Textbook Question
In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 5 and 6.
center (5, -4), radius 7
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0. Review of College Algebra
Basics of Graphing
2:31 minutesProblem 4
Textbook Question
CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The distance on a number line from a number to 0 is the _________ of the number.
Verified step by step guidance1
Understand that the problem is asking for a term related to the distance of a number from zero on a number line.
Recall that the distance from zero to any number on the number line is always a non-negative value.
This concept is known as the 'absolute value' of the number, which measures how far the number is from zero regardless of direction.
The absolute value of a number \(x\) is denoted as \(|x|\) and is defined as \(|x| = x\) if \(x \geq 0\), and \(|x| = -x\) if \(x < 0\).
Therefore, the correct term to fill in the blank is 'absolute value'.
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Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value
Absolute value represents the distance of a number from zero on the number line, regardless of direction. It is always non-negative and is denoted by vertical bars, e.g., |x|. For example, |−3| = 3 and |5| = 5.
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Number Line
A number line is a visual representation of real numbers arranged in order on a straight line, with zero at the center. Positive numbers lie to the right of zero, and negative numbers lie to the left, helping to understand concepts like distance and magnitude.
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Distance in Mathematics
Distance refers to the measure of how far apart two points are. On a number line, the distance between a number and zero is the absolute value of that number, reflecting the magnitude without considering direction.
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