/*! 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 90 For Exercises 87 through \(91,\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 90

For Exercises 87 through \(91,\) fill in each blank with "0, "positive," or "negative." For Exercises 92 and \(93,\) fill in each blank with "x" \(o r^{\text {tr }} y^{\prime \prime}\) (__,__) quadrant II

Short Answer

Expert verified
(negative, positive)

Step by step solution

01

Understanding Quadrant II

In a standard Cartesian coordinate system, Quadrant II is the top-left quadrant. Here, the x-values (horizontal axis) are negative, and the y-values (vertical axis) are positive.
02

Determine the x-value

In Quadrant II, any point's x-coordinate is to the left of the y-axis. Therefore, the x-coordinate is 'negative.'
03

Determine the y-value

In Quadrant II, any point's y-coordinate is above the x-axis. Therefore, the y-coordinate is 'positive.'
04

Fill in the Blanks

Based on the determinations from the previous steps, fill in the blanks as follows: (negative, positive). Thus, representing quadrants using these descriptions for Quadrant II.

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Quadrants in the Coordinate System
The concept of quadrants is essential in a Cartesian coordinate system. This system consists of two perpendicular axes, the x-axis (horizontal) and the y-axis (vertical), which intersect at a point called the origin. When these axes divide the plane, they form four quadrants. Each quadrant is like a unique section, having its own characteristics based on the signs of the x-coordinate and y-coordinate.
  • Quadrant I: Both x and y coordinates are positive.
  • Quadrant II: The x-coordinate is negative, and the y-coordinate is positive. This is because it is located on the top-left section of the plane.
  • Quadrant III: Both x and y coordinates are negative.
  • Quadrant IV: The x-coordinate is positive, and the y-coordinate is negative.
Understanding which quadrant a point is in can tell you a lot about its position relative to the axes. It helps in determining the signs of the coordinates without needing to calculate further. Reading graphs becomes much simpler with this knowledge.
Delving into the x-coordinate
The x-coordinate in a Cartesian coordinate system is responsible for indicating how far along the horizontal axis a point is. It tells you about the position of the point in relation to the y-axis.
The x-coordinate is written as the first value in an ordered pair \(x,y\). Depending on its value, the x-coordinate can tell us a lot about which quadrant a point would fall into:
  • Positive x-coordinate: The point is located to the right of the y-axis, either in Quadrant I or Quadrant IV.
  • Negative x-coordinate: The point lies to the left of the y-axis, either in Quadrant II or Quadrant III.
  • x-coordinate is zero: The point is exactly on the y-axis and does not belong to any quadrant.
These characteristics of the x-coordinate are crucial, especially when trying to locate specific points on a plane or analyzing graphs.
Exploring the y-coordinate
The y-coordinate plays a pivotal role in pinning down the exact vertical position of a point on a Cartesian plane. Its role is analogous to how a building's floor number indicates which level you are on. This coordinate helps specify how high or low a point is relative to the x-axis.
The y-coordinate appears second in an ordered pair \(x,y\), providing insights about the quadrant a point falls into:
  • Positive y-coordinate: The point is above the x-axis, situated in Quadrant I or Quadrant II.
  • Negative y-coordinate: The point is below the x-axis, located in Quadrant III or Quadrant IV.
  • y-coordinate is zero: The point lies exactly on the x-axis, thus not residing in any quadrant.
Since the y-coordinate dictates vertical positioning, it aids in various mathematical calculations, graphing functions, and understanding spatial relationships between points.

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. Assume each exercise describes a linear relationship. Write the equations in slope-intercept form. See Example 8 . In \(2002,\) crude oil production by OPEC countries was about 28.7 million barrels per day. In \(2007,\) crude oil production had risen to about 34.5 million barrels per day. (Source: OPEC) a. Write two ordered pairs of the form (years after 2002 , crude oil production) for this situation. b. Assume that crude oil production is linear between the years 2002 and 2007 . Use the ordered pairs from part (a) to write an equation of the line relating year and crude oil production. c. Use the linear equation from part (b) to estimate the crude oil production by OPEC countries in 2004

Solve. Assume each exercise describes a linear relationship. Write the equations in slope-intercept form. See Example 8 . The birth rate in the United States in 1996 was 14.7 births per thousand population. In 2006 , the birth rate was 14.14 births per thousand. (Source: Department of Health and Human Services, National Center for Health Statistics) CAN'T COPY THE IMAGE a. Write two ordered pairs of the form (years after 1996 birth rate per thousand population). b. Assume that the relationship between years after 1996 and birth rate per thousand is linear over this period. Use the ordered pairs from part (a) to write an equation of the line relating years to birth rate. c. Use the linear equation from part (b) to estimate the birth rate in the United States in the year 2016 .

See Examples 1 through 7 . Find an equation of each line described. Write each equation in slope-intercept form (solved for \(y\) ), when possible. Through \((2,3)\) and \((0,0)\)

See Examples 1 through 7 . Find an equation of each line described. Write each equation in slope-intercept form (solved for \(y\) ), when possible. With slope 0, through \((6.7,12.1)\)

Solve. Assume each exercise describes a linear relationship. Write the equations in slope-intercept form. See Example 8 . In 2006 , there were 935 thousand eating establishments in the United States. In 1996 , there were 457 thousand eating estab. lishments. (Source: National Restaurant Association) a. Write an equation describing the relationship between time and number of eating establishments. Use ordered pairs of the form (years past 1996, number of eating establishments in thousands). b. Use this equation to predict the number of eating establishments in 2010
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

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.