Determine the real number x and y if (x-yj)(3+5j) is the conjugate of -6-24j

Answers

Answer 1

The values of the variables x and y such that the conjugate of - 6 - j 24 is found are 3 and 3, respectively.

How to find the value of two variables associated with the conjugate of a complex number

Let α + i β be a complex number, whose conjugate is the complex number α - i β. In this problem we find the values of the variables x and y such that:

(x + i y) · (3 + i 5) = - 6 + i 24

3 · x + i 3 · y + i 5 · x + i² 5 · y = - 6 + i 24

(3 · x - 5 · y) + i (5 · x + 3 · y) = - 6 + i 24

Then, we need to solve the following system of linear equations:

3 · x - 5 · y = - 6

5 · x + 3 · y = 24

Now we proceed to solve the system algebraically. Clear x in the first equation:

x = (- 6 + 5 · y) / 3

x = - 2 + (5 / 3) · y

Substitute x on the second equation and clear y:

5 · [- 2 + (5 / 3) · y] + 3 · y = 24

- 10 + (25 / 3) · y + 3 · y = 24

34 / 3 · y = 34

(1 / 3) · y = 1

y = 3

Finally, we substitute on y in the first equation:

x = - 2 + (5 / 3) · 3

x = - 2 + 5

x = 3

The values of the variables x and y are 3 and 3, respectively.

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Related Questions

Rewrite the expression 3(12 - 10) using the distributive property of multiplication over subtraction.

Answers

The resulting expression using the distributive property of multiplication over subtraction is 3(12) - 3(10).

What is distributive property of multiplication?

The distributive property of binary operations extends the distributive law, which states that in elementary algebra, equality is always true.

For instance, given the expression;

A(B - C)

We will have to distribute A over B and C to have;

A(B - C) = AB - AC

Applying the rule to the given expression

3 (12 - 10)

3(12) - 3(10)

This shows that the given expression can also be written as 3(12) - 3(10)

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Please help me ASAP I’ll mark brainly

Answers

1. The scholar made a mistake in the last step

where he said x=3.5

SCHOLA DIVIDED 7 BY 2 INSTEAD OF DIVIDING BY 0.5

[tex]0.5x = 7 \\ \frac{0.5x}{0.5} = \frac{7}{0.5} \\ x = 14

AS A RESULTS GOT WRONG ANSWER . x is supposed to be 14.

Coffee Shop PricesCup CostSmall $2Regular $4Large $5David and Jon are placing coffee orders for their friends.David orders 10 large cups of coffee. Jon orders 4 fewer large cups than David. Jon pays for his orders with a $50 bill.Jon wants to know how much he spent on coffee.What is a good plan to find the amount Jon spent on coffee?3rd grade student

Answers

Step 1:

Cost of large cup = $5

Step 2:

Number of large David orders = 10 cups

A good plan to find the amount Jon spent is to find the number of large cups Jon orders from the number of large cups David orders.

Jon order 4 fewer large cups

Therefore,

Jon order = 6 cups

Step 3:

A good plan to find the amount Jon spent is to find the number of large cups Jon orders from the number of large cups David orders.

The amount Jon spent on coffee = 6 x $5 = $30

6. Diagram this statement. Then answer the questions (22) that follow. One third of the 60 questions on the test were true false. (a) How many of the questions on the test were true- false? (b) How many of the questions on the test were not true- false? (C) What percent of the questions were true-false?

Answers

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Cylinder A has radius r, height h, and a volume of 10 pi cubic units. Cylinder B hastwice the radius and twice the height.hATBWhat is the volume of cylinder B?I2r2h

Answers

Volume of a cylinder:

[tex]V=h*r^2*\pi[/tex]

For cylinder A:

[tex]10\pi cm^3=h*r^2*\pi[/tex]

For cylinder B:

[tex]V_B=2h*(2r)^2*\pi[/tex]

Simplify the equation for volumen of cylinder B:

[tex]\begin{gathered} V_B=2h*4r^2*\pi \\ V_B=8*(h*r^2*\pi) \end{gathered}[/tex]

in the equation for the volume of cylinder A you have the value of h*r^2*π:

[tex]\begin{gathered} V_B=8*(10\pi cm^3) \\ V_B=80\pi cm^3 \end{gathered}[/tex]Then, the volume of cylinder B is 80π cubic centimeters.

which part of the aldr braiding expresses 3 + 7 D is the c o e f f i n c i e n t

Answers

the coefficient is the number that accompanies the variable, so:

[tex]3+7D[/tex]

The coefficient is 7

the area of a trapezoid is given by the formula A= h(a+b)/2. solve for the formula for b.

Answers

The formula is

[tex]A=\frac{(a+b)\cdot h}{2}[/tex]

To solve for b, first, we multiply the equation by 2

[tex]\begin{gathered} 2A=2\cdot\frac{(a+b)\cdot h}{2} \\ 2a=(a+b)\cdot h \end{gathered}[/tex]

Then, we divide the equation by h

[tex]\begin{gathered} \frac{2A}{h}=\frac{(a+b)h}{h} \\ \frac{2A}{h}=a+b \end{gathered}[/tex]

At last, we subtract a from each side

[tex]\frac{2A}{h}-a=a-a+b[/tex]Hence, the final expression is[tex]b=\frac{2A}{h}-a[/tex]

11) Describe the number and type of roots for 2x2 + 19x - 33 = 0.[A] 2 real solutions [B] 2 complex solutions [C] 1 real solution[D] 1 complex solution

Answers

Explanation:

The first thing we will do is to solve for x in the equation:

Using factorization method:

The factors are +22 and -3. This because the addition of this number will give you the coefficient of x (19) while the multiplication will give -66

HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST

Answers

The rational number between -1/3 and 1/-2 could be;  -6 / 18, -6/12.

What are natural numbers, rational numbers, and irrational numbers?

Natural numbers are: 1, 2, 3, ..Rational numbers are numbers which can be written in the form of a/b where a and b are integers. Example: 1/2, 3.5 (which is writable as 7/5). Irrational numbers are those real numbers which are not rational numbers.

We are asked to find that rational number between -1/3 and 1/-2.

LCM of 3 and 2

3 x 2 = 6

Then we get;

-1/3 x 6/6 = -6 / 18

1/-2 x 6/6 = -6/12

Hence, the rational number between -1/3 and 1/-2 could be;  -6 / 18, -6/12.

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Patrick is responsible for choosing the company his local community group will use for having T-shirts printed. He must choose between Initial Me and Monogram Mania. Both companies charge an initial set-up fee and then charge per T-shirt printed.

The graph shows the cost of purchasing T-shirts from Initial Me and the cost of purchasing T-shirts from Monogram Mania.

Which statements are true about Initial Me and Monogram Mania?

Select each correct answer.

Answers

Step 1:

The initial cost of Initial Me = 50

The initial cost of Monogram Mania = 80

Step 2:

Both Initial Me and Monogram Mania cost the same for 10 T-shirts printed of 130

Step 3:

Monogram Mania charges less per T-shirt printed than Initial Me charges.

The average cost of Monogram Mania is less than that of Initial Me.

Final answer

Monogram Mania charges less per T-shirt printed than Initial Me charges.

I am canfusing in this question can you solve it.

Answers

Answer:

Step by step explanation:

The three sides of a triangle are n, 4n - 2, and 4n - 7. If the perimeter of the triangle is 45 cm, what is the length of each side? Separate multiple entries with a comma.

Answers

Perimeter of a triangle and equationsAnswer

6, 22, 17

Explanation

Step 1: writing the equation

We have a triangle with sides n, 4n - 2, and 4n - 7

We obtain its perimeter if we add all its sides:

n + 4n - 2 + 4n - 7

Since the perimeter is 45 cm, then:

n + 4n - 2 + 4n - 7 = 45

combining like terms:

n + 4n +4n = 9n

and

-2 - 7 = -9

then, we have:

n + 4n - 2 + 4n - 7 = 45

9n - 9 = 45

Step 2: finding n

Now we solve the equation:

9n - 9 = 45

↓ taking -9 to the right

9n - 9 + 9 = 45 + 9

9n = 54

↓ taking 9 to the right

n = 54/9 = 6

Then, n = 6

Step 3: sides measure

Since the measure of the first side is given by n,

then its length is

n = 6

SInce the measure of the second side is given by 4n-2,

then its length is

4n - 2 = 4 · 6 - 2

= 24 - 2

= 22

SInce the measure of the third side is given by 4n - 7,

then its length is

4n - 7 = 4 ·6 - 7

= 24 - 7

= 17

That is why the measures are 6, 22 and 17.

Translate to an algebraic expression Twice "a"The translation is ...

Answers

Okay, here we have this:

Considering that twice an amount generally indicates taking two of the things in question; generally this indicates multiplying by 2.

This mean that if we have "twice a" when transferring it to an algebraic expression we obtain: 2a.

Based on your knowfedgs of the two data sets described below, would you espect a scatter plot describing the two data sets to have a positive, a negative, or nocorrelationduration of usage and the charge in the battery of a mobile phone

Answers

We expect the variable to have a negative correlation.

This means that the more we use the phone the lower the charge will be.

Can you please help me with 44Please use all 3 forms of the expression such as : down/up. As _,_ And limits

Answers

Answer:

[tex]\begin{gathered} x-\text{intercept}=-3\text{ and 1} \\ y-\text{intercept}=\text{ -9} \end{gathered}[/tex][tex]\begin{gathered} x=1\text{ multiplicity 3} \\ x=-3\text{ multiplicity 2} \\ \lim _{x\rightarrow\infty}(x-1)^3(x+3)^2=\infty \\ \lim _{x\rightarrow-\infty}(x-1)^3(x+3)^2=-\infty \end{gathered}[/tex]

Step-by-step explanation:

To find the x-intercepts factor the function to the simplest form:

[tex]h(x)=(x-1)^3(x+3)^2[/tex]

As we can see the zeros to the function would be 1 and -3, then its:

[tex]\begin{gathered} x-\text{intercept}=-3\text{ and 1} \\ y-\text{intercept}=\text{ -9} \end{gathered}[/tex]

Zero has a "multiplicity", which refers to the number of times that its associated factor appears in the polynomial. Therefore, this function has multiplicity:

[tex]\begin{gathered} x=1\text{ multiplicity 3} \\ x=-3\text{ multiplicity 2} \end{gathered}[/tex]

For the end behavior:

down/up

As x approaches infinity f(x) approaches infinity

As x approaches -infinity f(x) approaches -infinity

[tex]\begin{gathered} \lim _{x\rightarrow\infty}(x-1)^3(x+3)^2=\infty \\ \lim _{x\rightarrow-\infty}(x-1)^3(x+3)^2=-\infty \end{gathered}[/tex]

32. Which statement is true if m and n are parallel? A slope m = slope (n)B slope m= -1 (Divide) slope (n)C slope m= 1 (Divide) slope (n)D slope m= -1 x slope (n)

Answers

Two lines that parallel, their slopes are equals.

L1 and L2 are parallel only if the slopes of the lines are s1 and s12 are identical

therefore the correct answer is A. slope m = slope (n) since they say that two slopes the same

Fill in the table using this function rule. y = 2x+4

Answers

The complete table using the given linear equation is x y

-4 -4

-2 0

0 4

2 8

What are linear equations?

A linear equation is one that has the form Ax+By=C. This definition comes from mathematics. It consists of two variables combined with a constant value that exists in each of them.

The values of the variables will be obtained when the system of linear equations is solved; this is referred to as the solution of a linear equation.

Given the linear equation y = 2x + 4

If x = -4

y =2(-4) + 4

y = -4

If x = -2

y =2(-2) + 4

y = 0

If x = 0

y =2(0) + 4

y = 4

If x = 2

y =2(2) + 4

y = 8

Hence the complete table using the function is

x y

-4 -4

-2 0

0 4

2 8

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Complete question

Fill in the table using this function rule. y=2x -4

x y

-4 ?

-2 ?

0 ?

2 ?

111. 12 people fit comfortably in a 5 feet by 5 feet area. Use this value to estimate the size of a crowd that is 25feet deep on both sides of the street along a 3-mile section of a parade route (Hint: 1 mile - 5 280 ft)

Answers

Answer:

The estimated crowd is of 380160 people.

Step-by-step explanation:

We solve this question applying a proportion on the following format:

People divided by area.

Let's do the drawing:

12 people fit comfortably in a 5 feet by 5 feet area.

So

12 people fitting in an area of 5*5 = 25 ft².

Area of the street:

3 miles = 3*5280 ft = 15840 ft

25 feet on both sides. So, the total area in which the crowd is sparsed is:

A = 15840*25*2= 792000 ft².

Now we apply the ratio:

People over area.

[tex]\frac{12}{25}=\frac{x}{792000}[/tex]

Applying cross multiplication:

25x = 12*792000

x = (12*792000)/25

x = 380160

The estimated crowd is of 380160 people.

A regular hexagon has sides 2 feet long. What is the exact area of the hexagon? What is the approximate area of the hexagon?

Answers

The formula for the area of a hexagon is

[tex]A=\frac{3\sqrt[]{3}}{2}s^2[/tex]

where 's' is the length of one side of the regular hexagon.

The side of our regular hexagon is 2 feet, therefore, its area is

[tex]\begin{gathered} A=\frac{3\sqrt[]{3}}{2}\cdot(2)^2=6\sqrt[]{3} \\ 6\sqrt[]{3}=10.3923048454\ldots\approx10 \end{gathered}[/tex]

The exact area of the hexagon is 6√3 ft², which is approximately 10 ft².

The directions for a weed spray concentrate state that 3 tablespoons of the concentrate should be mixed with 4 gallons of water. How many tablespoons of concentrate need to be mixed with 5 gallons of water?

Answers

The given information is:

- 3 tablespoons of the concentrate should be mixed with 4 gallons of water.

The ratio of tablespoons to gallons of water is:

[tex]\frac{3\text{ tablespoons}}{4\text{ gallons of water}}[/tex]

Then, we can apply proportions to find how many tablespoons of concentrate need to be mixed with 5 gallons of water, so:

[tex]\begin{gathered} \frac{3}{4}=\frac{x}{5} \\ Isolate\text{ x} \\ x=\frac{5*3}{4} \\ x=\frac{15}{4} \\ x=3.75\text{ tablespoons} \end{gathered}[/tex]

It is needed 3.75 tablespoons of the concentrate.

what angle is Supplementary to angle 2 and what are the Verticle angles in this picture?

Answers

Suplementary angle = 180° - angle 2

is Angle 1,

because Angle 2 + Angle 1 = 180°

Part 2. Vertical angles are

Angles 2 and 5

The time spent waiting in the line is approximately normally distributed. The mean waiting time is 5 minutes and the standard deviation of the waiting time is 3 minutes. Find the probability that a person will wait for more than 1 minute. Round your answer to four decimal places.

Answers

We were given the following details:

This is a normal distribution. Normal distributions are solved using the z-score

[tex]\begin{gathered} \mu=5min \\ \sigma=3min \end{gathered}[/tex]

The z-score for a value, X is calculated using the formula:

[tex]\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ The\text{ probability that a person will wait more than 1 minute implies that: }X=1 \\ Z=\frac{1-5}{3} \\ Z=-\frac{4}{3} \\ At\text{ Z =}-\frac{4}{3}\text{, pvalue =}0.091759 \\ The\text{ probability that a person waits more than 1 minute is given by:} \\ P=1-0.091759 \\ P=0.908241\approx0.9082 \\ P=0.9082\text{ or }90.82\text{\%} \end{gathered}[/tex]

if you're lonely then be lonely with me but I need your help

Answers

Assuming question is:[tex]-5(7+x)+2\frac{5}{6}x=0[/tex]

Let's use distributive property to simplify:

[tex]-35-5x+2\frac{5}{6}x=0[/tex]

Now we add up the x's and take number to another side:

[tex]\begin{gathered} -5x+2\frac{5}{6}x=35 \\ -2\frac{1}{6}x=35 \end{gathered}[/tex]

We make 2 and one-sixth into improper fraction and divide to get x:

[tex]\begin{gathered} -\frac{13}{6}x=35 \\ x=\frac{35}{-\frac{13}{6}} \\ x=35\cdot-\frac{6}{13}=-\frac{210}{13} \end{gathered}[/tex]

x is "minus 210 over thirteen"

The sum of three consecutive integers is -39. What are the three numbers? Enter your answer as three numbers separated by a comma.

Answers

Answer:

-12, -13, and -14

Explanation:

x, y, and z are the three consecutive numbers and they sum -39, so we can write the following equation

x + y + z = -39

Since these numbers are consecutives, we get

y = x + 1

z = x + 2

So, replacing these equation on the first one and solving for x, we get

x + y + z = -39

x + (x + 1) + (x + 2) = -39

x + x + 1 + x + 2 = -39

3x + 3 = -39

3x + 3 - 3 = -39 -3

3x = -42

3x/3 = -42/3

x = -14

Then, y and z are

y = -14 + 1 = -13

z = -14 + 2 = -12

Therefore, the consecutive numbers are

-12, -13, and -14

what is the GCF of 6x+18/x^2-x-12

Answers

The GCF of the expression 6x+18/x^2-x-12 is (x+3)

How to find the GCF of the expression?

The GCF (Greatest Common Factor) of two or more numbers or expressions is the greatest number or expression among all the common factors of the given numbers or expressions

Given 6x+18/x²-x-12

We can write  6x+18/x²-x-12 as:

6x+18/x²-x-12 = 6x+18/x²-4x+3x-12          By factorization:

                       = 6(x+3) / (x+3)(x-4)

Since (x+3) is common to both the numerator and the denominator. Therefore, the greatest common factor (GCF)  is (x+3)

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Point-Slope Form: y + 2 = -7(x − 4)Rewrite the equation in slope-intercept form

Answers

Given the equation of a line in Point-Slope Form:

[tex]y+2=-7(x-4)[/tex]

You need to rewrite it in Slope-Intercept Form:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

Then, you have to solve for "y":

1. Apply the Distributive Property on the right side of the equation. Remember the Sign Rules for Multiplication:

[tex]\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}[/tex]

Then:

[tex]y+2=(-7)(x)+(-7)(-4)[/tex][tex]y+2=-7x+28[/tex]

2. Apply the Subtraction Property of Equality by subtracting 2 from both sides of the equation:

[tex]y+2-(2)=-7x+28-(2)[/tex][tex]y=-7x+26[/tex]

Hence, the answer is:

[tex]y=-7x+26[/tex]

What is the coordinate of the midpoint of S the midpoint of ST write your answer as an integer or a decimal or mixed number in simple Form.

Answers

We have a segment ST in a number line.

We can calculate the midpoint M as the average of the position of the endpoints S and T.

The position of S is 11 and the position of T is 13, so the midpoint will be:

[tex]M=\frac{S+T}{2}=\frac{11+13}{2}=\frac{24}{2}=12[/tex]

Answer: the midpoint is 12.

Valerie drives 400 meters up a hill that makes an angle of 20° with thehorizontal. To the nearest tenth of a meter what horizontal distance hasshe covered? A.425.7mt B.375.9mt C.1169.5mt or D.136.8mt

Answers

Given:

Valerie drives 400 meters up a hill that makes an angle of 20° with the horizontal.

To find:

The horizontal distance she has covered.

Solution:

The figure showing the scenario is as follows:

Let the horizontal distance traveled be x meters.

The horizontal distance traveled can be obtained using the trigonometric function cosine.

In the figure,

[tex]\begin{gathered} \cos 20=\frac{x}{400} \\ 0.94=\frac{x}{400} \\ x=400\times0.93969 \\ x=375.877 \end{gathered}[/tex]

Thus, the horizontal distance covered is 375.9 ft.

Thus, option B is correct.

320000 in decimal form

Answers

Answer:

320×10³

Step-by-step explanation:

This is the standard form for the number 320000

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What's the equation of the axis of symmetry of g(x)=x^{2}+4 x+3?A) x=0B) x=-2C) x=2D) x=3

Answers

Given a quadratic equation of the form:

[tex]f(x)=ax^2+bx+c[/tex]

The equation of the axis of symmetry is obtained using the formula:

[tex]x=-\frac{b}{2a}[/tex]

From the given quadratic equation:

[tex]\begin{gathered} g\mleft(x\mright)=x^2+4x+3 \\ a=1 \\ b=4 \end{gathered}[/tex]

Therefore, the equation of the axis of symmetry of g(x) is:

[tex]\begin{gathered} x=-\frac{4}{2\times1} \\ x=-2 \end{gathered}[/tex]

The correct option is B.

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Express M in terms of B and n: B = 3Mn 2 A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 9.5 ft by 5.5 ft by 9 ft. The container is entirely full. If, on average, its contents weigh 0.99 pounds per cubic foot, and, on average, the contents are worth $4.37 per pound, find the value of the containers contents. Round your answer to the nearest cent. what are the differences in methodology for assessing a cancer risk versus a non-cancer risk associated with environmental exposure to chemical contaminants? A set of pool balls contains 15 balls numbered 1-15.Without replacement: What is the probability that an odd number ball is pickedout of a box twice without the first one being replaced?With replacement: What is the probability that an even number ball is picked withthe first ball drawn being inserted back into the box? Write a paragraph/story using the following words: (expedition/ outdated/ equipment/ numb/ accomplishment/ brave/ vital) write 3500 in units with the appropriate prefixes A food truck vendor determined that 42% of his customers order a beverage with their food. What is the ratio of customers who order a beverage to customers who do not order a beverage? rebecca siddoway own and operate country candies. siddoway specializes in making rich, creamy toffees that she packages in attractive gift boxes and sells through the mail. what would be the advantage to siddoway if she decides to incorporate her business? I got the last question right that was similar so Im unsure what Im doing wrong for this one What is the volume of this triangle right prism 8 cm 15 cm 12 cm is the equation below represent a direct proportion. if so what is the constant 3x + 4 = y Put the following equation of a line into slope-intercept form, simplifying all fractions.4x + 20y = -180 Given the function [tex]y=(m^2-1)x^2+2(m-1)x+2[/tex] , find the values of parameter m for which the function is always positive. a firm wants to use an option to hedge 12.5 million in receivables from new zealand firms. the premium is $.03. the exercise price is $.55. if the option is exercised, what is the total amount of dollars received (after accounting for the premium paid)? group of answer choices Refer to your equation for the line that models the association between latitude and temperature of the cities: Yours y = -12 + 120 Computer calculated y = -1.07 + 119 What does the slope mean in the context of this situation? Point(2,8) , (4,7.5) rise over run so what's the answer determine which statements below are correct regarding merchandise available for sale during a period. (check all that apply.)multiple select question.beginning inventory ending inventory someone please help me Shade in 0.71 of the whole. With aging body fat increases in muscle mass declines the graph to the right shows the percent body fat in a group of adult women and men as they age from 25 to 75 years age is represented along the X-axis and percent body fat is represented along the Y-axis use interval notation to give the domain and range for the graph of the function for women Ride 'em Rodeo is a traveling rodeo show. Last night, there were 5 people wearingboots at the rodeo for every 2 people who were not wearing boots. If there were 125 people wearing boots at the rodeo last night, how many people werethere altogether?