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3 years ago

Which expression correctly shows x^6+2x^3+1 factored completely over the integers?

Mathematics

2 answers:

ira [324]3 years ago

8 0

Answer:

Option D, (x + 1)^2(x^2 - x + 1)^2

Step-by-step explanation:

Step 1: Factor

x^6 + 2x^3 + 1

(x + 1)^2(x^2 - x + 1)^2

Answer: Option D, (x + 1)^2(x^2 - x + 1)^2

BaLLatris [955]3 years ago

8 0

Option D is the answer!

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For your vegetable garden, you plan to plant 5 12 of it in corn, 1 6 in different kinds of beans, and 1 12 in tomatoes. You will

Ymorist [56]

Answer:

$\frac{2}{9}$ part of the garden will be planted in onions and squash combined.

Step-by-step explanation:

Given:

For your vegetable garden, you plan to plant 5 12 of it in corn, 1 6 in different kinds of beans, and 1 12 in tomatoes.

You will plant the remainder equally in eggplant, onions, and squash.

Now, to find the part of garden that will be planted in onions and squash combined.

Part of garden plan for planting corn = $\frac{5}{12}$

Part of garden plan for planting kinds of bean = $\frac{1}{6}$

Part of garden plan for planting tomatoes = $\frac{1}{12}$

So, adding all the parts of corn, beans and tomatoes:

$\frac{5}{12}+\frac{1}{6} +\frac{1}{12} \\\\=\frac{5+2+1}{12} \\\\=\frac{8}{12}$

Now, to get the rest of the parts of garden use to plant eggplant, onions, and squash we subtract $\frac{8}{12}$ from 1 whole:

$1-\frac{8}{12} \\\\=\frac{12-8}{12} \\\\=\frac{4}{12}$

As, given planting the remainder equally in eggplant, onions, and squash.

So, each will be planted in part of:

$\frac{4}{12} \div 3$

$=\frac{4}{12}\times \frac{1}{3}$

$=\frac{4}{36}$

On simplifying it:

$=\frac{1}{9}$ .

Thus, $\frac{1}{9}$ part of the garden for each eggplant, onions, and squash.

Now, to get the part of the garden will be planted in onions and squash combined we add $\frac{1}{9}$ part of garden planting for onions and $\frac{1}{9}$ of squash:

$\frac{1}{9} +\frac{1}{9} \\\\=\frac{1+1}{9} \\\\=\frac{2}{9}$

Therefore, $\frac{2}{9}$ part of the garden will be planted in onions and squash combined.

6 0

3 years ago

Read 2 more answers

-3(r+2)=40 whats is r in the equation , thanks :)

Tom [10]

Answer:

r = -46/3

Step-by-step explanation:

-3(r+2)=40

Distribute

-3r - 6 = 40

Add 6 to each side

-3r-6+6 = 40+6

-3r = 46

Divide by -3

r = 46/-3

r = -46/3

6 0

4 years ago

A number is multiplied by 5. If 5 is added to the product, you get 10. What is the number?

maria [59]

Answer:

The unknown number is 1.

Step-by-step explanation:

You have to form an expression. So let's make the unknown number as x. Firstly, a number is multiplied by 5 :

$x \times 5$

$= 5x$

Secondly, 5 is added to product and you will get 10 :

$5x + 5 = 10$

Lastly, you have to solve :

$5x + 5 = 10$

$5x = 10 - 5$

$5x = 5$

$x = 5 \div 5$

$x = 1$

4 0

3 years ago

Read 2 more answers

On a standard IQ test, the standard deviation is 15. How many random IQ scores must be obtained if we want to find the true popu

igor_vitrenko [27]

Answer:

We need at least 4238 scores.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.97}{2} = 0.015$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.015 = 0.985$ , so $z = 2.17$

Now, find the margin of error M

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

How many random IQ scores must be obtained if we want to find the true population mean (with an allowable error of 0.5) and we want 97 percent confidence in the results

We need at least n scores, in which N is found when $M = 0.5$ . So