Textbook Question
In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (- ∞, 5.5)
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 2, Problem 12
Plot the given point in a rectangular coordinate system. (- 5/2, 3/2)
Verified step by step guidance1
Understand the rectangular coordinate system: It consists of two perpendicular axes, the x-axis (horizontal) and the y-axis (vertical), which intersect at the origin (0, 0). Points are represented as ordered pairs (x, y).
Identify the given point: The point is (-5/2, 3/2), where -5/2 is the x-coordinate and 3/2 is the y-coordinate.
Interpret the x-coordinate (-5/2): Since it is negative, move 5/2 units to the left of the origin along the x-axis.
Interpret the y-coordinate (3/2): Since it is positive, move 3/2 units up from the x-axis at the position determined in the previous step.
Plot the point: Mark the location where the movements from the x-coordinate and y-coordinate intersect. This is the point (-5/2, 3/2) on the rectangular coordinate system.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Rectangular Coordinate System
A rectangular coordinate system, also known as the Cartesian coordinate system, consists of two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). Each point in this system is defined by an ordered pair (x, y), where 'x' represents the horizontal position and 'y' represents the vertical position. Understanding this system is essential for accurately plotting points and visualizing relationships between them.
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Graphs & the Rectangular Coordinate System
Ordered Pairs
An ordered pair is a pair of numbers used to represent a point in a coordinate system, written in the form (x, y). The first number, 'x', indicates the position along the x-axis, while the second number, 'y', indicates the position along the y-axis. For example, the point (-5/2, 3/2) means to move left 2.5 units on the x-axis and up 1.5 units on the y-axis, which is crucial for accurate plotting.
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Plotting Points
Plotting points involves marking a specific location on a coordinate grid based on its ordered pair. To plot the point (-5/2, 3/2), one would start at the origin (0, 0), move left to -2.5 on the x-axis, and then move up to 1.5 on the y-axis. This process is fundamental in graphing functions, analyzing data, and visualizing mathematical relationships.
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Related Practice
Textbook Question
Plot the given point in a rectangular coordinate system. (7/2, - 3/2)
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Textbook Question
Solve each equation in Exercises 1 - 14 by factoring. 7 - 7x = (3x + 2)(x - 1)
Textbook Question
In Exercises 9–20, find each product and write the result in standard form. (- 5 + 4i)(3 + i)
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Textbook Question
In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (- ∞, 3)
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Textbook Question
An electronic pass for a toll road costs \$30. The toll is normally \$5.00 but is reduced by 30% for people who have purchased the electronic pass. Determine the number of times the road must be used so that the total cost without the pass is the same as the total cost with the pass.