/*! 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 380 In the following exercises, eval... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 380

In the following exercises, evaluate. $$ -|r| \text { when } r=27 $$

Short Answer

Expert verified
-27

Step by step solution

01

Identify the absolute value

First, find the absolute value of the given value of r. The absolute value of r is written as \(|r|\). Since r = 27, \(|27| = 27\).
02

Apply the negative sign

Next, apply the negative sign to the absolute value calculated in the previous step. This means you need to find \(-|27|\).
03

Evaluate the expression

Finally, evaluate the expression. Since \(|27| = 27\), \(-|27| = -27\).

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.

absolute value
Absolute value is a concept in mathematics that represents the distance of a number from zero on the number line, regardless of direction. Think of it like this: no matter if the number is positive or negative, we always convert it to a positive number.
Absolute value is written using two vertical lines, one on either side of the number, like this: \(|r|\).

For example:
  • \(|5| = 5\)
  • \(|-5| = 5\)
In both cases, the distance from zero is 5. So the absolute value of both 5 and -5 is 5.
In our specific exercise, we were given \(r = 27\). Hence, \(|27| = 27\).
negative numbers
Negative numbers are numbers that are less than zero. They are usually written with a minus sign in front of them, like \(-5\). These numbers are found to the left of zero on the number line. It's sometimes helpful to visualize negative numbers as being 'below' zero, or as debts, if thinking about money.

In the exercise, we started out with a positive number \(r = 27\), but we had to apply a negative sign in front of the absolute value result in step 2. This gave us the expression \-|27|\.
Therefore, \(-|27| = -27\).
This combination of absolute values and negative signs is common in mathematics, and understanding it is crucial for evaluating many expressions.
evaluating expressions
Evaluating expressions involves performing all the operations in order to find the value of the expression. Each problem follows a set process, which may include handling absolute values and negative numbers, like in our example exercise.

Here's a simpler example:
  • Evaluate \(-|r|\) when \(r = -12\)
  • First, find the absolute value: \( |-12| = 12\)
  • Then, apply the negative sign: \( -|12| = -12\)
This step-by-step method makes it easier to solve complex problems by breaking them down into manageable parts.
The key is to deal with the absolute value first, then handle any negative signs, and finally, evaluate the whole expression step by step.
By following these steps carefully, you'll get the correct result every time.

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 the following exercises, translate and solve. The product of 15 and \(x\) is 75

In the following exercises, simplify each expression. $$ -52-(-17)-23 $$

In the following exercises, divide. $$ -162 \div(-1) $$

In the following exercises, solve the given applications. $$ -1 \cdot 6 $$

In the following exercises, compare the numbers, using \(<\) or \(>\) or=. (a) \(-5\\_|-5|\) (b) \(-|-2|\\_-2\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Calculus

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.