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3 years ago

6x^3 - 7x^2 - 3x = 0. Show the correct steps.

Mathematics

2 answers:

Jlenok [28]3 years ago

6 0

Hey there! :)

Answer:

x = -1/3, 0, 3/2.

Step-by-step explanation:

Starting with:

6x³ - 7x² - 3x = 0

Factor out a greatest common factor, or x from each term:

x(6x² - 7x - 3) = 0

Factor the expression inside of the parenthesis:

x(3x +1)(2x - 3) = 0

Use the Zero Product Property to find the solutions:

x = 0

---------

3x + 1 = 0

3x = -1

x = -1/3

-----------

2x - 3 = 0

2x = 3

x = 3/2

----------

The solutions to this equation are x = -1/3, 0, 3/2.

pishuonlain [190]3 years ago

5 0

Answer:

x = 0 or x = -1/3 or x = 3/2

Step-by-step explanation:

6x^3 - 7x^2 - 3x = 0

Factor out an x.

x(6x^2 - 7x - 3) = 0

To factor the trinomial, we try trial and error.

6x = 2x * 3x

-3 = -1 * 3 = -3 * 1

We need to place 2x and 3x and -1 and 3 or -3 and 1 in order to make the middle term come out as -7x.

x(3x + 1)(2x - 3) = 0

x = 0 or 3x + 1 = 0 or 2x - 3 = 0

x = 0 or 3x = -1 or 2x = 3

x = 0 or x = -1/3 or x = 3/2

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2 years ago

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Answer:

-Convenience Sampling

Step-by-step explanation:

Convenience Sampling is a sampling method that is employed simply because the samples are easy to reach or access. It is a non-probability system of sampling and not a very strong method of sampling. For a serious research such as the one being conducted by the Superintendent, who has ample time to perform the research, this is not a very good sampling method. A Convenience style of research would mean that he can just walk into a cafeteria with students and administer the test to them.

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3 years ago

Add. (3b + 5) + (2b + 4)

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Answer:

$\huge{ \fbox{ \sf{5b + 9}}}$

Step-by-step explanation:

$\star{ \text{( \: 3b + 5) + (2b + 4)}}$

$\text{Step \: 1 \: : \sf{Remove \: the \: unnecessary \: parentheses}}$

$\text{When \: there \: is \: a \: ( + ) \: in \: front \: of \: an \: expression \: in \: parentheses \:, there \: is \: no \: need \: to \: change \: the \: sign \: of \: each \: term \: in \: the \: expression.}$

$\text{That \: means, \: the \: expression \: remains \: the \: same. \: Just \: you \: have \: to \: remove \: the \: parentheses.}$

$\mapsto{ \sf{3b + 5 + 2b + 4}}$

$\text{Step \: 2 \: : Collect \: like \: terms.}$

$\text{Like \: terms \: are \: those \: which \: have \: the \: same \: base.}$

$\mapsto{ \sf{3b + 2b + 5 + 4}}$

$\mapsto{ \sf{5b + 5 + 4}}$

$\text{ Step \: 3 \: : \sf{Add \: the \: numbers : 5 \: and \: 4}}$

$\mapsto{ \boxed {\sf{ {5b + 9}}}}$

Hope I helped!

Best regards! :D

~ $\sf{TheAnimeGirl}$

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3 years ago

In a sociology class there are 1414 sociology majors and 1111 non-sociology majors. 33 students are randomly selected to present

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Answer: $0.4065$

Step-by-step explanation:

Given : In a sociology class there are 14 sociology majors and 11 non-sociology majors.

Total students = 14+11=25

Number of students are randomly selected = 3

Then, the number of ways to select 3 students from 25 students :-

$^{25}C_3=\dfrac{25!}{(25-3)!3!}=\dfrac{25\times24\times23\times22!}{22!3!}\\\\=2300$

Number of ways to select at least 2 of the 3 students re non-sociology majors :-

$^{14}C_1\times^{11}C_2+^{14}C_0\times ^{11}C_{3}\\\\=(14)\times\dfrac{11!}{2!(11-2)!}+(1)\times\dfrac{11!}{3!(11-3)!}\\\\=(14)(11\times5)+\dfrac{11\times10\times9}{6}\\\\=770+165=935$

The probability that at least 2 of the 3 students selected are non-sociology majors will be :-

$\dfrac{935}{2300}=0.40652173913\approx0.4065$

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