Which of the following are square roots of —8 + 8i/3? Check all that apply.

Which Of The Following Are Square Roots Of 8 + 8i/3? Check All That Apply.

Answers

Answer 1

Answer:

Options (2) and (3)

Step-by-step explanation:

Let, [tex]\sqrt{-8+8i\sqrt{3}}=(a+bi)[/tex]

[tex](\sqrt{-8+8i\sqrt{3}})^2=(a+bi)^2[/tex]

-8 + 8i√3 = a² + b²i² + 2abi

-8 + 8i√3 = a² - b² + 2abi

By comparing both the sides of the equation,

a² - b² = -8 -------(1)

2ab = 8√3

ab = 4√3 ----------(2)

a = [tex]\frac{4\sqrt{3}}{b}[/tex]

By substituting the value of a in equation (1),

[tex](\frac{4\sqrt{3}}{b})^2-b^2=-8[/tex]

[tex]\frac{48}{b^2}-b^2=-8[/tex]

48 - b⁴ = -8b²

b⁴ - 8b² - 48 = 0

b⁴ - 12b² + 4b² - 48 = 0

b²(b² - 12) + 4(b² - 12) = 0

(b² + 4)(b² - 12) = 0

b² + 4 = 0 ⇒ b = ±√-4

                     b = ± 2i

b² - 12 = 0 ⇒ b = ±2√3

Since, a = [tex]\frac{4\sqrt{3}}{b}[/tex]

For b = ±2i,

a = [tex]\frac{4\sqrt{3}}{\pm2i}[/tex]

  = [tex]\pm\frac{2i\sqrt{3}}{(-1)}[/tex]

  = [tex]\mp 2i\sqrt{3}[/tex]

But a is real therefore, a ≠ ±2i√3.

For b = ±2√3

a = [tex]\frac{4\sqrt{3}}{\pm 2\sqrt{3}}[/tex]

a = ±2

Therefore, (a + bi) = (2 + 2i√3) and (-2 - 2i√3)

Options (2) and (3) are the correct options.

Answer 2

Answer: b and c

Step-by-step explanation:


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2 (32 – (4 - 1)"

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I think the answer is 58 I’m not sure

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Answer:

c)-2 is greater than -6

Step-by-step explanation:

The answer is C because -2 is greater than -6

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Answer

the first one is the answer and none of the above

Step-by-step explanation:

Solve the proportion 2/7=x/42
A. 1/2
B. 12
C. 2/7
D. 6
Because algebra is going to help me raise a family, buy a house, and pay taxes.

Answers

Cross multiply. 2 times 42= 7x
84/7= 12
X= 12

Math will help you get a degree and you will raise a family with more money- afford a house— and pay your taxes.

Elwood invested $5,000 in a money market account and has been tracking its progress. He found that after 3 years, the account held $7,100 and after 8 years, the account held $10,350. Use this information to complete the statements. Over the first 3 years, the value of the account increased at ___ over the last 5 years. Over the entire 8 years, the value of the account increased at an average rate of approximately $___ annually.

Answers

Answer:

Given:

Principal= $5,000

After 3 years, Amount= $7,100

After 8 years, Amount= $10,350

Step-by-step explanation:

Interest after 3 years= $7,100- $5,000

                                   =$2,100

Interest in last 5 years= $10,350- $7,100

                                    =$ 3,250

Difference between first 3 years and last 5 years= $3,250- $2,100

                                                                                 =$1,150

Amount= Principal*[tex](1+r/100)^{t}[/tex]

10,350=5000[tex](1+r/100)^{8}[/tex]

[tex]\frac{10350}{5000}[/tex]=[tex](1+r/100)^{8}[/tex]

2.07=[tex](1+r/100)^{8}[/tex]

[tex]2.07^{1/8}[/tex]=1+[tex]\frac{r}{100}[/tex]

1.095-1=[tex]\frac{r}{100}[/tex]

0.095*100=r

r=9.5%

Average rate=[tex]\frac{5000*9.5*1}{100}[/tex]

                    =$475

Answer:

drop down 1 a slower rate per year

drop down 2 670

Step-by-step explanation:

as in three years you get $7100

you take that and subtract it by your starting amount (5000)

7100-5000= 2100

then divide 2100 by the number of years (3)

to get your annual rate of 700$

then you take the 8 year total and subtract it from your 3 year total

10350-7100= 3250

Then divide that by 5 because that how many years it has been

to get the annual rate of 650

making the 5 year rate slower.

The to find the average rate over all 8 year you take 10350 and subtract it from your starting number 5000

10350-5000= 5350

then take 5350 and divide it by the number of years (8)

you then get you average rate of 668.75

668.75=670

Hope this helps!

For every 2 girls in Mr Hegarty's class there are 3 boys. What is the ratio of girls to boys in the class?
Give your answer in its simplest form.

Answers

Answer:

2Girls:3Boys

Step-by-step explanation:

gdfgdsfgdsgsdfgdsgdsfgdsfgdsfg

Type SSS, SAS, ASA, SAA, or HL

To justify why the two larger triangles are
Congruent.

Answers

I’m assuming the answer is HL since they only gave us two letters.

The theorem that justifies why ΔADB ≅ ΔCBE is the: SAA congruence theorem.

What is the SAA Congruence Theorem?

The SAA congruence theorem states that two triangles can be proved to be congruent triangles if they both have two pairs of congruent angles and a pair of non-included congruent sides.

Thus:

ΔADB and ΔCBE have:

two pairs congruent angles: ∠ABC ≅ ∠CBE and ∠BAD ≅ ∠BCEone pair of non-included congruent sides: AD ≅ EC

Therefore, the theorem that justifies why ΔADB ≅ ΔCBE is the: SAA congruence theorem.

Learn more about the SAA congruence theorem on:

https://brainly.com/question/2102943

HELP ME PLEASE!!!!!!!

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Given:

The graph of a line.

To find:

The equation of line and values of m and b. Check whether it is proportional or linear.

Solution:

From the given graph it is clear that, the line passes through (0,4) and (2,0). So, the equation of line is

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-4=\dfrac{0-4}{2-0}(x-0)[/tex]

[tex]y-4=\dfrac{-4}{2}(x)[/tex]

[tex]y-4=-2x[/tex]

Adding 4 on both sides, we get

[tex]y=-2x+4[/tex]

On comparing this equation with slope intercept form, i.e., [tex]y=mx+b[/tex], we get

[tex]m=-2\text{ and }b=4[/tex]

All lines are linear. If a line passes through the origin then it is proportional.

From the given graph it is clear that the line is not passing through the origin, i.e., (0,0). So, it is linear not proportional.

Therefore, the value of m is -2 and the value of b is 4. The equation of line is [tex]y=-2x+4[/tex].  The line linear not proportional because it does not passing through the origin.

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Answers

Step-by-step explanation:

Opposite angles in a cyclic quadrilateral are supplementary.

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Answers

Answer:

x=4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

6(x+4)−8x=16

(6)(x)+(6)(4)+−8x=16(Distribute)

6x+24+−8x=16

(6x+−8x)+(24)=16(Combine Like Terms)

−2x+24=16

−2x+24=16

Step 2: Subtract 24 from both sides.

−2x+24−24=16−24

−2x=−8

Step 3: Divide both sides by -2.

-2x/-2=-8/-2

x=4

Answer:

X=8

Step-by-step explanation:

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Answers

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A) v = 1/2 x pi x r^2 x h/3

V = 1/2 x pi x 12^2 x 35/3

V = 1/2 x pi x 144 x 35/3

V = 840pi

B) sa =1/2 x pi x r(r + sqrt(h^2+r^2))

Sa = 1/2 x pi x 12(12+ sqrt(35^2+12^2))

Sa= 923.63 round as needed.

C) volume of hemisphere with 4cm diameter:

2/3 x pi x 2^3 = 5.33pi

Divide volume of semi cone by volume of hemisphere:

840pi/5.33pi = 157.5

slove : 28/36 = 14/y

Answers

Answer:

y = 18

Step-by-step explanation:

i) reduce the fraction with 4

[tex] \frac{28}{36} = \frac{14}{y} [/tex]

[tex] \frac{28 \div 4}{36 \div 4} = \frac{14}{y} [/tex]

[tex] \frac{7}{9} = \frac{14}{y} [/tex]

ii) simplify the equation with cross multiplication

[tex] \frac{7}{9} = \frac{14}{y} [/tex]

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[tex]7y = 126[/tex]

iii) divide both sides of the equation by 7

[tex] \frac{7y}{7} = \frac{126}{7} [/tex]

[tex]y = 18[/tex]

Answer:

Step-by-step explanation:

Apply proportions

y =(36*14)/28 = 18

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Answers

Answer:

y = 6/(x - 8).

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2 = k/3

k = 6.

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A residential community was polling households to find out whether they wanted to get their TV signal from a satellite or cable. The results are shown in the Venn diagram.

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Answer:

What are the results? What's the question?

Step-by-step explanation:

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Step-by-step explanation:

Trust me no cap

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Answers

Answer:

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Answers

Answer:

Please check the explanation.

Step-by-step explanation:

If the lines are identical, there must be an infinite number of solutions. In other words, they are the coordinate of all the points on that line.

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Given the line

3y = 2x-9

As the system of equations has an infinite number of solutions, it means the lines must be identical.

So, the other line can be obtained by multiplying the line 3y = 2x-9 by any scalar number, let say by 2.

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6y = 4x-18 will be another line.

Thus, the system of equations become:

3y = 2x-9

6y = 4x-18

The graph is attached below.

The graph indicates that both lines are overlapping with each other. Hence, the lines will be identical and the system of the equations will have an infinite number of solutions.

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Answers

f(6)= 28, f(7)= 33, f(8)= 38, SO f(9)= 43

Evaluate the logarithm. ln(1/e^2)

Answers

Answer:

-2

Step-by-step explanation:

Notice that 1/e^2 = e^(-2), by power rules.

Now ln(e^x)=x.

So ln(1/e^2) = ln(e^(-2))=-2

2.

Select the correct answer.

Which transformation of the parent square root function will result in the given domain and range?

domain: [2,00)

range: (3, 0)

A.

B.

; (b) = (x + 2) + 3

g(x) = (x - 2)2 + 3

h(x) = (x – 3): –

k(x) = (x + 3)} – 2

Oc.

OD.

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Answer:

I think the correct answer of these qusion is g(x)=(x_2)2+3

Tyler's brother works in a shoe store. He earns a commission. He makes 2.5% of the amount he sells. Last week he sold $900 worth of shoes. How much was his commission? (step by step explanation please)

Answers

Answer:

22.5

Step-by-step explanation:

multiply 900 by .025 to get 22.5.

When you multiply by a percentage to find an amount, move the decimal place over to the left by 2 places and then multiply by the number (in this case 900). Whatever number you receive is the answer.. :)

Subtract 36.12 − 3.76 = ______

Answer for Blank 1:

Answers

Answer:

32.36

Step-by-step explanation:

Answer:

32.36

Step-by-step explanation:

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(_,8)
*will give 10 points*​

Answers

the answer would be (6,8)

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What is the solution to this linear system? Enter a value in each box to create an ordered pair.


( , )

Answers

Answer:

(1, 2)

Step-by-step explanation:

From the graph attached,

Two lines are representing linear system of equation.

Since, solution of any system of linear equations is a common point of the two lines.

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Answers

Answer:

I don' t understand what you need help with

The probability of drawing two green jacks from a bag at random without replacement is 227 .

The probability of drawing a green jack first is 27 .

What is the probability of drawing a second green jack, given that the first jack drawn was green?

4/189
10/189
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Answers

Answer:

7/27 or C in other words.

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Answers

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Answer:

75

Step-by-step explanation:

it will take 3 week for 3×25 and 5 week for 5×15. I hope this helps.

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