Write the equation of the circle with the given information: Center: (3,-3) Radius: 2sqrt{6} ​

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:

https://brainly.com/question/10662770

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.

Step-by-step explanation:

side of square = 10

area of square = side² = 10² = 100 cm²

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

Use the Distributive Property, which states the following:-

[tex]\sf{a(b+c)=ab+ac}[/tex]

Where

we distribute a by multiplying it times b and c

a, b, and c can be either constants (numbers) or variables (letters)

Distribute:-

[tex]\sf{\displaystyle\frac{1}{4}(x+24)}}[/tex]

Multiply the term before the parentheses by the terms inside the parentheses:-

[tex]\sf{\displaystyle\frac{1}{4} x+6}}[/tex]

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

➾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 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:

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

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:

- The inequality translated in numerical form

Step-by-step explanation:

Answer:

g(x) = 4x + 5

Step-by-step explanation:

f(x) + g(x) = 10x + 7 , then

6x + 2 + g(x) = 10x + 7 ← subtract 6x + 2 from both sides

g(x) = 10x + 7 - 6x - 2 ← collect like terms

g(x) = 4x + 5

Let's find

Option D

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

Answer:

30 days

Step-by-step explanation:

1.5 Kg = 1500 g

Using 50 g a day

Number of days

= 1500 / 50

= 30 days.

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

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:

Take lcm and see

Step-by-step explanation:

5/27 ;4/15 ;7/18

Answer:

[tex] {x}^{2} = {8.6}^{2} + {11.5}^{2} \\ {x}^{2} = 73.96 + 132.25 \\ x = \sqrt{206.21} \\ x = 14.185 \\ x = 14.19[/tex]

14.19

Answer: [tex]560m^2[/tex]

Step-by-step explanation:

First begin by finding the surface area of the base, which is simply length * width. In this case,

[tex]14*14 = 196 m^2[/tex]

Next, find the surface area of one of the sides of the pyramid. This formula for this is:

[tex]\frac{1}{2}*base*height[/tex]

Since we know the height to be 13 meters and the base to be 14 meters, we can solve for one side.

[tex]\frac{1}{2}*14*13 = 91 m^2[/tex]

We multiply this by 4 to give us all 4 sides of the pyramid:

[tex]91m^2 * 4 = 364m^2[/tex]

Adding together the surface area of the sides and the base gives us:

[tex]196m^2 + 364m^2=560m^2[/tex]

Answer:

Answer:

The cross product is 47 i - 61 j + 17 k.

Step-by-step explanation:

Given that-

a = < -1, -3, -8 > , b = < 7, 4, -5 >

The cross product is

a × b =\begin{gathered}\left[\begin{array}{ccc}i&j&k\\-1&-3&-8\\7&4&-5\end{array}\right]\end{gathered}⎣⎢⎡i−17j−34k−8−5⎦⎥⎤

        = i ( - 3 × -5 - 4 × -8 ) - j ( -1 × -5 - (-8) × 7 ) + k ( -1 × 4 - 7 × -3 )

        = i ( 15 + 32 ) -j ×( 5 + 56 ) + k ( -4 + 21 )

        = i ( 47) - j (61 ) + k (17)

        = 47 i -61 j + 17 k

As we know that if two vectors A & B are perpendicular then

A . B = 0

So here only the given vector b = < 7,4, -5> is perpendicular to the resulting vector .

Step-by-step explanation:

47, -61, 71>; yes

Answer:

x(x-2)

Step-by-step explanation:

x^2−2x

Factor out an x

x(x-2)

This is not a special product

Answer:

I think it is 12 4/5

Step-by-step explanation:

hope this helps if not let me now

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:

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:

whats the problem it doesnt say anything

Answer:

x=4, y=9

Step-by-step explanation:

Solve with substitution.

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!

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:

$1540.80

Step-by-step explanation:

Answer: 1540.80

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