Which of the following numbers is rational?

Multiplying z₁ and z₂ involves calculating their products

The product of z₁ and z₂ is r₁r₂(cos(Θ₁ + Θ₂) + isin(Θ₁ + Θ₂))

The numbers are given as:

z₁ = r₁(cosΘ₁ + isinΘ₁)

z₂ = r₂(cosΘ₂ + isinΘ₂)

The product is represented as:

z₁ * z₂ = r₁(cosΘ₁ + isinΘ₁) * r₂(cosΘ₂ + isinΘ₂)

This gives

z₁ * z₂ = r₁r₂(cosΘ₁ + isinΘ₁) (cosΘ₂ + isinΘ₂)

Expand

z₁ * z₂ = r₁r₂(cosΘ₁cosΘ₂ + icosΘ₁sinΘ₂+ isinΘ₁cosΘ₂  + i²sinΘ₁sinΘ₂ )

In complex numbers,

i² = -1.

So, we have:

z₁ * z₂ = r₁r₂(cosΘ₁cosΘ₂ + icosΘ₁sinΘ₂+ isinΘ₁cosΘ₂  - sinΘ₁sinΘ₂ )

Rewrite as:

z₁ * z₂ = r₁r₂(cosΘ₁cosΘ₂  - sinΘ₁sinΘ₂ + icosΘ₁sinΘ₂+ isinΘ₁cosΘ₂  )

Apply sine and cosine ratios

z₁ * z₂ = r₁r₂(cos(Θ₁ + Θ₂) + isin(Θ₁ + Θ₂))

Hence, the product of z₁ and z₂ is r₁r₂(cos(Θ₁ + Θ₂) + isin(Θ₁ + Θ₂))

Read more about complex numbers at:

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Answer:

47

Step-by-step explanation:

because you know that a triangle is 180 degrees and you have the other two degrees, so all you have to do is add 90 (the little box in the corner means 90) +43=133 and subtract by 180 giving you 47 as your answer.

Answer:

Heya! ^^

let's first look at some terms that may help us understand the concept of the question better.

______________________________________

★ Angle sum property of triangle states that the sum of all the angles of a triangle equals 180°

______________________________________

now let's come over what the question says.

we've been given a right angled triangle with measure of one of its angle as 43°.

we've to calculate the measure of the third angle named " x "

therefore ,

[tex]by \: angle \: sum \: property \: of \: triangle \\ \\ 90\degree + 43\degree + x = 180\degree \\ \\ 133\degree + x = 180\degree \\ \\ x = 180\degree - 133\degree \\ \\ x = 47\degree[/tex]

thus the measure of x is 47°.

hope helpful :D

Answer:

A

Step-by-step explanation:

Hey there!

In this question, it is asking us what table doesn't have a proportional relationship

In table A, there is no seen relation ship between the numbers, columns, or rows

In all of the other tables, the numbers in each column is increasing by a number again and again meaning A is the incorrect table.

Answer:

A i believe

Step-by-step explanation:

Its not B because it is proportional by 0.6666666

Its not C because it is proportional by 3

It not D because its proportional by 1.33333333

Please mark as brainliest

Answer:

m3 and m4 are supplementary

Step-by-step explanation:

since m3 and m4 are supplementary, we can state that m3 and m4 are supplementary
see full explanation in the vid below

Hii!

let me answer this for you before i head out!

So, how many days are in 1 week? 7.

To rent daily, we need to find out the price for 1 single month.

1 month is $154

7 times what is 154?

7x22 is 154

Therefore, to rent a room everyday, it would cost 22$ for the first month.

437 divided by 2 is 218

218 divided by 7 is 31

Hope it helps

Sorry if its wrong!

Answer:

soln,

a

y=5/4×-15

Answer:

C: y = -5/4x - 15

Step-by-step explanation:

A perpendicular line is always the negative reciprocal of the slope. In this case, the slope is 4/5. Therefore, the negative reciprocal is -5/4. Only look at the numbers connected to X for the slope, do not look at the constant.

Answer:

210

Step-by-step explanation:

There are 7 choices for president.

Then there are 6 choices for vice-president.

Finally, there are 5 choices for treasurer.

7 × 6 × 5 = 210

Answer:

Take lcm and see

Step-by-step explanation:

5/27 ;4/15 ;7/18

q=w/ 3-7

q(3-7)= w

hope this helps :)

Answer:

w = 3q + 21

Step-by-step explanation:

assuming you mean

q = [tex]\frac{w}{3}[/tex] - 7 ( add 7 to both sides )

q + 7 = [tex]\frac{w}{3}[/tex] ( multiply both sides by 3 to clear the fraction )

3(q + 7) = w , that is

w = 3q + 21

Answer:

The weight, in pounds, of one bag of beans.

Step-by-step explanation:

Since we know that there are 15 bags of beans, we can eliminate the first option and anything about something other than th e beans. Also, we know that we are not given the information on how heavy the bag of beans are, so with process of elimination, the 3rd one is the answer.

I hope this helped!

It would be greatly appreciated if you marked this answer as brainliest!

Answer:

If I am correct to work out the surface area you need to do base times height so the calculation would be...

32(base) × 30(height)

which equals 960 square inches

Please do check with someone else the answer, as I am not that confident and new

The cost of similar carpet in the client's bedroom is $225

Given Data

if 307.2 square feet of carpet will cost $576

the 120 square feet of carpet will cost $x

cross multiplying we have

x = 120*576/307.2

x = 69120/307.2

x = $225

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Answer:

b and d option are correct

Answer:

B, D

Step-by-step explanation:

B, D

x cannot be in a root.  (A)

x cannot be in the denominator.  (C)

Answer:

Step-by-step explanation:

Surface area of rectangular prism:

length = l = 20 in

width = w = 12 in

height = h = 5 in

[tex]\boxed{\text{surface area of rectangular prism = 2*[lw + wh + hl]}}[/tex]

                                              = 2* [ 20*12 + 12*5 + 5*20]

                                              = 2* [240 + 60 + 100]

                                               = 2 * 400

                                               = 800 in²

Using the vertex of the quadratic equation, it is found that a maximum height of 78.75 feet is reached after 2.13 seconds.

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

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

[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]

Considering the coefficient a, we have that:

In this problem, the height is modeled by:

h(t) = -16t² + 68t + 6.5.

The coefficients are a = -16, b = 68, c = 6.5, and the vertex will be given by:

[tex]x_v = -\frac{b}{2a} = -\frac{68}{-32} = 2.13[/tex]

[tex]y_v = -\frac{b^2 - 4ac}{4a} = -\frac{68^2 - 4(-16)(6.5)}{-64} = 78.75[/tex]

A maximum height of 78.75 feet is reached after 2.13 seconds.

More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967

The time it would take to travel a distance of 640 kilometers is 1 hour

From the question, we are to determine how long it would take the airplane to travel a distance of 640 kilometers.

From the give information,

The airplane flies with a constant speed of 640 km/h.

Speed = 640 km/h

Distance to be covered = 640 km

From the formula,

[tex]Speed = \frac{Distance}{Time}[/tex]

We can write that

[tex]Time= \frac{Distance}{Speed}[/tex]

∴ [tex]Time = \frac{640 \ km}{640 \ km/h}[/tex]

Time = 1 hour

Hence, the time it would take to travel a distance of 640 kilometers is 1 hour

Lear more on Speed, distance and time here: https://brainly.com/question/17146782

Answer:

$1540.80

Step-by-step explanation:

Answer: 1540.80

Step-by-step explanation: i got it right on my ixl

Answer:

Step-by-step explanation:

Answer:

whats the problem it doesnt say anything

Step-by-step explanation:

- The distance traveled to get to the top of the hill will be equal to the distance traveled to get to the bottom of the hill. Distance down the hill = Distance up the hill = 187.5 meters.

- Only the speed of going up the hill and down the hill will be different.

Answer:

The question is not showing what we are supposed to find.

b+3b+10

Answer:

30 days

Step-by-step explanation:

1.5 Kg = 1500 g

Using 50 g a day

Number of days

= 1500 / 50

= 30 days.

➾Firstly, we will find the measure of [tex]\angle[/tex]ACB.

We know that,

Sum of all interior angles of a triangle = 180°.

[tex]\rightarrow[/tex][tex]\angle[/tex]BAC + [tex]\angle[/tex]ABC + [tex]\angle[/tex]ACB = 180°

[tex]\rightarrow[/tex] 40°+70°+[tex]\angle[/tex]ACB = 180°

[tex]\rightarrow[/tex] 110°+[tex]\angle[/tex]ACB = 180°

[tex]\rightarrow[/tex] [tex]\angle[/tex]ACB = 180°-110°

[tex]\rightarrow[/tex][tex]\angle[/tex]ACB = 70°

So, the measure of [tex]\angle[/tex]ACB = 70°.

➾ Side BC of the triangle is extended till D. So, we have to find the measure of [tex]\angle[/tex] ACD.

As we know that,

Sum of any two or more angles that lie on a straight line = 180°.

So, [tex]\sf\angle{ACB}[/tex]+[tex]\sf\angle{ACD}[/tex] = 180°

[tex]\rightarrow[/tex] 70° + [tex]\sf\angle{ACD}[/tex] = 180°

[tex]\rightarrow[/tex][tex]\sf\angle{ACD}[/tex] = 180°-70°

[tex]\rightarrow[/tex][tex]\sf\angle{ACD}[/tex] = 110°.

Therefore, measure of [tex]\sf\angle{ACD}[/tex] = 110°.

____________________________

Hope it helps you:)

The vectors u = ❬6, –9❭ and v = ❬–24, 36❭ are parallel to each other because the cosine of the angle θ is equal to -1. (Right choice: A)

By linear algebra we can use the definition of dot product to determine the relationship between two vectors, whose cases are described below:

And the expression for the cosine of the angle between the two vectors is:

[tex]\cos \theta = \frac{\vec u \,\bullet\,\vec v}{\|\vec u\|\cdot \|\vec v\|}[/tex]     (1)

Where [tex]\|\vec u\|[/tex] and [tex]\|\vec v\|[/tex] are the norms of the two vectors, which are determined by Pythagorean theorem.

Now we proceed to calculate the angle between the two vectors:

[tex]\cos \theta = \frac{(6)\cdot (-24)+(-9)\cdot (36)}{(3\sqrt{13})\cdot (12\sqrt{13})}[/tex]

cos θ = -1

Thus, the vectors u = ❬6, –9❭ and v = ❬–24, 36❭ are parallel to each other because the cosine of the angle θ is equal to -1. (Right choice: A)

To learn more on vectors, we kindly invite to check this verified question: https://brainly.com/question/13322477

Answer:

x(x-2)

Step-by-step explanation:

x^2−2x

Factor out an x

x(x-2)

This is not a special product

The given expression is the square of a binomial, such that:

(2x + 1)^2 = 4x^2 + 4x + 1

Then the correct option is C.

We want to see if:

(2x + 1)^2

Is equivalent to (4x^2 + 1).

First, this is false, let's prove that.

We have the square of a binomial (2x + 1)^2. Remember the general formula:

(a + b)^2 = a^2 + 2ab + b^2

So if we apply this to our expression we get:

(2x + 1)^2 = (2x)^2 + 2*2x*1 + 1^2 = 4x^2 + 4x + 1

Then, the correct option is C.

If you want to learn more about binomials, you can read:

https://brainly.com/question/15246027

Step-by-step explanation:

side of square = 10

area of square = side² = 10² = 100 cm²

P.S : ARE YOU SURE THE OPTIONS ARE CORRECT ???