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AysviL [449]
3 years ago
14

What are the real and complex solutions of the polynomial equation X^3-216=0

Mathematics
1 answer:
vazorg [7]3 years ago
3 0

Answer:

6,\ -3+3\sqrt{3}i,\ -3-3\sqrt{3}i

Step-by-step explanation:

Factor the equation x^3-216=0 using formula for difference of the cubes:

x^3-216=(x-6)(x^2+6x+36),

then

x-6=0\ or\ x^2+6x+36=0.

1. The equation x-6=0 has real solution x=6.

2. The equation x^2+6x+36=0 has negative discriminant D=6^2-4\cdot 36=36-144=-108, then it has two complex solutions

x_{1,2}=\dfrac{-6\pm 6\sqrt{3}i}{2}=-3\pm3\sqrt{3}i.

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krek1111 [17]

Answer:

9=0.6q where q is the number of questions on the exam.

Step-by-step explanation:

3 0
3 years ago
The dishwasher Marlin wants costs $720. This week only, the dishwasher is discounted by 25%. Marlin must pay 6% sales tax. Which
Mkey [24]

Answer:

C, both methods save the same amount of money

Step-by-step explanation:

First, we need to calculate what each answer choice will equal.

For A, it asks us to add the sales tax and then take the discount off. So, to find out what the sales tax is equal to, we multiply 720 x 0.06 (because 6% is equal to 0.06).

720 x 0.06 = 43.2

Add the sales tax to the original amount and you get 763.2.

Now we take the discount, which is 25% or 1/4.

1/4 of 763.2 is 190.8.

Subtract the discount from the price and you get 572.4.

For B, it says to take the discount first and then add the sales tax.

25% = 1/4, so 1/4 of 720 is equal to 180.

Subtract 180 from 720, and you get 540.

Now add the sales tax.

540 x 0.06 = 32.4.

540 + 32.4 = 572.4.

The answer is C, both methods save the same amount of money!

7 0
3 years ago
A number is multiplied by 2. Then that product is multiplied by 5. Write to explain how you know what digit is in the ones place
Kazeer [188]
When you multiply a number by 5 and then by 2 it is the same as multiplying by 10. multiplying by 10 means you add a zero to the end of the number so the digit in the ones column will be always be zero
3 0
3 years ago
The probability that an American CEO can transact business in a foreign language is .20. Twelve American CEOs are chosen at rand
NNADVOKAT [17]

Answer with Step-by-step explanation:

We are given that

The probability that an American CEO can transact business in  foreign language=0.20

The probability than an American CEO can not transact business in foreign language=1-0.20=0.80

Total number of American CEOs  chosen=12

a. The probability that none can transact business in a foreign language=12C_0(0.20)^0(0.80)^{12}

Using binomial theorem nC_r(1-p)^{n-r}p^r

The probability that none can transact business in a foreign language=\frac{12!}{0!(12-0)!}(0.8)^{12}=(0.8)^{12}

b.The probability that at least two can transact business in a foreign language=1-P(x=0)-p(x=1)=1-((0.8)^{12}+12C_1(0.8)^{11}(0.2))=1-((0.8)^{12}+12(0.8)^{11}}(0.2))

c.The probability that all 12 can transact business in a foreign language=12C_{12}(0.8)^0(0.2)^{12}

The probability that all 12 can transact business in a foreign language=\frac{12!}{12!}(0.2)^{12}=(0.2)^{12}

5 0
3 years ago
Determine the factors of x2 − 8x − 12.
statuscvo [17]

Answer:

This polynomial cannot be factored because it is prime. Hope this helps. :)

Step-by-step explanation:

hope this helps :)

7 0
3 years ago
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