Call Now to Set Up Tutoring:

(888) 888-0446

Create an account to track your scores
and create your own practice tests:

Create an Account Create a Practice Test

Flashcards: Solve Simple System of Two Variable Linear and Quadratic Equations: CCSS.Math.Content.HSA-REI.C.7

Find the points of intersection of $y = 51 x^{2} - 46$ $\displaystyle y = 51 x^{2} - 46$ and $\displaystyle y = 26 x + 27$. Round your answers to the nearest hundredth.

$\left( 8.96 , 5.74 \right) , \left( -8.69 , 7.97 \right)$ $\displaystyle \left( 8.96 , 5.74 \right) , \left( -8.69 , 7.97 \right)$

$\left( -4.39 , -17.43 \right) , \left( 2.5 , 10.63 \right)$ $\displaystyle \left( -4.39 , -17.43 \right) , \left( 2.5 , 10.63 \right)$

$\left( 1.48 , 102.48 \right), \left( -0.97 , -22.47 \right)$ $\displaystyle \left( 1.48 , 102.48 \right), \left( -0.97 , -22.47 \right)$

$\left( 1.12 , -3.84 \right) , \left( 8.17 , -15.05 \right)$ $\displaystyle \left( 1.12 , -3.84 \right) , \left( 8.17 , -15.05 \right)$

$\left( -4.02 , 5.3 \right) , \left( -2.85 , 0.66 \right)$ $\displaystyle \left( -4.02 , 5.3 \right) , \left( -2.85 , 0.66 \right)$

Report an Error Copyright Notice

All Common Core: High School - Algebra Resources

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

Want to review Common Core: High School - Algebra but don’t feel like sitting for a whole test at the moment? Varsity Tutors has you covered with thousands of different Common Core: High School - Algebra flashcards! Our Common Core: High School - Algebra flashcards allow you to practice with as few or as many questions as you like. Get some studying in now with our numerous Common Core: High School - Algebra flashcards.

Flashcards: Solve Simple System of Two Variable Linear and Quadratic Equations: CCSS.Math.Content.HSA-REI.C.7

Find the points of intersection of $y = 51 x^{2} - 46$ $\displaystyle y = 51 x^{2} - 46$ and $\displaystyle y = 26 x + 27$. Round your answers to the nearest hundredth.

$\left( 8.96 , 5.74 \right) , \left( -8.69 , 7.97 \right)$ $\displaystyle \left( 8.96 , 5.74 \right) , \left( -8.69 , 7.97 \right)$

$\left( -4.39 , -17.43 \right) , \left( 2.5 , 10.63 \right)$ $\displaystyle \left( -4.39 , -17.43 \right) , \left( 2.5 , 10.63 \right)$

$\left( 1.48 , 102.48 \right), \left( -0.97 , -22.47 \right)$ $\displaystyle \left( 1.48 , 102.48 \right), \left( -0.97 , -22.47 \right)$

$\left( 1.12 , -3.84 \right) , \left( 8.17 , -15.05 \right)$ $\displaystyle \left( 1.12 , -3.84 \right) , \left( 8.17 , -15.05 \right)$

$\left( -4.02 , 5.3 \right) , \left( -2.85 , 0.66 \right)$ $\displaystyle \left( -4.02 , 5.3 \right) , \left( -2.85 , 0.66 \right)$

Report an Error Copyright Notice

Flashcards: Solve Simple System of Two Variable Linear and Quadratic Equations: CCSS.Math.Content.HSA-REI.C.7

Find the points of intersection of $y = 51 x^{2} - 46$ $\displaystyle y = 51 x^{2} - 46$ and $\displaystyle y = 26 x + 27$. Round your answers to the nearest hundredth.

Your answer:

$\left( 8.96 , 5.74 \right) , \left( -8.69 , 7.97 \right)$ $\displaystyle \left( 8.96 , 5.74 \right) , \left( -8.69 , 7.97 \right)$

Your answer:

$\left( -4.39 , -17.43 \right) , \left( 2.5 , 10.63 \right)$ $\displaystyle \left( -4.39 , -17.43 \right) , \left( 2.5 , 10.63 \right)$

Your answer:

$\left( 1.12 , -3.84 \right) , \left( 8.17 , -15.05 \right)$ $\displaystyle \left( 1.12 , -3.84 \right) , \left( 8.17 , -15.05 \right)$

Your answer:

$\left( -4.02 , 5.3 \right) , \left( -2.85 , 0.66 \right)$ $\displaystyle \left( -4.02 , 5.3 \right) , \left( -2.85 , 0.66 \right)$

Correct answer:

$\left( 1.48 , 102.48 \right), \left( -0.97 , -22.47 \right)$ $\displaystyle \left( 1.48 , 102.48 \right), \left( -0.97 , -22.47 \right)$

Explanation:

The first step to solving this problem is to set the equations equal to each other.

$51 x^{2} - 46 = 26 x + 27$ $\displaystyle 51 x^{2} - 46 = 26 x + 27$

Now subtract the right hand side, to make it zero, so we can use the quadratic equation.

$51 x^{2} - 46 - 26 x - 27 = 0$ $\displaystyle 51 x^{2} - 46 - 26 x - 27 = 0$

$51 x^{2} - 26 x - 73 = 0$ $\displaystyle 51 x^{2} - 26 x - 73 = 0$

Recall the quadratic equation.

$x =\frac{ -b \pm\sqrt{ b^{2} - 4 a c }}{ 2 a }$ $\displaystyle x =\frac{ -b \pm\sqrt{ b^{2} - 4 a c }}{ 2 a }$

Where $\uptext{a}$ $\displaystyle \uptext{a}$, $\uptext{b}$ $\displaystyle \uptext{b}$, and $\uptext{c}$ $\displaystyle \uptext{c}$ correspond to coefficients in the following quadratic equation.

$a x^{2} + b x + c = 0$ $\displaystyle a x^{2} + b x + c = 0$

In this case, a = 51 $\displaystyle a = 51$ , b = -26 $\displaystyle b = -26$ , c = -73 $\displaystyle c = -73$ .

Now plug these values in.

$x =\frac{ 26 \pm\sqrt{\left( -26 \right)^2- 4 \cdot 51 \cdot -73 }}{ 2 \cdot 51 }$ $\displaystyle x =\frac{ 26 \pm\sqrt{\left( -26 \right)^2- 4 \cdot 51 \cdot -73 }}{ 2 \cdot 51 }$

$x =\frac{ 26 \pm 4 \sqrt{973} }{ 102 }$ $\displaystyle x =\frac{ 26 \pm 4 \sqrt{973} }{ 102 }$

Split this up into $\displaystyle 2$ equations.

$x =\frac{ 26 + 4 \sqrt{973} }{ 102 }$ $\displaystyle x =\frac{ 26 + 4 \sqrt{973} }{ 102 }$

$\displaystyle x = 1.48$

$x = - \frac{2 \sqrt{973}}{51} + \frac{13}{51}$ $\displaystyle x = - \frac{2 \sqrt{973}}{51} + \frac{13}{51}$

$\displaystyle x = -0.97$

Since we want points, we need to plug these values into one of the original equations.

$p_{1} = 51 \cdot 1.48 + 27$ $\displaystyle p_{1} = 51 \cdot 1.48 + 27$

$p_{1} = 75.48 + 27$ $\displaystyle p_{1} = 75.48 + 27$

$p_{1} = 102.48$ $\displaystyle p_{1} = 102.48$

So the first intersection point is at $\left( 1.48 , 102.48 \right)$ $\displaystyle \left( 1.48 , 102.48 \right)$

Now we need to find the last point of intersection.

$p_{2} = 51 \cdot -0.97 + 27$ $\displaystyle p_{2} = 51 \cdot -0.97 + 27$

$p_{2} = -49.47 + 27$ $\displaystyle p_{2} = -49.47 + 27$

$p_{2} = -22.47$ $\displaystyle p_{2} = -22.47$

So the second intersection point is at $\left( -0.97 , -22.47 \right)$ $\displaystyle \left( -0.97 , -22.47 \right)$

Flashcards: Solve Simple System of Two Variable Linear and Quadratic Equations: CCSS.Math.Content.HSA-REI.C.7

Find the points of intersection of $y = 24 x^{2} - 70$ $\displaystyle y = 24 x^{2} - 70$ and $\displaystyle y = 48 x + 93$. Round your answers to the nearest hundredth.

$\left( 8.87 , -6.51 \right) , \left( -2.84 , -3.34 \right)$ $\displaystyle \left( 8.87 , -6.51 \right) , \left( -2.84 , -3.34 \right)$

$\left( 8.38 , 18.56 \right) , \left( -2.93 , 4.26 \right)$ $\displaystyle \left( 8.38 , 18.56 \right) , \left( -2.93 , 4.26 \right)$

$\left( -2.8 , 3.57 \right) , \left( -8.72 , -7.49 \right)$ $\displaystyle \left( -2.8 , 3.57 \right) , \left( -8.72 , -7.49 \right)$

$\left( 7.61 , 14.19 \right) , \left( -6.06 , -16.25 \right)$ $\displaystyle \left( 7.61 , 14.19 \right) , \left( -6.06 , -16.25 \right)$

$\left( 3.79 , 183.96 \right), \left( -1.79 , 50.04 \right)$ $\displaystyle \left( 3.79 , 183.96 \right), \left( -1.79 , 50.04 \right)$

Report an Error Copyright Notice

Flashcards: Solve Simple System of Two Variable Linear and Quadratic Equations: CCSS.Math.Content.HSA-REI.C.7

Find the points of intersection of $y = 24 x^{2} - 70$ $\displaystyle y = 24 x^{2} - 70$ and $\displaystyle y = 48 x + 93$. Round your answers to the nearest hundredth.

Your answer:

$\left( 8.87 , -6.51 \right) , \left( -2.84 , -3.34 \right)$ $\displaystyle \left( 8.87 , -6.51 \right) , \left( -2.84 , -3.34 \right)$

Your answer:

$\left( 8.38 , 18.56 \right) , \left( -2.93 , 4.26 \right)$ $\displaystyle \left( 8.38 , 18.56 \right) , \left( -2.93 , 4.26 \right)$

Your answer:

$\left( -2.8 , 3.57 \right) , \left( -8.72 , -7.49 \right)$ $\displaystyle \left( -2.8 , 3.57 \right) , \left( -8.72 , -7.49 \right)$

Your answer:

$\left( 7.61 , 14.19 \right) , \left( -6.06 , -16.25 \right)$ $\displaystyle \left( 7.61 , 14.19 \right) , \left( -6.06 , -16.25 \right)$

Correct answer:

$\left( 3.79 , 183.96 \right), \left( -1.79 , 50.04 \right)$ $\displaystyle \left( 3.79 , 183.96 \right), \left( -1.79 , 50.04 \right)$

Explanation:

The first step to solving this problem is to set the equations equal to each other.

$24 x^{2} - 70 = 48 x + 93$ $\displaystyle 24 x^{2} - 70 = 48 x + 93$

Now subtract the right hand side, to make it zero, so we can use the quadratic equation.

$24 x^{2} - 70 - 48 x - 93 = 0$ $\displaystyle 24 x^{2} - 70 - 48 x - 93 = 0$

$24 x^{2} - 48 x - 163 = 0$ $\displaystyle 24 x^{2} - 48 x - 163 = 0$

Recall the quadratic equation.

$x =\frac{ -b \pm\sqrt{ b^{2} - 4 a c }}{ 2 a }$ $\displaystyle x =\frac{ -b \pm\sqrt{ b^{2} - 4 a c }}{ 2 a }$

$a x^{2} + b x + c = 0$ $\displaystyle a x^{2} + b x + c = 0$

In this case, a = 24 $\displaystyle a = 24$ , b = -48 $\displaystyle b = -48$, $\displaystyle c = -163$ .

Now plug these values in.

$x =\frac{ 48 \pm\sqrt{\left( -48 \right)^2- 4 \cdot 24 \cdot -163 }}{ 2 \cdot 24 }$ $\displaystyle x =\frac{ 48 \pm\sqrt{\left( -48 \right)^2- 4 \cdot 24 \cdot -163 }}{ 2 \cdot 24 }$

$x =\frac{ 48 \pm 4 \sqrt{1122} }{ 48 }$ $\displaystyle x =\frac{ 48 \pm 4 \sqrt{1122} }{ 48 }$

Split this up into $\displaystyle 2$ equations.

$x =\frac{ 48 + 4 \sqrt{1122} }{ 48 }$ $\displaystyle x =\frac{ 48 + 4 \sqrt{1122} }{ 48 }$

$\displaystyle x = 3.79$

$x = - \frac{\sqrt{1122}}{12} + 1$ $\displaystyle x = - \frac{\sqrt{1122}}{12} + 1$

$\displaystyle x = -1.79$

Since we want points, we need to plug these values into one of the original equations.

$p_{1} = 24 \cdot 3.79 + 93$ $\displaystyle p_{1} = 24 \cdot 3.79 + 93$

$p_{1} = 90.96 + 93$ $\displaystyle p_{1} = 90.96 + 93$

$p_{1} = 183.96$ $\displaystyle p_{1} = 183.96$

So the first intersection point is at $\left( 3.79 , 183.96 \right)$ $\displaystyle \left( 3.79 , 183.96 \right)$

Now we need to find the last point of intersection.

$p_{2} = 24 \cdot -1.79 + 93$ $\displaystyle p_{2} = 24 \cdot -1.79 + 93$

$p_{2} = -42.96 + 93$ $\displaystyle p_{2} = -42.96 + 93$

$p_{2} = 50.04$ $\displaystyle p_{2} = 50.04$

So the second intersection point is at $\left( -1.79 , 50.04 \right)$ $\displaystyle \left( -1.79 , 50.04 \right)$

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)

View Tutors

Mai
Certified Tutor

University of Jordan, Bachelor of Science, Pharmacy. University of British Columbia, Master of Science, Pharmacy.

View Tutors

Heather
Certified Tutor

Dickinson College, Bachelor of Science, French. Iowa State University, Master of Arts, Multi-/Interdisciplinary Studies, Gene...

View Tutors

Margery
Certified Tutor

University of South Alabama, Bachelor of Science, Mathematics and Statistics.

Popular Subjects

Spanish Tutors in New York City, Biology Tutors in Philadelphia, ACT Tutors in Philadelphia, SAT Tutors in Boston, Statistics Tutors in Houston, Biology Tutors in New York City, SAT Tutors in San Diego, Math Tutors in Houston, English Tutors in Atlanta, Biology Tutors in Dallas Fort Worth

Popular Courses & Classes

ACT Courses & Classes in Boston, Spanish Courses & Classes in Philadelphia, GRE Courses & Classes in Seattle, SAT Courses & Classes in Atlanta, LSAT Courses & Classes in Chicago, Spanish Courses & Classes in New York City, MCAT Courses & Classes in Phoenix, LSAT Courses & Classes in Seattle, ISEE Courses & Classes in Miami, ISEE Courses & Classes in Phoenix

Popular Test Prep

ISEE Test Prep in Atlanta, LSAT Test Prep in Philadelphia, SSAT Test Prep in Denver, ACT Test Prep in Denver, ISEE Test Prep in Washington DC, LSAT Test Prep in Atlanta, ACT Test Prep in Boston, GRE Test Prep in Seattle, ISEE Test Prep in Phoenix, MCAT Test Prep in Philadelphia

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Create an account to track your scores
and create your own practice tests:

Flashcards: Solve Simple System of Two Variable Linear and Quadratic Equations: CCSS.Math.Content.HSA-REI.C.7

All Common Core: High School - Algebra Resources

Flashcards: Solve Simple System of Two Variable Linear and Quadratic Equations: CCSS.Math.Content.HSA-REI.C.7

Flashcards: Solve Simple System of Two Variable Linear and Quadratic Equations: CCSS.Math.Content.HSA-REI.C.7

Flashcards: Solve Simple System of Two Variable Linear and Quadratic Equations: CCSS.Math.Content.HSA-REI.C.7

Flashcards: Solve Simple System of Two Variable Linear and Quadratic Equations: CCSS.Math.Content.HSA-REI.C.7

Report an issue with this question