Multiply: (–4 + i)(2 – 3i)
a. –5 – 10i


b. –8 + 11i


c. –5 + 14i


d. –11 + 14i

Answers

Answer 1

The result of the product of the given complex numbers as required to be determined is; Choice C; -5 + 14i.

What is the product of the given complex numbers?

It follows from the task content that the result of the product of the given complex numbers is to be determined.

On this note, since the required product to be evaluated is; (–4 + i) (2 – 3i).

We can therefore multiply as follows;

-8 + 12i + 2i - 3i².

However, it is noteworthy to know that; i² = -1.

Hence, we have that;

-8 + 14i + 3

= -5 + 14i

On this note, it follows that the result of the product of complex numbers as required is; -5 + 14i.

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Related Questions

Anyone knows the answer ?

Answers

The solution for the question found using the double angle formula for cosine is -[tex]\frac{7}{25}[/tex].

What are double angle formulae?

There are some trigonometric formulas that are known as double angle formulae because they contain double angles, such as Sin 2x, Cos 2x, and Tan 2x.

The double angle formula for cosine is

Cos 2θ = Cos²θ - Sin²θ

           =2Cos²θ – 1

            = 1 – 2Sin²θ

Given sinθ = [tex]\frac{4}{5}[/tex]

         cos(2θ) = 1-2sin²θ = [tex]1-2[/tex]×( [tex]\frac {4}{5}[/tex])² = [tex]1-[/tex] [tex]\frac{32}{25}[/tex] = [tex]\frac{-7}{25}[/tex]

Therefore Cos(2θ) fund using double angle formula is -[tex]\frac{7}{25}[/tex]

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The solution for the question found using the double angle formula for cosine is -.7/-25

What are double angle formulae?

There are some trigonometric formulas that are known as double angle formulae because they contain double angles, such as Sin 2x, Cos 2x, and Tan 2x.

What is angle?

An angle is a measure of the amount of rotation between two rays or lines that share a common endpoint, called the vertex of the angle. The two rays or lines are called the sides of the angle, and the endpoint is called the vertex. The size of an angle is typically measured in degrees or radians, with one full rotation around a point (360 degrees or 2π radians) being equal to a full circle.

The double angle formula for cosine is

Cos 2θ = Cos²θ - Sin²θ

          =2Cos²θ – 1

           = 1 – 2Sin²θ

Given sinθ = 4/5

        cos(2θ) = 1-2sin²θ = 1-2×(4/5 )² =  1-32/25 = -7/25

Therefore Cos(2θ) fund using double angle formula is -

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please help me plsssssssssssssss

Answers

Answer:

this should help you out

Use the defined variables for the verbal model to write an equation in slope-intercept form that relates the variables.
$2/pound × Pounds of peaches + $1.50/pound × pounds of apples = $15
Let x represent the number of pound of peaches.
Let y represent the number of pounds of apples.
An equation is y = ___
Graph the equation.

Answers

An equation is y = -4x/3 + 10.

A graph of the equation is shown in the image attached below.

How to write an equation to model this situation?

In order to write and graphically solve an equation that model this situation, we would assign variables to the number of pound of peaches and number of pounds of apples respectively, and then translate the word problem into algebraic equation as follows:

Let the variable x represent the number of pound of peaches.Let the variable y represent the number of pounds of apples.

Next, we would translate the word problem into an algebraic equation as follows;

$2/pound × Pounds of peaches = 2x.

$1.50/pound × pounds of apples = 1.50y

Combining the two expressions above, we have the following:

2x + 1.50y = 15

Making y the subject of formula, we have:

1.50y = 15 - 2x

y = (15 - 2x)/1.50

y = -4x/3 + 10

Therefore, an equation in slope-intercept form that relates the variables is y = -4x/3 + 10.

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Find the measurement of the angle I dictated for each trapezoid.

Answers

The measures of missing angles in trapezoids are listed below:

Case 5: m ∠ J = 75°, Case 7: m ∠ T = 118°

How to determine the measures of missing angles

In this question we must determine the measures of missing angles in trapezoids. There are two hints to determine the values of the missing angles:

Any pair of angles along one of the two parallel lines and between the other two congruent sides have the same measure. Any pair of angles between two parallel lines are supplementary angles. Two angles are supplementary when the sum of their measures equals 180°.

Now we proceed to determine the missing angles in every trapezoid:

Case 5

m ∠ K + m ∠ J = 180°

21 · x + 15 · x = 180°

36 · x = 180°

x = 5

m ∠ J = 15 · x

m ∠ J = 15 · 5

m ∠ J = 75°

Case 7

m ∠ U = m ∠ T

m ∠ T = m ∠ U

m ∠ T = 118°

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One solution.

2x - 1 = ____x - 1

Answers

so since the problems are the same the answer would be 2

the blank space must be 2 or x must be zero, I don't know what you mean by one solution

the blank must equal 2 because on the right side the coefficient of x is 2 so it must be same

i have been trying to figure this out for hours-

answer choices:

SSS

SAS

ASA

AAS

HL

Not Congruent

Answers

Answer:  The answer is SAS

elijah used 3/4 of the memory on his cell phone memory card if the memory card can hold 32 gigabytes how many gigabytes did elijah used

Answers

Elijah used 24 gigabytes memory on his cell.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Elijah used 3/4 of the memory on his cell phone memory card.

And, The memory card can hold 32 gigabytes.

Now,

Since, The memory card can hold 32 gigabytes.

And, She used 3/4 of the memory on his cell phone memory card.

Hence. The used memory = 3/4 of 32

                                         = 3/4 × 32

                                         = 3 × 8

                                          = 24 gigabytes

Thus, Elijah used 24 gigabytes memory on his cell.

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Wilmer cashed his paycheck at Check Express. The fee at Check Express is 9% of the amount of the check. His paycheck was $291. How much was the fee for Wilmer to cash his paycheck?​

Answers

Answer:

$26.19

Step-by-step explanation:

9% as a decimal is 0.09.

So, the fee is [tex](291)(0.09)=\$26.19[/tex].

Answer:

$26.19

Step-by-step explanation:

.09 x 291 = 26.19

simplify expression: 3f+8(2m-7)

Answers

After simplification we got the above expression in the form 3f + 16m -56

What is simplify in mathematics?

The word "simplify" implies to turn something in a simpler form.

In mathematics, simplify an expression means write an expression in such a way that is comparatively less complicated than before. The main purpose of simplify an expression is to make it easy to solve as well as calculation.

How to simplify the above expression?

3f + 8(2m-7)

we rearrange the expression by removing the parenthesis.

we remove the parenthesis by multiplying the factors.

3f + 8 × 2m - 8 × 7

3f + 16m -56

the above expression has no like terms to add or subtract so it is kept in this form.

Hence, 3f + 16m -56 is the simpler form.

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Prime numbers are the _______ _______of all numbers

Answers

The numbers which have only two factors either 1 and the number itself are called prime numbers.

What is prime numbers?

Prime number is a natural number greater than 1 that is not a product of two smaller natural numbers while a natural number greater than 1 that is not prime is called a composite number

Therefore a prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29

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Aponi is a member of the Shoshone Native American Indian
tribe. Her name means "butterfly." Aponi uses beads to make
hair barrettes with a butterfly design. The number of beads she
uses is proportional to the number of hair barrettes she makes.
Aponi graphs a line that shows the number of hair barrettes
she makes and the total number of beads she uses. Two
points on the line are (2, 150) and (5, 375).
What does the slope of the line mean in this situation?
O Aponi uses 45 beads to make each hair barrette.
Aponi uses 75 beads to make each hair barrette.
Aponi uses 150 beads to make each hair barrette.
O Aponi uses 225 beads to make each hair barrette.

Answers

A line that shows the number of hair barrettes she makes and the total number of beads she uses is y = 75x.

What is the graph's line's equation?

In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, you must first determine the slope and y-intercept. The slope is the ratio of the change in y to the change in x. Find two locations on the line, and then draw a sloping triangle joining them.

What is the name for a straight line?

A line is a perfectly straight, one-dimensional figure that extends infinity in both directions and has no thickness. To stress that a line has no "wiggles" anywhere along its length, it is sometimes referred to as a straight line or, more archaically, a right line.

Two points on the line are (2, 150) and (5, 375)

y - 150 = ( (375-150) / (5-2) )  (x-2)

y - 150 = 75 (x-2)

y = 75x

Equation of line is y = 75x

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is y= 2x3 an exponential function?

Answers

Answer:

No it is not an exponential function

Help ASAP PLSSS!! I’d really appreciate it! Thank youuu!

Answers

Angle 1 (R) and angle C are congruent since they have no markings

C = 180 - (80 + 45)
C = 180 - 125
C = 55

I teach geometry :)

Find a quartic function

Answers

The quartic equation y = x⁴ - x³ - 5 · x² - x - 6 has x = - 2 and x = 3 as its only real zeros. (Correct choice: C)

What quartic equation contains a given set of zeros?

Quartic equations are polynomials of grade 4, whose standard form is described below:

y = a · x⁴ + b · x³ + c · x² + d · x + e

Where a, b, c, d, e are real coefficients. A value of x is a zero of a polynomial when the result is equal to zero. The quickest way to find the polynomial is by evaluating each expression at x = - 2 and x = 3:

x = - 2

y = (- 2)⁴ - (- 2)³ - 5 · (- 2)² - (- 2) - 6

y = 16 + 8 - 20 + 2 - 6

y = 0

x = 3

y = 3⁴ - 3³ - 5 · 3² - 3 - 6

y = 81 - 27 - 45 - 3 - 6

y = 0

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PLS HELP ME!!!
COSINE RULE I THINK!!
please explain in some detail and will mark brainliest

Answers

Answer:

Step-by-step explanation:

if there is any triangle ABC and a,b,c are sides opposite angles A,B,C respectively , then

[tex]cos~A=\frac{b^2+c^2-a^2}{2bc} \\cos~B=\frac{c^2+a^2-b^2}{2ca} \\cos~C=\frac{a^2+b^2-c^2}{2ab}[/tex]

B=101

a= 3 cm

b=y

c=1 cm

use formula for cos B

cos 101=cos(90+11)=sin 11

[tex]-sin~11=\frac{1^2+3^2-y^2}{2 \times 3 \times 1} \\-6 \times sin~11=1+9-y^2\\y^2=10+6~sin~11\\y^2\approx 10+6\times 0.1908\\y^2 \approx11.1448\\y\approx3.338[/tex]

Answer:

2.16

Step-by-step explanation:

To find the length y:

Since we have an angle with two sides next to it, it is 'cosy', so we can use the cosine rule to find y. Let's make y = a for the formula.

Using the cosine formula:

a^2 = b^2 + c^2 - 2bc cos(A)

where b=1, c=3 and A=101

substitute these values in the formula:

a ^2 = 1^2 + 3^2 - 2(1)(3) × cos(101)

a ^2 = 4.647970...

Square root to find a:

a = √4.647970...

a = 2.16

thus, y = 2.16 to 3sf

Divide the polynomials. If there is a remainder, enter the remainder in fraction form. x^4+3x^3-x-2/x+1

Answers

The polynomial x⁴ + 3x³ - x - 2 will have a remainder of 1 when divided by x + 1 and the result can be written in the form (x³ + 2x² + 2x - 3) + 1/(x + 1).

How to divide the polynomial

Using the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder

We shall divide the polynomial x⁴ + 3x³ - x - 2 by x + 1. as follows;

x⁴ divided by x equals x³

x + 1 multiplied by x³ equals x⁴ + x³

subtract x⁴ + x³ from x⁴ + 3x³ - x - 2 will result to 2x³ - x - 2

2x³ divided by x equals 2x²

x + 1 multiplied by 2x² equals 2x³ + 2x²

subtract 2x³ + 2x² from 2x³ - x - 2 will result to 2x² - x - 2

2x² divided by x equals 2x

x + 1 multiplied by 2x equals 2x² + 2x

subtract 2x² + 2x from 2x² - x - 2 will result to -3x - 2

-3x divided by x equals -3

x + 1 multiplied by -3 equals -3x - 3

subtract -3x - 3 from -3x - 2 will result to a remainder of 1.

Therefore, the polynomial x⁴ + 3x³ - x - 2 divided by x + 1 gives a quotient x³ + 2x² + 2x - 3 and a remainder of 1 and can be written as (x³ + 2x² + 2x - 3) + 1/(x + 1).

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Question
Enter a linear equation that models the situation.
A drugstore sells pens for $1.40 each and notebooks for $2 each. The owner would like to sell $40 of these
items each day. Use p for the number of pens and n for the number of notebooks.
A linear equation that models the situation is
= 40.

Answers

A linear equation that models the situation is 1.4p + 2n = 40.

This equation represents the total daily revenue from the pens (1.4p) and notebooks (2n) and sets it equal to the target revenue of $40. The variables p and n represent the number of pens and notebooks sold, respectively. This equation can be used to determine the number of pens and notebooks that need to be sold in order to reach the target revenue of $40.

Answer:

1.40p+2n=40

Step-by-step explanation:

100 points please answer

Answers

The best answer is to simplifying each of the identity separately to get the same expression on both sides. Option C

What are trigonometric identities?

Trigonometric identities are described mathematically as equalities consisting of trigonometric functions that proves true for all the value of occurring variables for which both sides of equality are defined.

These involve certain functions of one, two or more angles.

They also are different from triangle identities, which involves angles and side lengths of a triangle.

To verify a trigonometric identity, we take the following steps;

Convert the equalities to terms of sine and cosine.Solve the identities at possible timesThen, simplify the left-hand side of the equation, before simplifying the right-hand side.

Hence, the best option is C

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a parking lot contains only cars and motor bikes. if there are 18 vehicles and 50 tires in the parking lot, how many cars and bikes are there?

Answers

Answer:

Step-by-Step:5 cars and 14 bikes

3p-3p+2s-6s+2q-3q+8r-7r

Is it ok to not put the p in this equation as the 3p is minus

Answers

Answer:

- 4s - q + r

Step-by-step explanation:

that's right. You do not put the p since 3p and -3p cancel out to give zero. I'll solve the question for you:-

⇒3p-3p+2s-6s+2q-3q+8r-7r

add or subtract the like terms(terms having same variables), then out of the two like terms, put the sign of the greater number, for e.g. 2q-3q = -1q

⇒0 - 4s - 1q + 1r

⇒- 4s - q + r Answer

hope that helps...

Determine where the graph of the given function is concave upward and concave downward. Find the coordinates of all inflection points.
g(t) = t^2 - 27/t

Answers

The coordinates of the inflection points are (3, 0) and it concave upwards

How to determine the coordinates of the inflection points.

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

g(t) = t^2 - 27/t

Express properly

So, we have

g(t) = t² - 27/t

Calculate the second derivative

So, we have

g''(t) = 2 - 54/t³

Set the differentiated equation to 0

2 - 54/t³ = 0

So, we have

2t³ = 54

Divide by 2

t³ = 27

Take the cube roots

t = 3

Substitute t = 3 in g(t) = t² - 27/t

g(3) = 3² - 27/3

g(3) = 0

This means that the inflection point occurs at t = 3 and the coordinates of the inflection point are (3, 0)

How to determine the point of concave upward and concave downward

Recall that

g''(t) = 2 - 54/t³

Next, we check if the second derivative exist at t = 0,

g''(0) = 2 - 54/0³

g(0) = undefined

The undefined value implies that the graph has a vertical inflection point at t = 0

And as such, the graph of the function is concave upward

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Help please! How do I write an equation in standard form using the information on the graph?

Answers

Answer:

  3x -y = 2

Step-by-step explanation:

You want a standard form equation for the line through the points (0, -2) and (2, 4).

Slope

The slope of the line is the "rise" divided by the "run". The given point on the right is 3 grid squares above the one on the left. It is one grid square to the right. So, the slope is ...

  m = (squares above)/(squares to the right) = 3/1 = 3

If we consider the actual x- and y-values represented by these grid squares, then the slope is ...

  m = (4 -(-2))/(2 -0) = 6/2 = 3

Intercept

The point (0, -2) tells you the y-intercept is -2. That is where the line crosses the y-axis.

Slope-intercept equation

With this information, we can write the slope-intercept form equation for the line:

  y = mx +b . . . . . . . line with slope m and y-intercept b

  y = 3x -2 . . . . . . . . line with slope 3 and y-intercept -2

Standard form

The standard form of an equation for a line is ...

  ax +by = c

where a, b, c are generally mutually-prime integers with a ≥ 0. If a=0, then b > 0.

We can rearrange the slope-intercept equation to put it into this form.

  y = 3x -2

  3x -y -2 = 0 . . . . . subtract y

  3x -y = 2 . . . . . . . add 2. This is the standard-form equation of the line.

Which of the following is the slope of the line y - 3x =0​

Answers

Answer:

-3

Step-by-step explanation:

Answer: The slope whould be 3

Step-by-step explanation:

Graph the line using the slope and y-intercept, or two points.

Slope: 3

y-intercept:

(0,0)

x|y

----

0|0

1|3

Convert the polar equation to rectangular form [tex]r=5cot(\theta)csc(\theta\))[/tex]

Answers

Answer:

[tex]\displaystyle x=\frac{1}{5}y^2[/tex]

Step-by-step explanation:

[tex]\displaystyle r=5\cot(\theta)\csc(\theta)\\\\r=5\biggr(\frac{\cos(\theta)}{\sin(\theta)}\biggr)\biggr(\frac{1}{\sin(\theta)}\biggr)\\\\r=\frac{5\cos(\theta)}{\sin^2(\theta)}\\\\r^2=\frac{5r\cos(\theta)}{\sin^2\theta}\\\\r^2\sin^2(\theta)=5r\cos(\theta)\\\\(r\sin(\theta))^2=5x\\\\y^2=5x\\\\x=\frac{1}{5}y^2[/tex]

I need to know the first and last one

Answers

The lines FE and GH are parallel to each orther.

What is congruent of the triangle?

The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.

Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."

Given that

ΔPEI = ΔGHI

here ∠pie = ∠gih

PI =HI

GI=EI

So both triangles are congruent

So the FE║GH.

Hence the lines FE and GH are parallel to each orther.

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Simplify to a single trig function

Answers

On solving the provided question we can say that - the value of the trignometric function will be -cos(t)+2cosec(t)

what is trigonometry?

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

here,

(sint(t) + cos(t))[tex]^{2}[/tex] =(sint +cost)(sint - cost)

=|  -cos(t)+2cosec(t) |

= -cos(t)+2cosec(t)

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2. What number is a common multiple of
5 and 9?

Answers

Pretty sure the answer is 45

Find the value of x.

Answers

Answer: x = 4

Step-by-step explanation:

Based on the given distances and angle measures, DE is congruent to XY, DF is congruent to ZX, and EF and ZY are congruent.

This means that:

[tex](4x-1)=15[/tex]

Simplify and solve for x.

[tex]4x-1=15\\4x=16\\x=4[/tex]

So, x = 4

The answer is x=4. I hope this helps

There are 9 players on a baseball team there are 6 teams in the league how many baseball players are in the league

Answers

Answer:

54

Step-by-step explanation:

Multiply 9 (players per team) and 6 (teams in the league) to find the total players in the league.

9 times 6 = 54

what is the quotient of g and 25

Answers

Answer:

the quotient of g and 25 is g/15.

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China's form of government was both like and unlike Japan's. For example, the emperors in China and Japan had quite different powers. The emperor in China was the sole ruler, whereas in Japan, the emperor had only loose control over the semi-independent uji. Uji controlled their own land, and their leaders struggled among themselves for the right to select the emperor and influence his decisions.While Japanese emperors depended on local leaders, the Chinese emperor ruled with the help of a bureaucracy of government officials. At least in theory, appointments to government jobs were based on merit. Any man who did well on an examination could become an official.During the 7th and 8th centuries, Japanese rulers adopted a Chinese style of government. Japanese tradition credits Prince Shotoku with starting this development. Borrowing Confucian ideas, the prince created ranks for government officials. In 604, he issued a set of guidelines called the Seventeen Article Constitution, which stated that the emperor was the supreme ruler: In a country there are not two lords; the people have not two masters. The sovereign is the master of the people of the whole country.Later rulers went much further in bringing Chinese-style changes to Japan. In the late 7th century, Emperor Tenmu and his wife and successor Empress Jit reformed and strengthened the central government. Control of the land was taken away from clan leaders and given to the emperor. The emperor then redistributed the land to all free men and women, and in return, people paid heavy taxes to support the imperial government.By the 700s, Japan's imperial government looked much like China's. It was strongly centralized and supported by a large bureaucracy. Over time, however, one key difference emerged. Although Prince Shotoku had called for government officials to be chosen on the basis of their ability, as in China, a powerful aristocracy developed in Japan during the 9th century. As a result, members of noble families held all the high positions in the government. Describe the intellectual and ideological movements that influenced the revolutions that swept the Atlantic world from 1750 to 1900. Electromagnetic radiation is a kind of (1) ____________________ that behaves like a(n) (2) ___________________ as it travels through space. (3) __________________ is one type of electromagnetic radiation. Other examples include X-rays, radio waves, and microwaves. opinin personal sobre el poema impresiones de Salom Urea In Silent Spring Rachel Carson makes up a fictional story about what life in the United States will be like if we don't save the environment, whereas in "A Case for Waawaatesi" Winona LaDuke A. Presents facts and evidence to convince readers to reduce light pollutionB. Tells a fable about how artificial light has destroyed the sleeping patterns of humansC. Relates a biographical story to inspire readers to get more sleepD. Discusses what the future would be like without fireflies or owls Is the simplified form of 2 square foot 3. Square Foot 12 rational true or false Two genes that are separated by 10 map units show a recombination percentage of 10%. Maisy and Oliver converted some pounds () into euros () at two different shops. Maisy converted 40 into 47.20 at shop A. Oliver converted 83 into 96.28 at shop B. Byron converted some pounds at one of these shops and received 68.44. What is the smallest amount that he could have converted?