We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Common Core: High School - Algebra : High School: Algebra

Study concepts, example questions & explanations for Common Core: High School - Algebra

Create An Account

All Common Core: High School - Algebra Resources

8 Diagnostic Tests 97 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : System Of Equations And Inequalities: Ccss.Math.Content.Hsa Ced.A.3

There are 3 apples in a small fruit basket and 7 apples in a large fruit basket. If Sally buys a total of 5 fruit baskets that have a combined total of 31 apples, write a system of equations that represents Sally's situation.

Possible Answers:

$\\3s+7l=31 \\s+4l=5$

$\\3s+7l=31 \\4s+l=5$

$\\3s+7l=31 \\s+l=5$

$\\3s+7l=5 \\s+l=31$

$\\3s+7l=31 \\2s+3l=5$

Correct answer:

$\\3s+7l=31 \\s+l=5$

Explanation:

To write the appropriate equation for this situation, start by identifying what is known.

$\\\text{small fruit basket}=3\text{ apples} \\\text{large fruit basket}=7\text{ apples}$

Now write the equation in words.

$\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=31\text{ apples}$

Let

$\\s=\text{small fruit basket} \\l=\text{large fruit basket}$

therefore the equation becomes,

3s+7l=31

Now, since there are 5 fruit baskets set up another equation.

$\\\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=5\text{ baskets} \\s+l=5$

From here set up the system of equation for this situation.

$\\3s+7l=31 \\s+l=5$

Report an Error

Example Question #1 : System Of Equations And Inequalities: Ccss.Math.Content.Hsa Ced.A.3

There are 5 apples in a small fruit basket and 10 apples in a large fruit basket. If Sally buys a total of 5 fruit baskets that have a combined total of 40 apples, write a system of equations that describes Sally's situation.

Possible Answers:

$\\5s+l=40 \\s+l=5$

$\\s+10l=40 \\s+l=5$

$\\5s+10l=40 \\3s+l=5$

$\\5s+10l=40 \\s+l=5$

$\\5s+10l=40 \\s+2l=5$

Correct answer:

$\\5s+10l=40 \\s+l=5$

Explanation:

To write the appropriate equation for this situation, start by identifying what is known.

$\\\text{small fruit basket}=5\text{ apples} \\\text{large fruit basket}=10\text{ apples}$

Now write the equation in words.

$\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=40\text{ apples}$

Let

$\\s=\text{small fruit basket} \\l=\text{large fruit basket}$

therefore the equation becomes,

5s+10l=40

Now, since there are 5 fruit baskets set up another equation.

$\\\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=5\text{ baskets} \\s+l=5$

From here set up the system of equation for this situation.

$\\5s+10l=40 \\s+l=5$

Report an Error

Example Question #1 : System Of Equations And Inequalities: Ccss.Math.Content.Hsa Ced.A.3

There are 15 apples in a small fruit basket and 20 apples in a large fruit basket. If Sally buys a total of 5 fruit baskets that have a combined total of 95 apples, write a system of equations that represents Sally's situation.

Possible Answers:

$\\5s+20l=95 \\s+l=5$

$\\15s+20l=95 \\s+4l=5$

$\\15s+20l=95 \\s+l=5$

$\\15s+20l=95 \\s+2l=5$

$\\15s+20l=95 \\3s+l=5$

Correct answer:

$\\15s+20l=95 \\s+l=5$

Explanation:

To write the appropriate equation for this situation, start by identifying what is known.

$\\\text{small fruit basket}=15\text{ apples} \\\text{large fruit basket}=20\text{ apples}$

Now write the equation in words.

$\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=95\text{ apples}$

Let

$\\s=\text{small fruit basket} \\l=\text{large fruit basket}$

therefore the equation becomes,

15s+20l=95

Now, since there are 5 fruit baskets set up another equation.

$\\\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=5\text{ baskets} \\s+l=5$

From here set up the system of equation for this situation.

$\\15s+20l=95 \\s+l=5$

Report an Error

Example Question #11 : System Of Equations And Inequalities: Ccss.Math.Content.Hsa Ced.A.3

There are 5 apples in a small fruit basket and 10 apples in a large fruit basket. If Sally buys a total of 5 fruit baskets that have a combined total of 40 apples, how many small baskets does Sally have?

Possible Answers:

s=2

s=5

s=1

s=4

s=3

Correct answer:

s=2

Explanation:

To write the appropriate equation for this situation, start by identifying what is known.

$\\\text{small fruit basket}=5\text{ apples} \\\text{large fruit basket}=10\text{ apples}$

Now write the equation in words.

$\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=40\text{ apples}$

Let

$\\s=\text{small fruit basket} \\l=\text{large fruit basket}$

therefore the equation becomes,

5s+10l=40

Now, since there are 5 fruit baskets set up another equation.

$\\\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=5\text{ baskets} \\s+l=5$

From here set up the system of equation for this situation.

$\\5s+10l=40 \\s+l=5$

Now, solve the second equation for .

$\\s+l=5 \\s=5-l$

Substitute this into the first equation.

$\\5s+10l=40 \\5(5-l)+10l=40 \\25-5l+10l=40 \\25+5l=40 \\5l=15 \\l=3$

Now substitute this value into the second equation to solve for .

$\\s+l=5 \\s=5-3\\s=2$

Report an Error

Example Question #441 : High School: Algebra

There are 5 apples in a small fruit basket and 10 apples in a large fruit basket. If Sally buys a total of 5 fruit baskets that have a combined total of 40 apples, how many large baskets does Sally have?

Possible Answers:

l=2

l=5

l=3

l=1

l=4

Correct answer:

l=3

Explanation:

To write the appropriate equation for this situation, start by identifying what is known.

$\\\text{small fruit basket}=5\text{ apples} \\\text{large fruit basket}=10\text{ apples}$

Now write the equation in words.

$\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=40\text{ apples}$

Let

$\\s=\text{small fruit basket} \\l=\text{large fruit basket}$

therefore the equation becomes,

5s+10l=40

Now, since there are 5 fruit baskets set up another equation.

$\\\# \text{ small fruit baskets}+\# \text{ large fruit baskets}=5\text{ baskets} \\s+l=5$

From here set up the system of equation for this situation.

$\\5s+10l=40 \\s+l=5$

Now, solve the second equation for .

$\\s+l=5 \\s=5-l$

Substitute this into the first equation.

$\\5s+10l=40 \\5(5-l)+10l=40 \\25-5l+10l=40 \\25+5l=40 \\5l=15 \\l=3$

Report an Error

Example Question #1 : Rearrange Formulas And Solve Equations: Ccss.Math.Content.Hsa Ced.A.4

To calculate the slope of a line, the following formula is used.

$m=\frac{y_2-y_1}{x_2-x_1}$

Solve this equation for y_2 .

Possible Answers:

y_2=(x_2-x_1)m+y_1

y_2=x_2m-x_1+y_1

y_2=x_2-x_1m+y_1

y_2=(x_2-x_1)m

y_2=(x_2-x_1)+y_1m

Correct answer:

y_2=(x_2-x_1)m+y_1

Explanation:

This question is asking to rearrange the slope formula to highlight a quantity of interest, specifically y_2 .

To rearrange the formula, perform algebraic operations. Recall that whatever operation that is done to one side needs to also be done on the other side in order to keep the equation balanced.

First, multiply both sides by the quantity (x_2-x_1) in order to move it from the right side of the equation to the left side. Performing the opposite operation allows for rearranging to occur.

$\\(x_2-x_1)\cdot m=\frac{y_2-y_1}{x_2-x_1}\cdot (x_2-x_1) \\\\(x_2-x_1)m=y_2-y_1$

Next, add y_1 to both sides of the equation.

$\\(x_2-x_1)m+y_1=y_2-y_1+y_1 \\(x_2-x_1)m+y_1=y_2$

Therefore, the equation solved for y_2 is

y_2=(x_2-x_1)m+y_1

Report an Error

Example Question #2 : Rearrange Formulas And Solve Equations: Ccss.Math.Content.Hsa Ced.A.4

To calculate the slope of a line, the following formula is used.

$m=\frac{y_2-y_1}{x_2-x_1}$

Solve this equation for y_1 .

Possible Answers:

y_1=(x_2-x_1)m+y_2

y_1=(x_2-x_1)m-y_2

y_1=-(x_2-x_1)m+y_2

y_1=-(x_2-x_1)m+y_2m

y_1=-(x_2-x_1)m-y_2

Correct answer:

y_1=-(x_2-x_1)m+y_2

Explanation:

This question is asking to rearrange the slope formula to highlight a quantity of interest, specifically y_1 .

To rearrange the formula, perform algebraic operations. Recall that whatever operation that is done to one side needs to also be done on the other side in order to keep the equation balanced.

First, multiply both sides by the quantity (x_2-x_1) in order to move it from the right side of the equation to the left side. Performing the opposite operation allows for rearranging to occur.

$\\(x_2-x_1)\cdot m=\frac{y_2-y_1}{x_2-x_1}\cdot (x_2-x_1) \\\\(x_2-x_1)m=y_2-y_1$

Next, subtract y_2 to both sides of the equation.

$\\(x_2-x_1)m-y_2=y_2-y_1-y_2 \\(x_2-x_1)m-y_2=-y_1$

Now, divide by negative one on both sides.

$\frac{(x_2-x_1)m-y_2}{-1}=-\frac{y_1}{-1}$

-(x_2-x_1)m+y_2=y_1

Therefore, the equation solved for y_1 is,

y_1=-(x_2-x_1)m+y_2

Report an Error

Example Question #33 : Creating Equations✭

To calculate the slope of a line, the following formula is used.

$m=\frac{y_2-y_1}{x_2-x_1}$

Solve this equation for x_2

Possible Answers:

$x_2=\frac{y_2+y_1}{m}+x_1$

$x_2=-\frac{y_2-y_1}{m}+x_1$

$x_2=\frac{y_2-y_1}{m}+x_1$

$x_2=\frac{y_2-y_1}{m}-x_1$

$x_2=-\frac{y_2-y_1}{m}-x_1$

Correct answer:

$x_2=\frac{y_2-y_1}{m}+x_1$

Explanation:

This question is asking to rearrange the slope formula to highlight a quantity of interest, specifically x_2 .

To rearrange the formula, perform algebraic operations. Recall that whatever operation that is done to one side needs to also be done on the other side in order to keep the equation balanced.

First, multiply both sides by the quantity (x_2-x_1) in order to move it from the right side of the equation to the left side. Performing the opposite operation allows for rearranging to occur.

$\\(x_2-x_1)\cdot m=\frac{y_2-y_1}{x_2-x_1}\cdot (x_2-x_1) \\\\(x_2-x_1)m=y_2-y_1$

Next divide by on both sides.

$\frac{(x_2-x_1)m}{m}=\frac{y_2-y_1}{m}$

$x_2-x_1=\frac{y_2-y_1}{m}$

Now add x_1 to both sides.

$x_2-x_1+x_1=\frac{y_2-y_1}{m}+x_1$

$x_2=\frac{y_2-y_1}{m}+x_1$

Report an Error

Example Question #34 : Creating Equations✭

To calculate the slope of a line, the following formula is used.

$m=\frac{y_2-y_1}{x_2-x_1}$

Solve this equation for x_1 .

Possible Answers:

$x_1=\frac{y_2-y_1}{m}+x_2$

$x_1=\frac{y_2-y_1}{m}-x_2$

$x_1=-\frac{y_2+y_1}{m}+x_2$

$x_1=-\frac{y_2-y_1}{m}-x_2$

$x_1=-\frac{y_2-y_1}{m}+x_2$

Correct answer:

$x_1=-\frac{y_2-y_1}{m}+x_2$

Explanation:

This question is asking to rearrange the slope formula to highlight a quantity of interest, specifically x_1 .

To rearrange the formula, perform algebraic operations. Recall that whatever operation that is done to one side needs to also be done on the other side in order to keep the equation balanced.

First, multiply both sides by the quantity (x_2-x_1) in order to move it from the right side of the equation to the left side. Performing the opposite operation allows for rearranging to occur.

$\\(x_2-x_1)\cdot m=\frac{y_2-y_1}{x_2-x_1}\cdot (x_2-x_1) \\\\(x_2-x_1)m=y_2-y_1$

Next divide by on both sides.

$\frac{(x_2-x_1)m}{m}=\frac{y_2-y_1}{m}$

$x_2-x_1=\frac{y_2-y_1}{m}$

Now subtract x_2 from both sides.

$x_2-x_1-x_2=\frac{y_2-y_1}{m}-x_2$

$-x_1=\frac{y_2-y_1}{m}-x_2$

Finally, divide by negative one.

$x_1=-\frac{y_2-y_1}{m}+x_2$

Report an Error

Example Question #3 : Rearrange Formulas And Solve Equations: Ccss.Math.Content.Hsa Ced.A.4

The equation for a circle centered at (0,0) is,

x^2+y^2=r^2

Solve the equation for .

Possible Answers:

r=x+y

r=x-y

$r=\sqrt{x^2+y^2}$

$r=\sqrt{x^2-y^2}$

r=x^2+y^2

Correct answer:

$r=\sqrt{x^2+y^2}$

Explanation:

This question is asking to rearrange this formula to highlight a quantity of interest, specifically .

To rearrange the formula, perform algebraic operations. Recall that whatever operation that is done to one side needs to also be done on the other side in order to keep the equation balanced.

To isolate take the square root of each side.

x^2+y^2=r^2

$\sqrt{x^2+y^2}=\sqrt{r^2}$

$\sqrt{x^2+y^2}=r$

Therefore, the equation solved for is

$r=\sqrt{x^2+y^2}$

Report an Error

View Tutors

Justin
Certified Tutor

Vanderbilt University, Bachelor, Computer Science, Mathematics, & Philosophy.

View Tutors

Ria
Certified Tutor

University of British Columbia, Bachelor in Arts, Psychology.

View Tutors

John
Certified Tutor

Arizona State University, Bachelor of Science, Microbiology.

All Common Core: High School - Algebra Resources

8 Diagnostic Tests 97 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SAT Tutors in Houston, Calculus Tutors in Washington DC, ISEE Tutors in San Diego, LSAT Tutors in Boston, LSAT Tutors in Houston, Algebra Tutors in Chicago, Statistics Tutors in New York City, English Tutors in Philadelphia, Math Tutors in Seattle, Math Tutors in Dallas Fort Worth

Popular Courses & Classes

SSAT Courses & Classes in New York City, ISEE Courses & Classes in Seattle, Spanish Courses & Classes in San Diego, SSAT Courses & Classes in Philadelphia, MCAT Courses & Classes in Seattle, GMAT Courses & Classes in New York City, SSAT Courses & Classes in Boston, ISEE Courses & Classes in Los Angeles, SSAT Courses & Classes in San Diego, MCAT Courses & Classes in Boston

Popular Test Prep

ACT Test Prep in Washington DC, GRE Test Prep in Atlanta, GRE Test Prep in San Diego, MCAT Test Prep in Phoenix, SSAT Test Prep in Denver, SAT Test Prep in Atlanta, ISEE Test Prep in Los Angeles, SSAT Test Prep in Houston, MCAT Test Prep in Denver, ISEE Test Prep in Denver

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

Common Core: High School - Algebra : High School: Algebra

Study concepts, example questions & explanations for Common Core: High School - Algebra

All Common Core: High School - Algebra Resources

Example Questions

Example Question #2 : System Of Equations And Inequalities: Ccss.Math.Content.Hsa Ced.A.3

Example Question #1 : System Of Equations And Inequalities: Ccss.Math.Content.Hsa Ced.A.3

Example Question #1 : System Of Equations And Inequalities: Ccss.Math.Content.Hsa Ced.A.3

Example Question #11 : System Of Equations And Inequalities: Ccss.Math.Content.Hsa Ced.A.3

Example Question #441 : High School: Algebra

Example Question #1 : Rearrange Formulas And Solve Equations: Ccss.Math.Content.Hsa Ced.A.4

Example Question #2 : Rearrange Formulas And Solve Equations: Ccss.Math.Content.Hsa Ced.A.4

Example Question #33 : Creating Equations✭

Example Question #34 : Creating Equations✭

Example Question #3 : Rearrange Formulas And Solve Equations: Ccss.Math.Content.Hsa Ced.A.4

All Common Core: High School - Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: