/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 96 Write a system of inequalities w... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 96

Write a system of inequalities whose solution set includes every point in the rectangular coordinate system.

Short Answer

Expert verified
The system of inequalities that includes every point in the rectangular coordinate system is: \(x \geq -\infty\), \(x \leq \infty\), \(y \geq -\infty\), and \(y \leq \infty\)

Step by step solution

01

Understanding Rectangular Coordinate System

The rectangular coordinate system is essentially a plane that extends infinitely in all four directions: up, down, left, and right. Therefore, all points in this system must be included in any inequality (or system of inequalities) that will define this system.
02

Defining Inequalities to Include All Points

Because the plane extends infinitely in all directions, you can write two inequalities that always hold true, no matter what the x and y values are. Those inequalities are \(x \geq -\infty\) and \(x \leq \infty\). Similarly, for the y-coordinate, the inequalities are \(y \geq -\infty\) and \(y \leq \infty\)
03

Writing The Final System of Inequalities

Therefore, the system of inequalities that includes every point in the rectangular coordinate system is: \(x \geq -\infty\), \(x \leq \infty\), \(y \geq -\infty\), and \(y \leq \infty\)

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

In more U.S. marriages, spouses have different faiths. The bar graph shows the percentage of households with an interfaith marriage in 1988 and \(2008 .\) Also shown is the percentage of households in which a person of faith is married to someone with no religion. (GRAPH CANT COPY) The formula $$1-\frac{1}{2} x+2=$$ models the percentage of U.S. households with an interfaith marriage, \(I, x\) years after \(1988 .\) The formula $$N=\frac{1}{4} x+6$$ models the percentage of U.S. households in which a person of faith is married to someone with no religion, \(N, x\) years after I988. Use these models to solve. a. In which years will more than \(34 \%\) of U.S. households have an interfaith marriage? b. In which years will more than \(15 \%\) of U.S. households have a person of faith married to someone with no religion? c. Based on your answers to parts (a) and (b), in which years will more than \(34 \%\) of households have an interfaith marriage and more than \(15 \%\) have a faith/no religion marriage? d. Based on your answers to parts (a) and (b), in which years will more than \(34 \%\) of households have an interfaith marriage or more than \(15 \%\) have a faith/no religion marriage?

How do you determine if an ordered pair is a solution of an inequality in two variables, \(x\) and \(y ?\)

On your next vacation, you will divide lodging between large resorts and small inns. Let \(x\) represent the number of nights spent in large resorts. Let \(y\) represent the number of nights spent in small inns. Write a system of inequalities that models the following conditions: You want to stay at least 5 nights. At least one night should be spent at a large resort. Large resorts average \(\$ 200\) per night and small inns average \(\$ 100\) per night. Your budget permits no more than \(\$ 700\) for lodging. b. Graph the solution set of the system of inequalities in part (a). c. Based on your graph in part (b), how many nights could you spend at a large resort and still stay within your budget?

What does it mean if a system of linear inequalities has no solution?

$$\text { Factor: } 25 x^{2}-81$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Statistics

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.