The expression (3+i)(1+2i) can be written Jim the form a +bi, where a and b are integers. What are the values of a and b?

The Expression (3+i)(1+2i) Can Be Written Jim The Form A +bi, Where A And B Are Integers. What Are The

Answers

Answer 1

Answer:

a = 1

b = 7

Step-by-step explanation:

We start by opening the brackets

We have;

3 + 6i + i - 2

= 1 + 7i

comparing with a + bi

a = 1 and b = 7


Related Questions

what is 100 times 7 plus 23

Answers

100 times 7= 700 any number times 100 you would add two zeros, 700+23=723

Hope this helps :]

Nathaniel invested $37,000 in an account paying an interest rate of 5.7% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $70,900?

Answers

Answer:

11

Step-by-step explanation:

\text{Compounded Daily:}

Compounded Daily:

A=P\left(1+\frac{r}{n}\right)^{nt}

A=P(1+  

n

r

​  

)  

nt

 

Compound interest formula

A=70900\hspace{35px}P=37000\hspace{35px}r=0.057\hspace{35px}n=365

A=70900P=37000r=0.057n=365

Given values

70900=

70900=

\,\,37000\left(1+\frac{0.057}{365}\right)^{365t}

37000(1+  

365

0.057

​  

)  

365t

 

Plug in values

70900=

70900=

\,\,37000(1.0001562)^{365t}

37000(1.0001562)  

365t

 

Simplify

\frac{70900}{37000}=

37000

70900

​  

=

\,\,\frac{37000(1.0001562)^{365t}}{37000}

37000

37000(1.0001562)  

365t

 

​  

 

Divide by 37000

1.9162162=

1.9162162=

\,\,1.0001562^{365t}

1.0001562  

365t

 

\log\left(1.9162162\right)=

log(1.9162162)=

\,\,\log\left(1.0001562^{\color{blue}{365t}}\right)

log(1.0001562  

365t

)

Take the log of both sides

\log\left(1.9162162\right)=

log(1.9162162)=

\,\,\color{blue}{365t}\log\left(1.0001562\right)

365tlog(1.0001562)

Bring exponent to the front

\frac{\log\left(1.9162162\right)}{\log\left(1.0001562\right)}=

log(1.0001562)

log(1.9162162)

​  

=

\,\,\frac{365t\log\left(1.0001562\right)}{\log\left(1.0001562\right)}

log(1.0001562)

365tlog(1.0001562)

​  

 

Divide both sides by log(1.0001562)

4164.8632402=

4164.8632402=

\,\,365t

365t

Use calculator

\frac{4164.8632402}{365}=

365

4164.8632402

​  

=

\,\,\frac{365t}{365}

365

365t

​  

 

Divide by 365

11.4105842=

11.4105842=

\,\,t

t

t\approx

t≈

\,\,11

11

Using compound interest, it is found that it would take 11 years for the value of the account to reach $70,900.

What is compound interest?

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.

Hence, the parameters are given as follows:

[tex]A(t) = 70900, P = 37000, n = 365, r = 0.057[/tex]

We have to solve for t, then:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]70900 = 37000\left(1 + \frac{0.057}{365}\right)^{365t}[/tex]

[tex]\left(1 + \frac{0.057}{365}\right)^{365t} = \frac{70900}{37000}[/tex]

[tex]\left(1 + \frac{0.057}{365}\right)^{365t} = 1.91621622[/tex]

[tex](1.00015616)^{365t} = 1.91621622[/tex]

[tex]\log{(1.00015616)^{365t}} = \log{1.91621622}[/tex]

[tex]365t\log{1.00015616} = \log{1.91621622}[/tex]

[tex]t = \frac{\log{1.91621622}}{365\log{1.00015616}}[/tex]

t = 11.41

Rounding to the nearest year, it would take 11 years for the value of the account to reach $70,900.

More can be learned about compound interest at https://brainly.com/question/25781328

#SPJ2

What single transformation maps ∆ABC onto ∆A'B'C'?

Answers

Answer:

A rotation 90 degrees clockwise

Step-by-step explanation:

A person can pay $9 for a membership to the history museum and then go to the museum for just $1 per visit. For a member of the history museum, what is the total cost of 23 visits?

Answers

Answer:

$32

Step-by-step explanation:

  Step one:

Given that membership is $9 and the cost per visit is $1

let the number of visits be x

and the total cost be y

the total cost  for the situation is modeled as

y=mx+c-----equation of a line

   Step two:

given that x=23, we can solve for the totals cost as

by substituting we have

y=1*23+9

y=23+9

y=32

The total cost for 23 visits is $32

PLEASE HELP!!! GIVING BRAINLIST

If x + 2y = 8 and x/2 -y= 10, then x = ?
A)-3
B) 0
C) 10
D) 14

Answers

Answer:

D. 14

make y the subject of the formula in equation 1 and then substitute it in equation 2

The ratio of football players to volleyball players is 7 : 3. If there are 210 football players,
how many volleyball players are there?

Answers

Answer:

90

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

210 divided by 7 = 30

30 x 3 = 90

PLEASE ANSWER ALL THE QUESTIONS WILL MARK BRAINLIEST!!!

Solve the equation 5x + (−2) = 6x + 4 using the algebra tiles.

What tiles need to be added to both sides to remove the smaller x-coefficient?
A. 5 negative x-tiles
B. 5 positive x-tiles
C. 6 negative x-tiles
D. 6 positive x-tiles

What tiles need to be added to both sides to remove the constant from the right side of the equation?
A. 2 negative unit tiles
B. 2 positive unit tiles
C. 4 negative unit tiles
D. 4 positive unit tiles

What is the solution?
A. x = –6
B. x = –2
C. x = 1
D. x = 2​

Answers

Answer:

1. A

2. C

3. A

Explanation:

5x+(-2)=6x+4

-5x -5x

(-2)=1x+4

-6=x

Answer:

What tiles need to be added to both sides to remove the smaller x-coefficient?

✔ 5 negative x-tiles

What tiles need to be added to both sides to remove the constant from the right side of the equation?

✔ 4 negative unit tiles

What is the solution?

✔ x = –6

Step-by-step explanation:

A room that is in the shape of a cube has a capacity of 1331 cubic feet. The room is ____ feet long​

Answers

Answer:

200020ft

Step-by-step explanation:

Factor:
25y + 27x
Plz help

Answers

Answer:

25y+27x

Step-by-step explanation:

You cannot factor this any further

Angie uses the equation E=0.03s + 25,000 to find her yearly earning E based on her total sales s. What is the independent variable

Answers

Answer:

25000

Step-by-step explanation:

it's independent because it's not related with her total sales s

30 points!!!!!!!!!!!!!!!!!!!!!!! Help ASAP!!! 1.) Line a passes through points (-2, 1) and (2, 9). Write an equation in slope intercept form that is parallel to line a.

Answers

Answer:

Step 1: Use slope formula* to determine slope (or m) using both points given.

[tex]\frac{9 - 1}{2 - (-2)}\\\\\frac{8}{4} = 2[/tex]

Step 2: Use slope-intercept formula** , ONE of the points given, and the slope we just found to solve for b.

[tex]1 = 2(-2) + b\\\\1 = -4 + b\\\\5 = b[/tex]

Step 3: Now we can set up an equation of this line in slope-intercept form.

[tex]y = 2x + 5[/tex]

*Slope formula: y₂ - y₁/x₂ - x₁

**Slope-intercept formula: y = mx + b

Answer:

The slope calculator helps find the slope of any line through two given points. ... To find the equation of a line for any given two points that this line passes through, use our ... to calculate the slope of the line passing through the points (3,8) and (-2, 10) . ... Make sure that the points you measure from are the same as step 1.

Step-by-step explanation:

The quotient of a number and (-3) is (-80) Find the number.

Answers

Answer:

240

Step-by-step explanation:

Find the ratios x:y:z if x:y=9:10 and y:z=5:3

Answers

Answer:

Step-by-step explanation:

Answer:

x : y : z = 9 : 10 : 6

Step-by-step explanation:

Expressing the ratio y : z = 5 : 3 in fractional form, that is

[tex]\frac{y}{z}[/tex] = [tex]\frac{5}{3}[/tex] ( cross- multiply )

5z = 3y ( divide both sides by 5 )

z = [tex]\frac{3}{5}[/tex] y = [tex]\frac{3}{5}[/tex] × 10 = 3 × 2 = 6

Thus

x : y : z = 9 : 10 : 6

A = p + prt solve for t

Answers

Answer:

t = [tex]\frac{A - p}{pr}[/tex]

Step-by-step explanation:

A = p + prt

A - p = p - p + prt

A - p = 0 + prt

A - p = prt

[tex]\frac{A - p}{pr}[/tex] = [tex]\frac{prt}{pr}[/tex]

[tex]\frac{A - P}{pr}[/tex] = t

Compare the two statements below and decide if the phrase: "In a plane," needs to be included in order to make a true statement.

1. In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.

versus

2. If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.





answer choices:

A) It does not need to be included. By leaving it out of the statement, the reader considers three dimensions not just the xy-plane. The two parallel lines would determine a plane. However, the transversal could intersect only one of the lines. This would allow the proof to use the Corresponding Angles Theorem.


B) It does not need to be included. By leaving it out of the statement, the reader considers three dimensions not just the xy-plane. The two parallel lines would determine a plane. However, the transversal could intersect only one of the lines. This would allow the proof to use the Angle Bisector Theorem.


C) It needs to be included as it forces the reader to consider only two dimensions, like the xy-plane. The two parallel lines would determine the plane and the transversal would intersect both lines. This would allow the proof to use the Corresponding Angles Theorem.


D) It needs to be included as it forces the reader to consider only two dimensions, like the xy-plane. The two parallel lines would determine the plane and the transversal would intersect both lines. This would allow the proof to use the Angle Bisector Theorem.

Answers

by any chance do you go to a higl school in Conroe bc I’m taking that exact test on canvas

Step-by-step explanation:

HELP ME FOR BRANLIEST

Answers

Answer: i dont know the answer but can i please have brainliest, i wanna know what it looks like and what it does

Step-by-step explanation:

please fill in the blanks i need this

Answers

Answer:

110

242

Step-by-step explanation:

To get the amount for Number of ships 5. you do 5*22.

Same for the the #11. you do 11*22.

Also, Pick me as the smartest please.

A distrubutor wants to make 1,000 pounds of trail mix that is 8% raisins. He will use a mix that is 5% raisins and a mix that is 20% raisins. How many pounds of each should he use?

Answers

Answer:

He should use 800 pounds of trail mix 5% raisins and 200 pounds of trail mix 20% raisins

Step-by-step explanation:

System of Equations

Let's call

x = pounds of trail mix 5% raisins

y = pounds of trail mix 20% raisins

The distributor wants to make 1,000 pounds of trail mix, thus:

x + y = 1,000     [1]

The mix must be 8% raisings as a combination of x and y, thus:

5x + 20y = 8*1,000 = 8,000

Dividing by 5:

x + 4y = 1,600     [2]

Subtracting [2] and [1]:

4y - y = 1,600 - 1,000

Operating:

3y = 600

y = 200

From [1]

x = 1,000 - y = 1,000 - 200

x = 800

He should use 800 pounds of trail mix 5% raisins and 200 pounds of trail mix 20% raisins

Answer:

5% raisin mix: 800 lbs

20% raisin mix: 200 lbs

Step-by-step explanation:

Let number of 5% be x; and number of 20% be a.

x + y = 1000

5% · x + 20% · y = 8% of 1000 pounds

0.05x + 0.2y = 80

x = 1000 - y

0.05(1000 - y) + 0.2y = 80

50 - 0.05y + 0.2y = 80

0.15y = 30

y = 200

x = 1000 - y

x = 1000 - 200

x = 800

0.1 is rational because it can be written as?

Answers

Answer:

0.1 is rational as it can be written as [tex]\frac{1}{10}[/tex]

Step-by-step explanation:

Rational decimals can be expressed as a fraction using integers, and 0.1 = [tex]\frac{1}{10}[/tex], so it is rational.

Answer:

There are various ways of writing 0.1

1/10

110

10%

Those are some ways for writing 0.1

Step-by-step explanation:

help me pleaseeeeeee

Answers

Step-by-step explanation:

Similar triangles

[tex] \frac{6}{uv } = \frac{8}{3} [/tex]

uv=18/8

uv= 2.25

I NEED HELP ASAP
The floor of a rectangular pen has a length that is two feet more than four times its width. What is the area of the pen?

Answers

length = 4w + 2

A = length x width
= (4w + 2) . w
= 4w^2 + 2w ft square

Evaluate 5w-w/x when w=6 and x=2

Answers

Substitute.

5(6) - (6)/(2)

30 - 6/2

30 - 3 = 27

Find the equation of a parabola that has a vertex of (3,7) and contains the point (-2,-6)

Answers

Answer:

Step-by-step explanation:

Which graph is the solution to the inequality below?

Answers

Answer:

it the third answer

Step-by-step explanation:

3(x-5)< 5x+7

x>-11

PLEASEEE HELP ME ANWSER THISSS ♥️♥️♥️♥️​

Answers

What proof do you need?

Help me please asap!!

Answers

Answer:

67

Step-by-step explanation:

180 - (53 + 60) = 67

The graph shows the volume of water in a sink, x minutes after the faucet is turned on.

Answers

Answer:

Conner is correct.

Step-by-step explanation:

Answer:

Connor is correct because the rate of water flowing is equal to the slope. Water is flowing at a rate that is equal to 2 gallons per minute.

Step-by-step explanation:

Kyle asked a random group of students what their favorite sport was. The results are below. Boys Girls Basketball 10 8 Football 25 7 Soccer 9 19 Baseball 18 22 If Kyle were to randomly select a girl to explain why she likes the sport chosen, what is the probability that he will pick a girl who likes football? A 12.5% B 27.1% C 40.3% D 44.6%

Answers

Answer:

The probability that Kyle will pick a girl who likes football is 12.5%.

Step-by-step explanation:

The data provided is as follows:

                         Boys        Girls       Total

Basketball          10             8             18

 Football           25             7             32

  Soccer             9             19             28

 Baseball           18            22            40

   Total               62           56            118

Compute the probability that Kyle will pick a girl who likes football as follows:

[tex]P(F|G)=\frac{n(G\cap F)}{n(G)}[/tex]

            [tex]=\frac{7}{56}\\\\=0.125\\\\=12.5\%[/tex]

Thus, the probability that Kyle will pick a girl who likes football is 12.5%.

The computer was regularly priced at $1500. If you order the computer over the Internet, you can save money as the price is only $1200.What percent discount (change) are you getting?

Answers

20 percent discount !!!

What is the equation of the line in the graph?

Answers

Answer:

                                                                                                                                         

Step-by-step explanation:

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