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3 years ago

Factor completely 15x^5 + 12x^4-24x^3-3x^2

Mathematics

1 answer:

diamong [38]3 years ago

7 0

Answer:

3x^2 (5x^3 + 4x^2 - 8x - 1)

Step-by-step explanation:

The given expression is 15x^5 + 12x^4-24x^3-3x^2

Here we have to find the GCF of all the above terms.

The GCF is 3x^2, let's take out 3x^2 and write the remaining terms in the parenthesis.

15x^5 + 12x^4-24x^3-3x^2

=3x^2 (5x^3 + 4x^2 - 8x - 1)

Therefore, the factors are 3x^2 and (5x^3 + 4x^2 -8x -1).

15x^5 + 12x^4-24x^3-3x^2 = 3x^2 (5x^3 + 4x^2 -8x -1)

Thank you.

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weqwewe [10]

Irrational numbers
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7 0

3 years ago

A particular country's exports of goods are increasing exponentially. The value of the exports, t years after 2008, can be ap

Alex_Xolod [135]

Answer:

a) For 2008 we have that t = 2008-2008 = 0 and we have:

$V(0)= 1.4e^{0.039*0}= 1.4$

For 2022 we have that t = 2022-2008=14 and if we replace we got:

$V(12) = 1.4 e^{0.039*14}=2.417$

b) $2.8 = 1.4 e^{0.039 t}$

We can divide both sides by 1.4 and we got:

$2 = e^{0.039 t}$

Now natural log on both sides:

$ln (2) = 0.039 t$

$t = \frac{ln(2)}{0.039}= 17.77 years$

Step-by-step explanation:

For this case we have the following model given:

$V(t) = 1.4 e^{0.039 t}$

Where V represent the exports of goods and the the number of years after 2008.

Part a

Estimate the value of the country's exports in 2008 and 2022

For 2008 we have that t = 2008-2008 = 0 and we have:

$V(0)= 1.4e^{0.039*0}= 1.4$

For 2022 we have that t = 2022-2008=14 and if we replace we got:

$V(12) = 1.4 e^{0.039*14}=2.417$

Part b

What is the doubling time for the value of the country's exports.

For this case we can set up the following condition:

$2.8 = 1.4 e^{0.039 t}$

We can divide both sides by 1.4 and we got:

$2 = e^{0.039 t}$

Now natural log on both sides:

$ln (2) = 0.039 t$

$t = \frac{ln(2)}{0.039}= 17.77 years$

3 0

3 years ago

A sparkling-water distributor wants to make up 200 gallons of sparkling water to sell for $5.00 per gallon. She wishes to mix th

Sedbober [7]

Assuming she make no profit and no loss from the business.

Let the number of gallons of the $8 grade water used be x, that of the $3 grade water, y, and that of the $4.50 grade water be z, then:

x + y + z = 200 . . . (1)
8x + 3y + 4.5z = 200(5) = 1,000 . . . (2)
z = 2y . . . (3)

Putting equation (3) into equations (1) and (2), we have:

x + y + 2y = 200
or x + 3y = 200 . . . (4)
and
8x + 3y + 4.5(2y) = 1000
or 8x + 3y + 9y = 1000
or 8x + 12y = 1000 . . . (5)

Multiplying equation (4) by 4, we have:
4x + 12y = 800 . . . (6)

Subtracting equation (6) from equation (5), we have:
4x = 200
or x = 200 / 4 = 50

Substituting for x into equation (4), we have:
50 + 3y = 200
or 3y = 200 - 50 = 150
or y = 150 / 3 = 50

Substituting for z into equation (3) gives:

z = 2(50) = 100

Therefore, 50 gallons each of the $8 grade water and the $3 grade water should be used and 100 gallons of the $4.50 grade water.

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3 years ago

I need help plzzzzzzz :))

SVEN [57.7K]

Answer:

C. Both Functions Have a y-intercept of -2

Step-by-step explanation:

In Function F it shows us that it has a y-intercept of -2, and in the equation of Function G it shows us that you would subtract 2 out of what the initial value would be:

(3 x 0 = 0)

0 - 2 would be -2 so it would have a y-intercept of -2.

4 0

2 years ago

DUE TODAY PLEASE HELP

Amiraneli [1.4K]

Answer: 6. 113.398 7. 354.882 8. 4.82803

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Step-by-step explanation:

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3 years ago