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3 years ago

Factor completely: 2x3 + 6x2 + 10x + 30

Mathematics

2 answers:

lisov135 [29]3 years ago

4 0

Answer: The required factored form of the given expression is $2(x+3)(x^2+5).$

Step-by-step explanation: We are given to factor the following cubic expression completely :

$E=2x^3+6x^2+10x+30~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

First we will take 2 common as it is multiplied to all the terms of the expression and then we will try to factorize the rest of the expression.

The factorization of expression (i) is as follows :

$E\\\\=2x^3+6x^2+10x+30\\\\=2(x^3+3x^2+5x+15)\\\\=2(x^2(x+3)+5(x+3))\\\\=2(x+3)(x^2+5).$

Thus, the required factored form of the given expression is $2(x+3)(x^2+5).$

qwelly [4]3 years ago

3 0

The complete factor from:

2x3 + 6x2 + 10x + 30
2x(x+3) + 10(x+3)
(x+3)(2x+10)
2(x+5)(x+3)

hope this help

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Please help its due today!! yes

Effectus [21]

Answer:

b. 5:3

c. 20:12 or 20 cups of flour and 12 eggs

d. 10 cups of flour

e. 9 eggs

Step-by-step explanation:

b. take one point from each number line and simplify it (example 15:9) and simplify it so you get your ratio of (5:3)

c. our ratio for one batch of cookies is 5:3 so mulitply 4 on both sides to find 4 batches of cookies

d. look at your numberline that represents number of eggs, 6 aligns with the number 10 on the numberline that shows "flour in cups" making your answer 10 cups of flour.

e. same thing as the problem before look at your numberline that shows cups of flour (which in this problem its 15) and see where that aligns on the "number of eggs" numberline above.

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3 years ago

A cone and its dimensions are shown in the diagram above.

Kisachek [45]

Answer:

The answer closest is answer D) 62.13

Step-by-step explanation:

I think u multiply them.

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2 years ago

A sequence can be generated by using an=4a(n-1)

WITCHER [35]

This problem is half understanding the question and half just plugging in numbers.

Understanding the Question:
So its saying that n = whole number bigger than one, making n = 2, 3, 4, 5, etc.

Now try plugging any number n into the $a_n = 4a_{n-1}$ equation. Let's use 2 to make it simple. If you plug in 2, you get:
$a_2 = 4a_{2-1}\\
a_2 = 4a_1$
Remember that the subscripts (the small numbers in the corner) are simply the term number. $a_1$ is term 1, $a_2$ is term 2, etc. The equation is saying that "term 2 = 4 times term 1."

If you keep plugging in random numbers for n, you'll see that the equation basically says, "a term = 4 times the term right before it." That makes it easy to plug and chug to get our answer.

Plugging and Chugging
Now we understand the question is asking for the first 4 terms, and each term is 4 times the last term. You're told that term 1, $a_1$ = 6. That makes the next four terms:

Term 2
$a_2 = 4a_{2-1}\\
 a_2 = 4a_1\\
 a_2 = 4(6)\\
 a_2 = 24$

Term 3
$a_3 = 4a_{3-1}\\ a_3 = 4a_2\\ a_3 = 4(24)\\ a_3 = 96$

Term 4
$a_4 = 4a_{4-1}\\ a_4 = 4a_3\\ a_4 = 4(96)\\ a_4 = 384$

Your first 4 terms are 4, 24, 96, and 384.

--------

Answer: A) F

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3 years ago

According to Padgett Business Services, 20% of all small-business owners say the most important advice for starting a business i

elena-s [515]

Answer:

a) There is a 6.88% probability that none of the owners would say preparing for long hours and hard work is the most important advice.

b) There is a 1.93% probability that six or more owners would say preparing for long hours and hard work is the most important advice.

c) There is a 10.32% probability that exactly five owners would say having good financing ready is the most important advice.

d) The expected number of owners who would say having a good plan is the most important advice is 2.28

Step-by-step explanation:

Questions a), b), c) are all solved as binomial distribution problems.

Question d) is a simple calculation.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $\pi$ is the probability of X happening.

For these problems

12 business owners were contacted, so $n = 12$ .

a. What is the probability that none of the owners would say preparing for long hours and hard work is the most important advice?

20% of all small-business owners say the most important advice for starting a business is to prepare for long hours and hard work, so $\pi = 0.2$ .

That is P(X=0) when $\pi = 0.2$ .

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 0) = C_{12,0}.(0.2)^{0}.(0.8)^{12} = 0.0688$

There is a 6.88% probability that none of the owners would say preparing for long hours and hard work is the most important advice.

b. What is the probability that six or more owners would say preparing for long hours and hard work is the most important advice?

20% of all small-business owners say the most important advice for starting a business is to prepare for long hours and hard work, so $\pi = 0.2$ .

This is:

$P = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)$

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 6) = C_{12,6}.(0.2)^{6}.(0.8)^{6} = 0.0155$

$P(X = 7) = C_{12,7}.(0.2)^{7}.(0.8)^{5} = 0.0033$

$P(X = 8) = C_{12,8}.(0.2)^{8}.(0.8)^{4} = 0.0005$

$P(X = 9) = C_{12,9}.(0.2)^{9}.(0.8)^{3} = 0.00006$

$P(X = 10) = C_{12,10}.(0.2)^{10}.(0.8)^{2} = 0.000004$

$P(X = 11) = C_{12,11}.(0.2)^{11}.(0.8)^{1} = 0.0000002$

$P(X = 12) = C_{12,12}.(0.2)^{12}.(0.8)^{0} = 0.000000004$

So:

$P = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) = 0.0155 + 0.0033 + 0.0005 + 0.000006 + 0.000004 + 0.0000002 + 0.000000004 = 0.0193$

There is a 1.93% probability that six or more owners would say preparing for long hours and hard work is the most important advice.

c. What is the probability that exactly five owners would say having good financing ready is the most important advice?

Twenty-five percent say the most important advice is to have good financing ready, so $\pi = 0.25$

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 5) = C_{12,5}.(0.25)^{5}.(0.75)^{7} = 0.1032$

There is a 10.32% probability that exactly five owners would say having good financing ready is the most important advice.

d. What is the expected number of owners who would say having a good plan is the most important advice?

Nineteen percent say having a good plan is the most important advice, so that is $0.19*12 = 2.28$

The expected number of owners who would say having a good plan is the most important advice is 2.28

4 0

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photoshop1234 [79]

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