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Nonamiya [84]
3 years ago
12

What is the factorization of 1000x^6 - 27?

Mathematics
1 answer:
OverLord2011 [107]3 years ago
5 0

Answer:

B

Step-by-step explanation:

Cube root 1000x^6 = 10x^2

Cube root of - 27 = 3

So the first part of the factorization process is 10x^2 - 3. There is no help here because all of the answers give this binomial as the first factor.

The second factor is (10x^2)^2 + (3)*10x^2 + 3^2)

Expanding you get 100x^4 + 30x^2 + 9

Be very careful when looking at 100x^4 because that is where the answer is found.

It has to be B

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If 2/3 of a certain number is subtracted from twice the number, the result is 20. Find the number.​
sleet_krkn [62]

Let x be the number.

Set up an equation:

2x - 2/3x = 20

Simplify:

1 1/3x = 20

Divide both sides by 1 1/3

X = 15

The number is 15

3 0
3 years ago
Read 2 more answers
Pregnant women metabolize some drugs at a slower rate than the rest of the population. The half-life of caffeine is about 4 hour
UkoKoshka [18]

Answer:

Husband:

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Woman:

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

Step-by-step explanation:

The amount of caffeine in the body can be modeled by the following equation:

C(t) = C(0)e^{rt}

In which C(t) is the amount of caffeine t hours after 8 am, C(0) is how much coffee they took and r is the rate the the amount of caffeine decreases in their bodies.

110 mg of caffeine at 8 am,

So C(0) = 110

Husband

Half life of 4 hours. So

C(4) = 0.5C(0) = 0.5*110 = 55

C(t) = C(0)e^{rt}

55 = 110e^{4r}

e^{4r} = 0.5

Applying ln to both sides

\ln{e^{4r}} = \ln{0.5}

4r = \ln{0.5}

r = \frac{\ln{0.5}}{4}

r = -0.1733

So for the husband

C(t) = 110e^{-0.1733t}

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

C(t) = 110e^{-0.1733t}

C(11) = 110e^{-0.1733*11} = 16.35

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Pregnant woman

Half life of 10 hours. So

C(10) = 0.5C(0) = 0.5*110 = 55

C(t) = C(0)e^{rt}

55 = 110e^{10}

e^{10r} = 0.5

Applying ln to both sides

\ln{e^{10r}} = \ln{0.5}

10r = \ln{0.5}

r = \frac{\ln{0.5}}{10}

r = -0.0693

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

C(t) = 110e^{-0.0693t}

C(11) = 110e^{-0.0693*11} = 51.33

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

7 0
3 years ago
Which of the following is an open statement?
7nadin3 [17]
I think is C that what i think:;;:::::);:;:)
4 0
3 years ago
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5. Mr. Martinez is getting a rug for his den and wants to make sure it will fit.He knows the area of the den is 547.35 square fe
evablogger [386]
No.

If the Den is 547.35 Square feet, and one side length is 26.7, you divide the Area by one side length to get the other. 547.35/26.7= 20.5

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3 years ago
What graph represents the solution set of this system of inequalities? {y≤2x 1} {y&gt;−2x−3}
Genrish500 [490]
Already been answered||Vhttps://brainly.com/question/8240602


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3 years ago
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