Answer:
I've done this b4
(0, 1), (2, 7), (3, 4), (-4, 1) , (-6, 7)
[30 PTS!!] Using mathematically precise language, explain in detail how you would multiply the complex number [tex]z_1=r_1(cos[/tex]θ[tex]_1+i sin[/tex]θ[tex]_1)[/tex] with the complex number [tex]z_2=r_2(cos[/tex]θ[tex]_2+isin[/tex]θ[tex]_2)[/tex].
Multiplying z₁ and z₂ involves calculating their products
The product of z₁ and z₂ is r₁r₂(cos(Θ₁ + Θ₂) + isin(Θ₁ + Θ₂))
How to multiply the complex numbers?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))
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Please help with this problem.
Answer:
whats the problem it doesnt say anything
Complete the reasons for the proof.
given:
m 3 = m 4
Prove 1 and 2 are supplementary
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
. The difference between the length and width of a rectangle is
7 cm. The perimeter of the rectangle is 22 cm. Find the length
and the width. (Remember, P= 21 + 2w.)
Answer:
Rectangle
Solve for length
l=4cm
w Width
7
cm
P Perimeter
22
cm
Using the formula
P=2(l+w)
Solving forl
l=P
2﹣w=22
2﹣7=4cm
What is the surface area? 34 in 30 in 34 in 32 in 36 in
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
Please help I will give brainliest.
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!
Jack has $1,331 in an account that earns 5% interest compounded annually.
To the nearest cent, how much will he have in 3 years?
Answer:
$1540.80
Step-by-step explanation:
Answer: 1540.80
Step-by-step explanation: i got it right on my ixl
determine how many ways a president, vice president and treasurer can be chosen from a math club that has 7 members.
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
Which expressions are polynomials?
Select each correct answer.
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)
Which of the following lines is perpendicular to the line with this equation ?
y =4/5X – 12
a. y= -4/5x +9
b. y=5/4x +4
c. y= -5/4x -15
d.y= 4/5x -5
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.
1. Which quadratic equation has 5 and - 4 as its solutions?
Answer:
x²-x-20
Step-by-step explanation:
Using Vieta's formula
x²-(sum of roots)x+(product of roots)=0
x²-(5+-4)x+(5×-4)=0
x²-x-20=0
Factor x^2−2x. Is this a special product?
Answer:
x(x-2)
Step-by-step explanation:
x^2−2x
Factor out an x
x(x-2)
This is not a special product
help , i need to finish this today :)
Use the equation of the curve of best fit to predict what the daily rental price for a two-bedroom condo will be in June and in January.
Type the correct answer in each box.
The daily rental price will be $ _____in June and $ _____ in January.
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!
In the figure shown, what is the measure of angle x?
Triangle ABC has measure of angle BAC equal to 40 degrees and the measure of angle ABC is equal to 70 degrees. The side BC of the triangle is extended till D. The angle ACD is labeled as x.
100 degrees
110 degrees
120 degrees
140 degrees
➾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:)
Val is going to plant b vegetable seeds in one garden and 3b + 10 vegetable seeds in another. How
many seeds is Val going to plant?
Val is going to plant seeds.
Answer:
The question is not showing what we are supposed to find.
b+3b+10
2.56x+0.14-187x
How to solve pls and answer
If u = ❬6, –9❭ and v = ❬–24, 36❭ with an angle θ between the vectors, are u and v parallel or orthogonal? Explain.
The vectors are parallel because cos θ = −1.
The vectors are parallel because u • v = 0.
The vectors are orthogonal because u • v = 0.
The vectors are orthogonal because cos θ = −1.
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)
How to determine the relationship between two vectors
By linear algebra we can use the definition of dot product to determine the relationship between two vectors, whose cases are described below:
Two vectors are orthogonal if and only if cos θ = 0.Two vectors are parallel if and only if cos θ = 1 or cos θ = -1.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
can someone help me.
Step-by-step explanation:
side of square = 10
area of square = side² = 10² = 100 cm²
P.S : ARE YOU SURE THE OPTIONS ARE CORRECT ???
C is a circle with centre (0,0)
L is a straight line with negative gradient.
The circle C and the line L intersect at the points A and B.
The coordinates of A are (-9,2)
The x coordinate of B is 7
Find an equation of L.
Answer:
Step-by-step explanation:
Which of the following tables does NOT show a proportional relationship?
A
B
C
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
rearrange q=w/3-7 to make w the subject
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
The flight of javelin released 6.5 feet from the ground at an initial velocity of 68 feet per second is modeled by the function h=-16^2+6.5 where h is the height of the javelin in feet after r seconds . Determine how many seconds it will take the javelin to reach the maximum height and find the maximum height. Round to the nearest hundredth if necessary
Using the vertex of the quadratic equation, it is found that a maximum height of 78.75 feet is reached after 2.13 seconds.
What is the vertex of a quadratic equation?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:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.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
Work out the size of angle x.
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
jason is wrapping a gift.The box he is using is a rectangular prism with a length of 20 inches a width 12 inches and a height of 5 inches.Find how many square inches of paper does he need to wrap the intire box?
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
Suppose that a classmate asked you why (2x + 112 is not (4x² + 1). What is your response to this classmate?
O A. An expression such as (2x + 1)2 is called the square of a monornial. The expression (2x + 1)2 is equal to (22• 2xX1. 1), thus it is not equivalent to
(4x2 +1)
B. The classmate is correct. An expression such as (2x + 1)2 is called the square of a binomial. The expression (2x + 1)2 is equal to (2)?(x} = (132, thus it is
equivalent to (4x + 1)
OC. An expression such as (2x + 1)2 is called the square of a binomial. The expression (2x + 1)2 is equal to (2x+ 1x2x + 1), thus it is not equivalent to
(4x + 1)
OD. An expression such as (2x + 1)2 is called the product of the sum and difference of two terms. The expression (2x + 1)2 is equal to (2x+ 1(2x - 1), thus it is
not equivalent to (4x2 + 1)
+
The given expression is the square of a binomial, such that:
(2x + 1)^2 = 4x^2 + 4x + 1
Then the correct option is C.
Are the expressions equivalent?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:
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4/15, 5/27, 7/18 Arrange the fractions in ascending order
Answer:
Take lcm and see
Step-by-step explanation:
5/27 ;4/15 ;7/18
Help me with this assignment please I don’t understand it
An airplane flies with a constant speed
of 640 km/h. How long will it take to
travel a distance of 640 kilometers?
The time it would take to travel a distance of 640 kilometers is 1 hour
Speed, distance and timeFrom 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
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The carpet for the office you completed cost $576. If you're using the same carpet in the new client's bedroom, how much will it cost? Round up to the nearest whole dollar. (Hint: You may want to find the area of each room and the cost of the carpet per square foot.)
$360 $280 $64 $225
with explanation please
The cost of similar carpet in the client's bedroom is $225
Given Data
Cost of Carpet = $576Area of Office = 16*19.2 = 307.2 square feetArea of Bedroom = 12*10 = 120 square feetif 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
Learn more about area of shapes here:
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3 A packet contains 1.5 kg of oats.
oats
OO
1.5kg
Every day Maria uses 50 g of oats to make porridge.
How many days does the packet of oats last?
Answer:
30 days
Step-by-step explanation:
1.5 Kg = 1500 g
Using 50 g a day
Number of days
= 1500 / 50
= 30 days.
