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3 years ago

How many complex roots does the equation below have? x^6+x^3+1=0

1 answer:

4 0

Here, x⁶ + x³ + 1 = 0
Now, Let, x³ = u
Then, x⁶ = u²

So, u² + u + 1 = 0
We know, b² - 4ac = 1² - 4(1)(1) = 1 - 4 = -3

<span>which is negative u has two complex roots.
So there are two complex values x</span>³.
Again, There are 3 complex cube roots of each of those two complex roots for u.

In short, Your Answer would be 3*2 = 6 Complex roots

Hope this helps!

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What is another way to describe 45 is it 45 tens 0 ones 9 tens 5 ones or 4 tens 5 ones

denis-greek [22]

Answer:

4 tens and 5ones

Step-by-step explanation:

there is a four in the tens place making it 40 and 5 in the ones place making it 45

8 0

3 years ago

Read 2 more answers

1. $239 television; 10% discount 2. $72 game; 20% discount

Fiesta28 [93]

These are 16 questions and 16 answers

Answer:

See below and the attachment.

Explanation:

From 1 to 10, find the sale price to the nearest cent:

1. $239 television; 10% discount

$Sale\text{ }price=Orignal\text{ }price-discount\\ \\ Sale\text{ }price=\$239-10\%\times \$239=\\\\ Sale\text{ }price=\$239-0.10\times \$239=\\\\ Sale\text{ }price=\$239-\$23.9=\$215.10$

2. $72 game; 20% discount

You can also multiply by the factor (1 - % discount);

For instance for 20% discount, the factor is 1 - 20% = 1 -0.20 = 0.80. Which means that you can multiply the original price by the factor 0.80 to get the sale price:

$Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$72\times(1-0.20)=\\\\ Sale\text{ }price=\$72\times0.80=\\\\ Sale\text{ }price=\$57.60$

3. $18.95 football; 15% discount

$Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$18.95\times(1-0.15)=\\\\ Sale\text{ }price=\$18.95\times0.85=\\\\ Sale\text{ }price=\$16.11$

4. $10.99 CD; 25% discount

$Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$10.99\times(1-0.25)=\\\\ Sale\text{ }price=\$10.99\times0.75=\\\\ Sale\text{ }price=\$8.24$

5. $149 MP3 player; 40% discount

$Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$149\times(1-0.40)=\\\\ Sale\text{ }price=\$149\times0.60=\\\\ Sale\text{ }price=\$89.40$

6. $213 ski jacket; 30% discount

$Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$213\times(1-0.30)=\\\\ Sale\text{ }price=\$213\times0.70=\\\\ Sale\text{ }price=\$149.10$

7. $595 refrigerator; 20% discount

$Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$595\times(1-0.20)=\\\\ Sale\text{ }price=\$595\times0.80=\\\\ Sale\text{ }price=\$476.00$

8. $64 video game; 25% discount

$Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$64\times(1-0.25)=\\\\ Sale\text{ }price=\$64\times0.75=\\\\ Sale\text{ }price=\$48.00$

9. $119 croquet set; 50% discount

You should not have problems with this: 50% discount means that you will pay half the price.

Hence, the sale price is:

$Sale\text{ }price=Orignal\text{ }price/2 \\\\ Sale\text{ }price=\$59.50$

10. $14.99 clock; 10% discount

$Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$14.99\times(1-0.10)=\\\\ Sale\text{ }price=\$14.99\times0.90=\\\\ Sale\text{ }price=\$13.49$

11. A radio is on sale for $50. If this price represents a 10% discount from the original price, what is the original price to the nearest nickel? Hint: need to use a proportion to find the whole.

First note that if the discount is 10%, the sale price is 100% - 10% = 90% of the original price.

Let's set the proportion that represents the proportionality between the two ratios, starting with the fact that $ is the 90% and original price is the 100% (the whole part):

First ratio: $50/90

Second ratio: x /100

Proportion: first ratio = second ratio

$\$50/90=x/100$

Solve for x:

$x=100\times\$50/90=\$55.55$

Hence, the original price is $55.55

12. A box of laundry detergent is on sale for $6.50. If this price represents a 40% discount from the original price, what is the original price to the nearest cent?

Use the same hint used in the question above: set a proportion.

Remember a 40% discount means that the sale price is 60% of the original price:

$\$6.50/60=x/100\\ \\ x=100\times\$6.50/60=\$10.83$

13. Determine the price of a $35 basketball that is on sale for 50% off the regular price.

Again, 50% discount means that the sale price will be half of the original price, or the original price will be double of the sale price.

Here, the original price is $35, hence the sale price is $35/2 = $17.50

14. Dominic bought a new alarm clock that was on sale for $18.75. If this price represents a 30% discount from the original price, what is the original price to the nearest cent?

Since the price is after a 30% discount, the sale price is a 70% of the original price, and you set the proportion:

$\$18.75/70=x/100$

Solve for x:

$x=100\times\$18.75/70=\$26.79$

15. Michael bought a new fishing rod. The regular price of the fishing rod was $125.99. He bought it on sale with a 15% discount. Sales tax of 3% is applied to the discounted total. What was the sale price with tax of Michael’s fishing rod to the nearest cent?

First find the the sale price after the 15% discount:

$\$125.99\times(1-0.15)=\$125.99\times0.85=\$107.09$

Now add the 3% tax:

$\$107.09\times1.03=\$110.30$

Hence, the sale price with tax is $110.30

The last answer (# 16) is in the attached file, since this already exceeds the number of characters allowed.

7 0

4 years ago

The Thompson family is traveling 1,500 miles to visit relatives. They plan to drive the same distance each day. If the Thompsons

nydimaria [60]

Answer:they will drive 500 miles each day.

Step-by-step explanation:

The Thompson family is traveling 1,500 miles to visit relatives. They plan to drive the same distance each day.

Let x represent the distance that they travel each day. If the Thompsons make the trip in 3 days, it means that the total distance that they travelled in 3 days would be

3 × x = 3x miles

Therefore , the distance that they will drive each day would be

3x = 1500

Dividing both sides of the equation by 3, it becomes

3x/3 = 1500/3

x = 500 miles

4 0

3 years ago

Answer the following question

Paha777 [63]

Answer:

Step-by-step explanation:

The areas are in sq. cm

3 0

4 years ago

Read 2 more answers

Please help evaluate?

Dominik [7]

3.

4^3 is equal to 64. Therefor log4(64) must be equal to 3.

3 0

3 years ago