Express the following division in the form of a + bi: (1+3i)(2+i)

Answers

Answer 1

Answer:

[tex](1 + i\,3) \cdot (2 + i) = -1 + i\,7[/tex]

Step-by-step explanation:

We proceed to present the procedure by algebraic means:

1) [tex](1 + i\,3)\cdot (2 + i)[/tex] Given

2) [tex]2\cdot (1 + i\,3) + i\,(1+i\,3)[/tex] Distributive and Commutative Properties

3) [tex]2 + i\,6 + i + i^{2} \,3[/tex] Distributive, Commutative and Associative Properties

4) [tex]2 + i\,7 -3[/tex] Definition of imaginary number/Distributive, Commutative and Associative Properties

5) [tex]-1 + i\,7[/tex] Commutative and Associative Properties


Related Questions

Solve for y:

76y = 19

Y =2/3
Y = 1/4

Answers

Answer:

y = 1/4

Step-by-step explanation:

76y = 19.

Get rid of the 76 by dividing 76 from both sides.

76y/76 = 19/76

19/76 simplified is 1/4.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{76y = 19}[/tex]

[tex]\textbf{DIVIDE 76 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{76y}{76} = \dfrac{19}{76}}[/tex]

[tex]\textbf{SIMPLIFY it}[/tex]

[tex]\mathsf{y = \dfrac{19}{76}}[/tex]

[tex]\mathsf{y = \dfrac{19\div19}{76\div19}}[/tex]

[tex]\mathsf{y = \dfrac{1}{4}}[/tex]

[tex]\huge\text{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\mathsf{y = \dfrac{1}{4}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

4feet times 15inches

Answers

This what I use on my phone to get an answer


Which represents g(x), the translated function?
O g(x) = (x + 4)3 + 6
O g(x) = (x – 4)3 + 6
O g(x) = (x + 6)3 – 4
O g(x) = (x - 6)2 - 4

Answers

Answer:

Im pretty sure its A but not 100% sure-

Step-by-step explanation:

Someone help out with this

Answers

Answer:

k <= 11

Step-by-step explanation:

8+k <= -3

k <= -3 -8

k <= 11

Mind answering this? It's due in a few days and I'll give the correct answer Brainliest.

Match the values of a, b, and c given the equation in the standard form below:

h = -16t^2 + 8t + 24

Answers

Answer:

a = -16  b = 8 and c =24

Step-by-step explanation:

h = -16t^2 + 8t + 24

A quadratic function can be in the form

ax^2 + bx+c

Replace x with t

-16 is the coefficient of the squared term  8 is the coefficient of the linear term and 24 is the constant

a = -16  b = 8 and c =24

SS below of my question

Answers

Answer:

its blurry

Step-by-step explanation:

Answer:

arccos(.34) = 70.12 ≈ 70

Step-by-step explanation:

Need help what would it be

Answers

2x-54 and x + 22 are vertical angles and equal each other. Set the two equations equal to each other and solve for x.

2x -54 = x + 22

Add 54 to both sides:

2x = x + 76

Subtract 1x from each side:

X = 76

The answer is x = 76

Don’t answer if you don’t know thanks. No links!

Answers

Answer:

12 by 12

Step-by-step explanation:

The area of a square is [tex]s^2[/tex], where [tex]s[/tex] is side length of the square. Therefore, we have:

[tex]s^2=144,\\s=\sqrt{144}=12[/tex]

Since all side lengths of a square are equal, the dimensions are 12 by 12.

Answer:

Step-by-step explanation:

area of square=l^2

144=l^2

[tex]\sqrt{144[/tex]=l

12=l

therefore the dimensions of square is 12 x 12.

Help please will be marked as brainliest if correct

Answers

Answer:

12.95

Step-by-step explanation:

1. 173.43

2. 325.54

3. 0.6794

4. 76.45

Unlock number: 12.95

Answer:

173.43

325.54

.6794

76.45

Step-by-step explanation:

A cone has a height of 16 feet and a radius of 6 feet. What is its volume? Use ​ ≈ 3.14 and round your answer to the nearest hundredth.

Answers

Answer:

602.88 ft^3

Step-by-step explanation:

(6^2)(3.14)(16)(1/3) = 602.88

Answer:

Step-by-step explanation:

V=1/3 πr²h

=1/3×π×6²×16

=192 π

≈192×3.14

≈602.88 ft³

can someone please help me with this? PLEASE I'm so confused.

Answers

Answer:   5005

==================================================

Explanation:

Let's say we had the slots A,B,C,D,E,F. Each slot represents where a flower would go.

For slot A, we have 15 different flowers to pick from.

Then slot B has 15-1 = 14 choices

C has 15-2 = 13 choices

and so on. We count our way down until we fill up slot F.

The count down looks like this: 15, 14, 13, 12, 11, 10

Multiply out those values: 15*14*13*12*11*10 = 3,603,600

If order mattered, then this represents the number of ways to select 6 flowers from a pool of 15 total.

However, order does not matter in this case. All that matters is the group overall.

For any group of 6 items, we have 6! = 6*5*4*3*2*1 = 720 different arrangements. That means the value 3,603,600 is too large exactly by a factor of 720.

We divide by 720 to get to (3,603,600)/720 = 5005 which is the final answer

It's the number of combinations where we select 6 from a pool of 15.

-------------------------------

As you can guess, you could use the nCr combination formula as an alternative route. Plug in n = 15 and r = 6 like so

[tex]_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{15} C _{6} = \frac{15!}{6!*(15-6)!}\\\\_{15} C _{6} = \frac{15!}{6!*9!}\\\\_{15} C _{6} = \frac{15*14*13*12*11*10*9!}{6!*9!}\\\\_{15} C _{6} = \frac{15*14*13*12*11*10}{6!}\\\\_{15} C _{6} = \frac{15*14*13*12*11*10}{6*5*4*3*2*1}\\\\_{15} C _{6} = \frac{3,603,600}{720}\\\\_{15} C _{6} = 5005\\\\[/tex]

In the third to last step, notice how we have the 15*14*13*12*11*10 up top and 6*5*4*3*2*1 down below.

This value 5005 can be found in Pascal's Triangle. Look in the row that has 1, 15, ... and count out 7 spaces from the left. You should arrive at 5005. However, you'll need a fairly large Pascal's Triangle to use this method.

Given:

Total number of flower cuts = 15 different flowers

Number of flowers Jeanine Baker wants to use = 6 flowers

To find:

Total number of ways 6 flowers can be chosen

Steps:

In this question, we need to find the total number of outcomes of choosing 6 random flowers from a total of 15 flowers

Let's give each flowers a letter, so there will be A, B, C, D, E, F, G, H, I, J, K, L, M, N and O.

Now let's find all the outcomes

Outcomes= ABCDEF, ABCDEG, ABCDEH, ABCDEI, ABCDEJ, ABCDEK, ABCDEL, ABCDEM, ABCDEN, ABCDEO.....

This method will take a lot of time so, i am going to use the formula

[tex]No.outcomes = \frac{n!}{r!(n-r)!}[/tex]

Here n = total number of items, and r = number of items chosen

Also the '!' means factorial, or the product of all positive numbers less then or equal to the number, so n! = n * (n-1) * (n-2) ..... * 1

So, now substituting the formula

[tex]No.outcomes = \frac{15!}{6! * (n-r)!}[/tex]

[tex]No.outcomes=\frac{15!}{6! * 9!}[/tex]

[tex]No.outcomes = \frac{15*14*13*12*11*10*9*8*7*6*5*4*3*2*1}{6*5*4*3*2*1*9*8*7*6*5*4*3*2*1}[/tex]

[tex]No.outcomes=\frac{15*14*13*12*11*10}{6*5*4*3*2*1}[/tex]          (cutting same numbers)

[tex]No.outcomes = \frac{7*13*3*11*10}{6}[/tex]                 (simplifying)

[tex]No.outcomes = \frac{30030}{6}[/tex]

[tex]No.outcomes=5005[/tex]

Therefore, the total number of ways the 6 flowers can be chosen is 5005 ways

Happy to help :)

If u need help in this topic feel free to ask

pleaseplease Help mee

Answers

Answer:

B. What is the average amount of points Jenny Ortiz scores in a game?

Step-by-step explanation:

Line m passes through points (8,9) and (4,4). Line n is perpendicular to m. What is the
slope of line n?

Answers

Answer:

Step-by-step explanation:

here x1=8 , y1=9 , x2=4 , y2=4

using formula

slipe(m)=y2-y1/x2-x1

=4-9/4-8

=-5/-4

=5/4

The area of the triangle below is 4.5 square inches. What is the length of the base?

Answers

Answer:

Can you please send the length of the height if possible.

Step-by-step explanation:

Also the the formula to solve this is the exact opposite of Area= base times height divided by 2.

first step you need to do is multiply 4.5 by 2 to get 9. then you have to divide 9 by the height. Then you will get the value of the height. Hope you understood!

Answer: 3

Step-by-step explanation: 3

Need help ASAP pls I have 20 min

Answers

Answer:

x > - 8

Step-by-step explanation:

x + 5 > -3

x > - 8

Find BC
Round to the nearest tenth.
7
140°
B
13

Answers

Answer:

The answer is

Step-by-step explanation:

This is from khan academy. so You need to watch a video on khan academy to get help.

Identify the center and the radius of the circle.
(x - 1)2 + (y + 3)? = 4

Answers

Comparing with Equation of circle( x - h )²+ ( y - k )² = r²,

center of circle = (h,k) = (1,-3)

Radius of circle =√4 = 2unit

You pick a card at random.

4
5
6


What is P(4)?

Write your answer as a fraction or whole number.

Answers

Answer:

It is 1/3

Step-by-step explanation:

can i have brainly?

write an expression equivalent to h^6/h^3 in the form of h^m

Answers

Answer:

[tex]h^3 = h^m[/tex]

Step-by-step explanation:

[tex]\frac{h^6}{h^3} = h^m[/tex]

6 - 3 = 3

keep the base same, therefore

[tex]h^3 = h^m[/tex]

Hope this helps!

The equivalent expression for the given expression is h³.

What is an equivalent expression?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is h⁶/h³.

h⁶ can be written as h³×h³

= h³×h³/h³

= h³

Therefore, the equivalent expression is h³.

To learn more about an equivalent expression visit:

https://brainly.com/question/28170201.

#SPJ2

Expand and simplify:
5(x - 2) + 3(1 - x)
(with the steps)​

Answers

Step-by-step explanation:

5x-10+3-3x

5x-3x-10+3

2x-7

hope it helps

Answer:

2x-7

Step-by-step explanation:

See image below:)

what is the common factor of 2x^3-4x^2-15x

Answers

Answer:

kbsishodhohror keviegieh

Answer:

[tex]2 {x}^{3} - 4 {x}^{2} - 15x \\ = x( {2x}^{2} - 4x - 15) \\ [/tex]

Find the mean absolute deviation in the following data set: 23, 42, 36, 63, 31

Answers

Answer:

39.2 is the mean

the deviation is 15.2

Step-by-step explanation:

the mean of a set of numbers is the sum divided by the number of terms = 39.2

the deviation measures the spread of a data distribution of the sample = 15.2

Answer:

10.8

Step-by-step explanation:

To find the mean absolute deviation, first you need to find the mean. To find the mean, add up 23 + 42 + 36 + 63 + 31 and you'll get 195. Divide 195 by the total of numbers, which is 5, and you'll get 39.

After finding the mean, you need to find the distance between the mean, which is 39, and the numbers given. 23 is 16, 42 is 3, 63 is 24, 31 is 8, and 36 is 3. Then, you'll need to calculate the mean of the distances that you got.

16 plus 3 plus 24 plus 8 plus 3 = 54. Once you got this, divide 54 by the total of numbers, which is 5, and you'll get 10.8.

The girls in Lana’s troop set a goal to sell 1,000 boxes of cookies this year. There are 13 girls in the troop. At least how many boxes of cookies should each girl sell to reach their goal?

Answers

Answer:

77 boxes

Step-by-step explanation:

Step 1:

Lana's troop must sell 1000 boxes of cookies, but there are 13 girls in total. Supposing that each girl will sell an equal amount of boxes, we can simply divide:

[tex]1000[/tex]÷[tex]13\approx76.92[/tex] boxes.

Step 2:

However, it would seem unlikely that the girls would decide to sell fractions of a box of cookies. We should round...up or down?

If we round down, each girl will sell 76 boxes of cookies. Hmm... then they would'nt be able to sell a total of 1000 boxes of cookies! We need to round up.

Therefore, each girl should sell at least [tex]\fbox{77}[/tex] boxes.

I hope this helps! Let me know if you have any questions :)

Which numbers are divisible by 10?

A)635

B)950

C)953

Answers

B because it has a 0 at the end and any number that has a zero at the end is divisible by 10

Find the measure Of K

Answers

Answer:

K = 10

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/ hyp

sin K = 11 / 61

Taking the inverse sin of each side

sin ^-1 ( sin K) = sin ^-1 (11/61)

K =10.38885782

K = 10

Juan has a box that is 3 feet long , 2 feet wide ,and 3 feet high . What is the volume of the box?

Answers

Answer:

18

Step-by-step explanation:

3*3*2

9*2

18

Finding simple interest without a calculator
Diane deposits $800 into an account that pays simple interest at a rate of 5% per year. How much interest will she be paid in the first 3 years

Answers

Answer: you answer is 120.

Step-by-step explanation: all you have to do is multyply 800*.15 because that is how much present it is.

please mark me brainiest

I = prt

I= 800×0.05×3= 120

Answer- 120 $

a block is pulled 0.90m to the right in 2.4s what is the blocks average speed to the nearest hundredths of m/s

Answers

Answer:

[tex]0.38\:\mathrm{m/s}[/tex]

Step-by-step explanation:

Average velocity is given by [tex]v=\frac{\Delta x}{\Delta t}[/tex], where [tex]\Delta x[/tex] is displacement and [tex]\Delta t[/tex] is change in time.

What we know:

[tex]\Delta x[/tex] is [tex]0.90\:\mathrm{m}[/tex] [tex]\Delta t[/tex] is [tex]2.4\:\mathrm{s}[/tex]

Solving for [tex]v[/tex]:

[tex]v=\frac{0.90}{2.4}=0.375\approx\boxed{0.38\:\mathrm{m/s}}[/tex]

Bob rents a dump truck. The dump truck costs
$85 per day and $0.35 per mile. Which expression
below would help Bob figure out how much (p) the
rental will cost him for a day?

Answers

Answer:

[tex]\text{d) }p=0.35x+85[/tex]

Step-by-step explanation:

Since the 85 dollar fee is fixed, there should be no coefficient or constant that accompanies it. However, the total cost of the miles is directly proportional to the number of miles he drives. Thus, 0.35 should be accompanied by a constant that represents the total number of miles he drove. In this case, that constant is [tex]x[/tex] and [tex]0.35x[/tex] will represent the cost from the number of miles he drives in addition to the 85$ flat fee, hence [tex]\implies \boxed{\text{d) }p=0.35x+85}[/tex]

Which polynomial is factored completely?

Answers

Answer: fourth answer

Step-by-step explanation:

you cant factor it

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