Find all of the real and imaginary solutions of x^3+8=0

Answers

Answer 1

Answer:

[tex]x=-2, \:1+\sqrt{3}i,\: 1-\sqrt{3} i[/tex]

Step-by-step explanation:

[tex]x^3+8=0,\\x^3=-8,\\\mathrm{For\:}x\in \mathrm{R}, x=-2[/tex]

Real solutions ([tex]x \in \mathrm{R}[/tex]): [tex]x=-2[/tex]

However, recall that [tex](\frac{-1\pm\sqrt{3}i}{2})^3=1[/tex].

Therefore:

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

Thus, for [tex]x^3=-8,\: x\notin \mathrm{R}[/tex]:

[tex]x=1\pm\sqrt{3}i[/tex].

Therefore, the real and nonreal solutions of [tex]x^3+8=0[/tex] are [tex]\fbox{$-2, \:1+\sqrt{3}i,\: 1-\sqrt{3}i$}[/tex].

Answer 2

Answer:

-2, 1 +/- i*sqrt(3)

(3 solutions)

Step-by-step explanation:

Because the left side is in the form a^3+b^3, we can factor it as (a+b)(a^2-ab+b^2) (good formula to remember)

So we have

(x+2)(x^2-2x+4)

We can see one value already

x+2 = 0

x = -2

now we solve for

x^2-2x+4 = 0

We can use the quadratic formula, and see that the determinant is negative (2^2-4*1*4 < 0)

Therefore we have two imaginary solutions

(-(-2) +/- sqrt(2^2-4*1*4))/)2*1) = (2 +/- sqrt(-12))/2 = (2 +/- 2sqrt(-3))/2 = 1+/- sqrt(-3) = 1 +/- i*sqrt(3)


Related Questions

A student was studying the relationship between how much money students spend on food and on entertainment per week. Based on a sample size of 270, he calculated a correlation coefficient (r) of .013 for these two variables. Which of the following is an an appropriate interpretation?

a. This low correlation of .013 indicates there is no relationship.
b. There is no linear relationship but there may be a nonlinear relationship.
c. This correlation indicates there is some type of linear relationship.

Answers

Answer:

The answer is "Option b".

Step-by-step explanation:

In this question, the value of the correlation coefficient is 0.013 from the given information. It is the equation, which realized the indeed closer their correlation coefficient is to -1 or 1, the greater the positive correlation, although in this case, the value of the correlation coefficient is 0.013, close to "0".

Plz help if you can help

Answers

Answer:

A) 2x = -20 and C) x = -10

Step-by-step explanation:

2/5x = -4

5 •  2/5x = 5(-4)        Multiply terms to eliminate the denominator

2x = -20       Cancel the multiplied terms

2x/2 = -20/2      Divide

x = -10

Hope this helps

what is the answer to
2x=24

Answers

Answer:

12

Step-by-step explanation:

you divide 24 by 2 because it is multiplication, and the opposite is division.

The answer is 12 because u divide

Zeke had 9 dvds. His mother bought d more DVD. Write an expression that shows how many dvds zeke has now

Answers

Answer: 9+d=x or x=9+d

d-the new dvds

x-the unknown total

9-the dvds Zeke owned before

Mr. Clark sold 280 bags of chips and 415 bottles of juice in 5 days. At this rate, Mr. Clark will sell bottles of juice in 12 days.

Answers

Answer:

is answer is 8,340

Step-by-step explanation:

add 280 and 415 and get 695

then multiply by 5 and get 3,475

then multiply 695 by 12 and get 8,340

A jar is filled with buttons of various colors. If the jar has a total of 420 buttons and 85% of the buttons are green, how many green buttons are in the jar?
Group of answer choices

Answers

420x.85=357
this makes since since 357/420= 85%. Brainlist ?

8. A cone shaped paper cup has a radius of 1.5 inches and a height of 3 inches. What is the volume of the cup?​

Answers

Answer:

[tex]V=7.06\ \text{inches}^3[/tex]

Step-by-step explanation:

Given hat,

The radius of cone shaped paper cup, r = 1.5 inches

The height of cone shaped paper cup, h = 3 inches

We need to find the volume of the cup. For a cone shaped, the volume is given by :

[tex]V=\dfrac{1}{3}\pi r^2 h[/tex]

Putting all the values in the above formula.

[tex]V=\dfrac{1}{3}\pi \times (1.5)^2 \times 3\\\\V=7.06\ \text{inches}^3[/tex]

So, the volume of the cup is [tex]7.06\ \text{inches}^3[/tex].

HELP PLS ASAP 25 POINTS YOU CAN SAVE MY GRADE PLS
Evaluate the expression below when x = 5.
3x(2x - 7)
A.) 0
B.) 24
C.) 45
D.) 143

Answers

Answer:

C.) 45

Step-by-step explanation:

3x(2x - 7)

3 * 5 (2 * 5 - 7)

15 * (10 - 7)

15 * 3

45

Hope this helps :)

What is 2/3-5/9 in 5th grade math

Answers

Answer:

0.111111

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solution

=2×3/3×3-5×1/9×1

=6/9-5/9

=6-5/9

=1/9

Please mark me brainliest.Ok

a mark is made on a long pole so that the ratio of two parts is 7:5 if the longer part is 35cm what is the length of each pole?​

Answers

Step-by-step explanation:

Let the two parts be 7x and 5x.

7x=35 :.X=5

5x= 5×5=25

Thus,Total length of pole is 35+25=60

You use 3
3
cans of soup to serve 5
5
people.

If you want to serve 20
20
people, what should you d

Answers

Answer:

I might be small brain (which i am)

Step-by-step explanation:

But given the pattern i think it is 18 cans of soup for 20 people

Kathy owned several real estate properties. She had to pay federal taxes on her income and property taxes on the properties. What would be another major cost of her investment?

A.
bank fees
B.
investment broker fees
C.
renovation and maintenance costs
D.
utilities

Answers

Answer:

The correct answer is C. Renovation and Maintencance costs

Step-by-step explanation:

#Plato :)

The major cost of her investment would be C. Renovation and Maintencance costs.

What is income tax?

Income tax is a tax applied on individuals or entities concerning income or profit earned by them.

The amount of additional tax paid for each new dollar of income received is known as; the marginal tax rate.

The Total taxes paid is divided by total income earned is the average tax rate. With a marginal tax rate of 10 percent, then the tax would be deducted from the following dollar of income at a rate of 10%.

Given that Kathy owned several real estate properties. She had to pay federal taxes on her income and property taxes on the properties.

The major cost of her investment would be C. Renovation and Maintencance costs.

Learn more about tax here:

brainly.com/question/10798743

#SPJ5

Which of the following fractions is equivalent to -88/248 in least common terms?

Answers

Answer:

Its would be A -11/31

Step-by-step explanation:

There are 564 men and women working in a facten
There are twice as many women as men.
How many men are working in the factory

Answers

1.128 men good luck on it^^^^^^^^^ hope it helps

Please help me! I’m begging you I’ll mark you brainly! I need it by now

Answers

Answer:

Boxes at the top are as follows

Monomial. 1. 4x

Binomial. 2. 4x+2

Trinomial. 3.

Polynomial. More than 3.

[tex] {5x}^{4} + {2x}^{3} + {12x}^{2} + 135 [/tex]

This would be an example of a polynomial ^

Omit the next highest term to get a trinomial etc

1. 4th degree. Leading term:

[tex] {x}^{4} [/tex]

Leading coefficient: x

2. 2nd degree. Leading term:

[tex] - {7x}^{2} [/tex]

Leading coefficient: -7x

It's a little confusing to read but that should be everything. Sorry it's not organized better

1. The value of y varies directly with x. If y = 30 when x =1/5
Which direct variation equation represents this relationship?

PLEASE HELP !!

Answers

Answer:

4. b) 30

5. c) y=2/3x+9

6. y=2x-5

Step-by-step explanation:

help ME PLS

WILL MARK BRAINLIEST

Answers

Answer:

62b+27nb-12n-12

Step-by-step explanation:

u gotta combine like terms

Answer:

-0.7 .................

Solve for x:
600
x + 124
Just enter the number.

Answers

Answer: -4. Reasoning: We are trying to get the angle of both lines to equal 180. If you add 60+124 together to see how much we have currently, your answer comes up to 184. That’s 4 over what we need, therefore, -4 would be needed to bring the current amount back down to 180.

A car was bought for $20,000 and has depreciated at a rate of 10% yearly. Find the price of the car 8 years later.

Answers

Answer:

$4,000

Step-by-step explanation:

10% of $20,000 is $2,000, which means the price of the car is decreasing by $2,000 each year. After 8 years, the price of the car has decreased by $16,000 ($2,000 times 8 years). The totals cost of the car is now $4,000, as it was originally $20,000, but decreased by $16,000. (20,000-16,000=4,000).

-5.8c +4.2 – 3.1 + 1.4c


Solve this for me

Answers

Answer:

-4.4c+1.1

Step-by-step explanation:

Given the sets above, select all (or the null set) of the element of: B

Answers

Given:

Universal set = {a, b, c, d, e, f, g, h}

A = {a, b, c, d}

B = {a, d, e}

C= {c, f, g, h}

To find:

The elements of set B'.

Solution:

Let universal set be U.

U = {a, b, c, d, e, f, g, h}

We know that,

Compliment of a set = Universal set - Set

It means,

[tex]B'=U-B[/tex]

[tex]B'=\{a, b, c, d, e, f, g, h\}-\{a,d,e\}[/tex]

[tex]B'=\{b, c,f, g, h\}[/tex]

Therefore, only b, c, f, g, h are the elements of set B'.

heyyy :) what is 15/ 4 ÷ 5/8

Answers

Answer:

6

Step-by-step explanation:

15/4 / 5/8 =

15/4 x 8/5=

120/40=

120/40 / 20/20= 6

hope it helpls

Answer:

6

Step-by-step explanation:

[tex]\frac{15}{4}[/tex] ÷ [tex]\frac{5}{8} =[/tex]  [tex](\frac{15}{4} )(\frac{8}{5} )= \frac{120}{20} = 6[/tex]

plsss i beg u hrlppp

Answers

Answer:

Step-by-step explanation:

collinear means co:together, or with like a coworker, and linear:line(s)

since points a, o, and d are on the same line, they are indeed collinear

triangle CDE is an equilateral since lines CE and ED are equal. 180/3 is 60, therefore each angle of triangle CDE has 60 degrees

triangle BCE: a right triangle.angle B is 90 degrees, C is 60 degrees E is 30 degrees.

Triangle ABE is a obtuse triangle, one angle is an obtuse angle, hence the name.angle A seems to be 120 Degrees and Angles Band E seem to be 30 degrees each

Pls answer I need it

Answers

Answer:

I think 3rd!

.

.

.

.

.

.

.

Answer:

44 photos

Step-by-step explanation:

y = 44 + 24x

this is a part of science too so pleae help

Answers

Second one where the wind is blowing 35 km/h east

this is velocity because it gives u both displacement over time and direction

the length of a living room is 12 feet and its width is 10 1/2 feet. The length of the room is being expanded by x feet. Select all the expressions that represent the area of the living room in square feet.

Answers

Answer:

(12+x)(10 1/2+x)

Step-by-step explanation:

round 429,713 to the nearest tens


will make brainliest

Answers

Answer:

429.7

Step-by-step explanation:

Answer:

429,710

Step-by-step explanation:

Angie has $1,900 in her savings account. If the bank pays 5% simple interest on savings, What is the total amount of money she will have in her account after 5 years?

Answers

1,900 x 0.05 x 5 = 475
It’s 475 for sure trust

Solve.
How much pure acid is in 860 milliliters of a 18​% ​solution?

The answer is ____ ml.

Answers

Answer:

The answer is 154.8 ml

Step-by-step explanation:

In this question, the amount of pure acid is 18% of the total solution, that is, 18% of 860 milliliters. So

0.18*860 = 154.8 ml

The answer is 154.8 ml

Are buying a drink and buying popcorn independent or dependant events

Answers

It's a Dependent events
I believe independent events
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