Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #61 : Factorials

Divide: $\frac{3(4!)}{2!+2!+3!}$

Possible Answers:

$\frac{18}{5}$

$\frac{36}{5}$

47900160

Correct answer:

$\frac{36}{5}$

Explanation:

In order to simplify the factorials, expand all the terms first.

$\frac{3(4!)}{2!+2!+3!} = \frac{3(4\times 3\times2\times 1)}{(2\times 1)+(2\times 1)+(3\times2\times 1)}$

Simplify the numerator and denominator.

$\frac{3(24)}{2+2+6} = \frac{72}{10}=\frac{36}{5}$

The answer is: $\frac{36}{5}$

Report an Error

Example Question #2871 : Algebra Ii

Multiply: $0!\cdot (3+2!)\cdot 0!$

Possible Answers:

120

$\textup{The answer is not given.}$

Correct answer:

Explanation:

Evaluate by expanding the factorial in the parentheses. The zero factorial is a special case which equals to one.

$0!\cdot (3+2!)\cdot 0! = 1\cdot (3+(2\times 1))\cdot 1 = 1\cdot (5) \cdot 1$

The answer is:

Report an Error

Example Question #68 : Factorials

Divide: $\frac{3!}{5!}\div 3!$

Possible Answers:

$\frac{1}{120}$

$\frac{1}{60}$

$\frac{3}{10}$

$\frac{3}{40}$

$\frac{1}{40}$

Correct answer:

$\frac{1}{120}$

Explanation:

Evaluate by expanding the terms of the factorials.

$\frac{3!}{5!}\div 3! = \frac{3\times2\times1 }{5\times4\times3\times2\times1 }\div (3\times2\times1 )$

Cancel out the common terms in the first fraction.

$\frac{1 }{5\times4 }\div (3\times2\times1 )$

Change the division sign to a multiplication and take the reciprocal of the second quantity.

$\frac{1 }{5\times4 }\times \frac{1}{(3\times2\times1 )} =\frac{1}{120}$

The answer is: $\frac{1}{120}$

Report an Error

Example Question #69 : Factorials

Solve: $\frac{(5+3)!}{2(2+2)!}$

Possible Answers:

440

1680

840

420

Correct answer:

840

Explanation:

Evaluate the terms in the parentheses first.

$\frac{(5+3)!}{2(2+2)!} =\frac{(8)!}{2(4)!}$

Expand the factorials.

$\frac{8\times7\times6\times5\times4\times3\times2\times1 }{2(4\times3\times2\times1 )}$

The fraction, after simplifying all the terms, becomes:

$\frac{8\times7\times6\times5}{2} = 4\times7\times6\times5 = 840$

The answer is: 840

Report an Error

Example Question #212 : Mathematical Relationships And Basic Graphs

Solve the factorials: $\frac{3!}{5!} \cdot \frac{(1+5)!}{(3!+1)}$

Possible Answers:

$\frac{3}{2}$

$\frac{121}{480}$

$\frac{36}{7}$

600

$\frac{121}{140}$

Correct answer:

$\frac{36}{7}$

Explanation:

Simplify the terms in parentheses first.

$\frac{3!}{5!} \cdot \frac{(1+5)!}{(3!+1)} = \frac{3!}{5!} \cdot \frac{6!}{(3!+1)}$

Evaluate each factorial by writing out the terms.

$\frac{3\times 2\times 1}{5\times 4\times 3\times 2\times 1} \cdot \frac{6\times 5\times 4\times 3\times 2\times 1}{([3\times 2\times 1]+1)}$

Simplify the parentheses.

$\frac{3\times 2\times 1}{5\times 4\times 3\times 2\times 1} \cdot \frac{6\times 5\times 4\times 3\times 2\times 1}{7}$

Simplify all the common terms.

$\frac{6\times 3\times 2\times 1}{7} = \frac{36}{7}$

The answer is: $\frac{36}{7}$

Report an Error

Example Question #71 : Factorials

Try without a calculator.

True or false: $5! \times 5! = 25!$

Possible Answers:

False

True

Correct answer:

False

Explanation:

It is not necessary - and in fact, without a calculator, it is inconvenient - to calculate 25! to determine whether this is true or false.

- or factorial - is defined to be the product of the integers from 1 to . Therefore,

$5! = 1 \times 2 \times 3 \times 4 \times 5 = 120$

$5! \times 5! =120 \times 120 = 14,400$

If we continue to look at factorials, we can see that

$6! = 1 \times 2 \times 3 \times 4 \times 5 \times 6 = 720$

$7! = 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 = 5,040$

$8! = 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8= 40,320$

It can already be seen that and all higher factorials will be greater than $5! \times 5!$ , so it follows that the statement $5! \times 5! = 25!$ is false.

Report an Error

Example Question #2872 : Algebra Ii

Simplify the expression.

$\frac{7!xy^2}{5!y}$

Possible Answers:

$\frac{7!xy}{5!}$

7xy

42xy

7!xy

Correct answer:

42xy

Explanation:

By expanding the factorials and the powers it is a lot easier to see what terms will cancel.

In this example everything in the denominator cancels leaving a 6,7,x, and y in the numerator.

$\frac{7!xy^2}{5!y}=\frac{7*6*5*4*3*2*1*x*y*y}{5*4*3*2*1*y}=7*6*x*y=42xy$

Report an Error

Example Question #73 : Factorials

Try without a calculator.

Which expression is equal to $\frac{1,000!}{999!}$ ?

Possible Answers:

1,000

999!

999

None of these

Correct answer:

1,000

Explanation:

- or factorial - is defined to be the product of the integers from 1 to . Therefore,

$1,000 ! = 1 \cdot 2 \cdot 3 \cdot 4 \cdot ...\cdot 999 \cdot 1,000$

and

$999 ! = 1 \cdot 2 \cdot 3 \cdot 4 \cdot ...\cdot 999$

Therefore,

$\frac{1,000!}{999!}$

is equal to

$\frac{1 \cdot 2 \cdot 3 \cdot 4 \cdot ...\cdot 999 \cdot 1,000}{1 \cdot 2 \cdot 3 \cdot 4 \cdot ...\cdot 999 }$

All of the factors from 1 to 999 can be canceled out in both numerator and denominator, so the expression is equal to

$\frac{ 1,000}{1 }=1,000$

Report an Error

Example Question #72 : Factorials

What is the value of ?

Possible Answers:

Correct answer:

Explanation:

! is the symbol for factorial, which means the product of the whole numbers less than the given number.

Thus, 4! = 4 * 3 * 2 * 1 = 24 .

Report an Error

Example Question #1 : Other Factorials

What is the value of $\frac{10!}{7!}$ ?

Possible Answers:

980

1.43

504

720

None of the other answers are correct.

Correct answer:

720

Explanation:

Since the factorial has the property

$\frac{n!}{(n+1)!}$

we can write 10! as:

$10 \cdot 9 \cdot 8 \cdot (7!)$ .

Thus, our expression can be written as

$\frac{10\cdot9\cdot8\cdot7!}{7!}=10\cdot9\cdot8=720$

Report an Error

View Algebra 2 Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View Algebra 2 Tutors

Joseph
Certified Tutor

Rutgers University-New Brunswick, Bachelor in Arts, Chemistry. Rutgers Graduate School of Biomedical Sciences, Current Grad S...

View Algebra 2 Tutors

Michael
Certified Tutor

Cleveland State University, Bachelor of Science, Mathematics.

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

MCAT Tutors in New York City, ISEE Tutors in Chicago, LSAT Tutors in Dallas Fort Worth, English Tutors in Houston, LSAT Tutors in San Francisco-Bay Area, MCAT Tutors in San Francisco-Bay Area, GRE Tutors in San Francisco-Bay Area, Computer Science Tutors in San Francisco-Bay Area, SSAT Tutors in Los Angeles, English Tutors in Atlanta

Popular Courses & Classes

SAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Miami, LSAT Courses & Classes in Atlanta, ISEE Courses & Classes in Philadelphia, ACT Courses & Classes in Chicago, GMAT Courses & Classes in Boston, MCAT Courses & Classes in New York City, GRE Courses & Classes in Boston, LSAT Courses & Classes in Denver, GRE Courses & Classes in Houston

Popular Test Prep

ACT Test Prep in Chicago, GRE Test Prep in Houston, GMAT Test Prep in Houston, GMAT Test Prep in Atlanta, GRE Test Prep in Dallas Fort Worth, LSAT Test Prep in Denver, GMAT Test Prep in Seattle, ISEE Test Prep in Houston, SAT Test Prep in Chicago, GRE Test Prep in Boston

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #61 : Factorials

Example Question #2871 : Algebra Ii

Example Question #68 : Factorials

Example Question #69 : Factorials

Example Question #212 : Mathematical Relationships And Basic Graphs

Example Question #71 : Factorials

Example Question #2872 : Algebra Ii

Example Question #73 : Factorials

Example Question #72 : Factorials

Example Question #1 : Other Factorials

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: