/*! 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 67 Determine whether each statement... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 67

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The rectangular coordinate system provides a geometric picture of what an equation in two variables looks like.

Short Answer

Expert verified
Yes, the statement makes sense. The rectangular coordinate system does provide a geometric representation of what an equation in two variables looks like. It enables the visual interpretation of the solution set of the equation.

Step by step solution

01

Understanding the statement

When we say 'The rectangular coordinate system provides a geometric picture of what an equation in two variables looks like', it means that using the rectangular coordinate system, we can visualize the solutions of an equation in two variables.
02

Understanding the rectangular coordinate system

A rectangular coordinate system is a two-dimensional graph in which each point is identified by an ordered pair of numbers (x, y). The first number corresponds to the x-coordinate and the second to the y-coordinate. It's called 'rectangular' because it forms a grid of rectangles.
03

Understanding how the coordinate system represents equations

If we take any equation in two variables, for example, \(y = 2x + 1\), we can use the coordinate system to represent it. Each solution of this equation corresponds to a point on the plane, and the collection of all such points forms a line. This line gives a 'picture' of what the equation looks like.
04

Concluding whether the statement makes sense

Given the explanations above, it can be concluded that the statement does make sense. The rectangular coordinate system does indeed provide a geometric representation of an equation in two variables. It allows us to visualize the set of all possible solutions to the equation.

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

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$V=\pi r^{2} h \text { for } h$$

A tennis club offers two payment options. Members can pay a monthly fee of \(\$ 30\) plus \(\$ 5\) per hour for court rental time. The second option has no monthly fee, but court time costs \(\$ 7.50\) per hour. a. Write a mathematical model representing total monthly costs for each option for \(x\) hours of court rental time. b. Use a graphing utility to graph the two models in a \([0,15,1]\) by \([0,120,20]\) viewing rectangle. c. Use your utility's trace or intersection feature to determine where the two graphs intersect. Describe what the coordinates of this intersection point represent in practical terms. d. Verify part (c) using an algebraic approach by setting the two models equal to one another and determining how many hours one has to rent the court so that the two plans result in identical monthly costs.

In Exercises \(127-130,\) solve each equation by the method of your choice. $$ \sqrt{2} x^{2}+3 x-2 \sqrt{2}=0 $$

When the sum of 1 and twice a negative number is subtracted from twice the square of the number, 0 results. Find the number.

An isosceles right triangle has legs that are the same length and acute angles each measuring \(45^{\circ} .\) (GRAPH NOT COPY) a. Write an expression in terms of \(a\) that represents the length of the hypotenuse. b. Use your result from part (a) to write a sentence that describes the length of the hypotenuse of an isosceles right triangle in terms of the length of a leg.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Pure Maths

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.