Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Problem 11

If \(x^2+2 x y+y^2=64\) and \(y-x=12\), which of the following could be the value of \(x\) ? A) \(-10\) B) \(-4\) C) 2 D) 10

Short Answer

Expert verified
The correct answer is: \(x = -10\) (Option A).

Step by step solution

01

Make y the subject in the second equation

In the equation \(y - x = 12\), add x to both sides to get: \(y = x + 12\)
02

Substitute the expression for y in the first equation

Replace \(y\) in the equation \(x^2 + 2xy + y^2 = 64\) with the expression from Step 1: \(x^2 + 2x(x + 12) + (x + 12)^2 = 64\)
03

Simplify the equation

Expand the equation and combine like terms: \(x^2 + 2x^2 + 24x + x^2 + 24x + 144 = 64\) Combine the x terms: \(4x^2 + 48x + 144 = 64\)
04

Further simplify the equation

To make the equation easier to solve, we can subtract 64 from both sides: \(4x^2 + 48x + 80 = 0\) Now, divide the entire equation by 4: \(x^2 + 12x + 20 = 0\)
05

Factor the quadratic equation

To solve for x, we need to factor the quadratic equation: \((x + 2)(x + 10) = 0\)
06

Find the values of x

Set each factor equal to 0 and solve for x: \(x + 2 = 0 \Rightarrow x = -2\) \(x + 10 = 0 \Rightarrow x = -10\)
07

Check the possible value of x

We have two potential solutions for x: -2 and -10. Let's see which of these is among the given options: A) \(x = -10\) - This value is among our solutions. B) \(x = -4\) - This value is not among our solutions. C) \(x = 2\) - This value is not among our solutions. D) \(x = 10\) - This value is not among our solutions. So, the correct answer is: \(x = -10\) (Option A).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A) NO CHANGE B) who C) whose D) whom

A submarine currently operating at 100 feet below the surface of the ocean begins to dive to increased depths at a rate of 30 feet per minute. Which of the following equations represents the submarine's depth below the surface, \(d\), in feet, \(m\) minutes after beginning to dive? A) \(d=100+30 \mathrm{~m}\) B) \(d=100-30 \mathrm{~m}\) C) \(d=100-30\) D) \(d=100 m-30\)

$$ 0.27(a+b)=0.15 a+0.35 b $$ An athletic trainer is attempting to produce a carbohydrate-electrolyte solution that is at \(27 \%\) carbohydrates by mass, which is the maximum amount of saturation allowed by her league. A supply company provides solutions that are at \(15 \%\) and \(35 \%\) carbohydrates by mass, respectively. Based on the equation above, if the trainer uses 10 quarts of the \(15 \%\) solution, how many quarts of the \(35 \%\) solution will she need? A) 180 B) 90 C) 30 D) 15 $$ f(x)=(x-b)^2-4 $$

A group of students at Omega High School is using staples and popsicle sticks to build a scale model of the Great Wall of China as part of a project detailing China's military history. The number of staples the students will need is three times the number of popsicle sticks they will need. If the students determine they need 84 staples for this particular project, how many popsicle sticks will they need?

A) NO CHANGE B) the providence of C) the provenance of D) providential for
See all solutions

Recommended explanations on English Textbooks

Phonology

Read Explanation

Summary Text

Read Explanation

International English

Read Explanation

Essay Prompts

Read Explanation

Global English

Read Explanation

Rhetoric

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free