0, and thus the probability is given as follows:

P(-2 < x < 2) = 0.16.

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Answer:

a)  The product of any two odd integers is an odd integer.

b)  The sum of two negative integers is always smaller than the smallest negative integer.

Step-by-step explanation:

Given:

Carry out a few examples to find a pattern:

Pattern:

Write the conjecture based on the found pattern.

Conjecture:  

Test the conjecture for accuracy using at least three sets of numbers.

Test:

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

Given:

Carry out a few examples to find a pattern:

Pattern:

Write the conjecture based on the found pattern.

Conjecture:  

Test the conjecture for accuracy using at least three sets of numbers.

Test:

A decaying exponential function is modeled as follows:

y = a(1 - r)^t.

In which the parameters are given as follows:

For this problem, the function is defined as follows:

y = 476000(0.81)^t.

Hence the values of the parameters are given as follows:

a = 476000, r = 0.19, meaning that the percent decay is of 19%.

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the interest the bond paid off is $7507.8125.

What is simple interest?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

The formula for simple interest is:

S = p*t*r/100

where P is the principal amount of money, R is the interest rate as a decimal, T is the time.

a bond that paid 7.75% simple interest earned $3,875 interest.

S = (3875*7.75*25)/100 = $7507.8125

Hence the interest the bond paid off is $7507.8125.

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Answer:

130°

Step-by-step explanation:

Since QS bisects ∠PQR, the measures of angles PQS and SQR must be the same

m ∠PQS = 3x + 5

m ∠SQR= 2x + 25

Setting these expressions equal to each other:
3x + 5 = 2x + 25

Subtract 2x from both sides

3x - 2x + 5 = 25

x + 5 = 25

Subtract 5 from both sides

x = 20

Therefore m ∠PQS which is  3x + 5:

m ∠PQS = 3(20) + 5 = 65°

m ∠SQR = ∠PQS =65°  also

Adding the two together we get

m ∠PQR = 65 + 65 = 130°

Answer:

The answer is b.

Step-by-step explanation:

For first row first column=18+72+10=100

For first row second column=-9+48-7=32

For first row third column=27-96+7=-62

Repeat this for the rest.

Hope this helps you.

The linear function graphed is defined as follows:

B. y = 3x + 2.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The line in this problem crosses the y-axis at y = 2, hence the intercept b is given as follows:

b = 2.

When x increases by one, y increases by three, hence the slope m of the function is given as follows:

m = 3.

This means that the function is defined as follows:

y = 3x + 2.

Meaning that the correct option is given by option B.

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Usain's speed in miles per hour is 22.72 mph.

Speed = Distance/Time

Distance = Speed X Time

Time = Distance / Speed

Given:

Usain run 100 yards in 9 sec.

So, he can 1760 yards in

= 9/100  x 1760

= 158.4 sec

As, his speed in yards/ sec= 100/9

So, 1760 yard= 1 mile and 3600 sec = 1 hour

Now, the speed in miles per hour

= 100/ 9 x 3600/1760

= 100/9 x 2.045

= 22.72 mph

Hence, the speed is 22.72 mph.

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The slope of the given  linear relationship is; 4/5

Slope tells us that a unit change in x, which  is the independent variable will result in a change in y by the amount of b. Thus;

slope = change in y/change in x

Slope = rise/run.

In terms of two coordinates, the slope can be  expressed as;

slope = (y₂ - y₁)/(x₂ - x₁)

From the graph attached, we are given the two coordinates as;

(-3, -2) and (2,2)

Thus;

Slope = (2 - (-2))/(2 - (-3))

Slope = 4/5

This is the slope of the linear relationship.

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