/*! 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 51 In Problems 49-58, find the valu... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 51

In Problems 49-58, find the value of each expression if \(x=3\) and \(y=-2\). \(|x|+|y|\)

Short Answer

Expert verified
5

Step by step solution

01

Understand Absolute Value

Absolute value represents the distance of a number from zero on the number line, regardless of direction. It is always a non-negative number.
02

Substitute Values

Substitute the given values into the expression: Substitute \(x = 3\) and \(y = -2\) into \(|x|+|y|\).
03

Calculate Absolute Values

Calculate the absolute values of \(x\) and \(y\): \(|x| = |3| = 3\)\(|y| = |-2| = 2\)
04

Add the Absolute Values

Add the absolute values from the previous step: \(3 + 2 = 5\)

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 an important concept in mathematics. It tells us how far a number is from zero on the number line, without considering if it's positive or negative.
For example, both 3 and -3 have an absolute value of 3, as they are each 3 units away from zero.
The notation for absolute value is two vertical bars around the number, like this: \(|x|\).
Whenever we see this notation, it means we should ignore the sign and only focus on the number's distance from zero.
To summarize, the absolute value of a number is always non-negative. That means it's either positive or zero.
substitution in expressions
Substitution in expressions is a technique used to replace variables with actual values. This helps us evaluate the expression.
Let's say we have an expression with variables, like \(|x| + |y|\), and we are given specific values for \(x\) and \(y\).
For instance, if \(x = 3\) and \(y = -2\), we substitute these values into the expression to replace \(x\) and \(y\).
Our expression becomes \(|3| + |-2|\).
basic arithmetic operations
Basic arithmetic operations include addition, subtraction, multiplication, and division. These are the foundational operations in algebra.
For this exercise, we focus on addition. After calculating the absolute values, we need to add them together.
In our example, after finding that \(|3| = 3\) and \(|-2| = 2\), we add these results together.
Thus, \(|3| + |-2| = 3 + 2 = 5\).
Understanding these basic operations is crucial as they form the building blocks for more complex mathematics.

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

Simplify each expression. Assume that all variables are positive when they appear. $$\sqrt{15 x^{2}} \sqrt{5 x}$$

Use a calculator to approximate each radical. Round your answer to two decimal places. $$\frac{\sqrt{5}-2}{\sqrt{2}+4}$$

The period \(T\), in seconds, of a pendulum of length \(l,\) in feet, may be approximated using the formula $$T=2 \pi \sqrt{\frac{l}{32}}$$ Express your answer both as a square root and as a decimal approximation. Find the period \(T\) of a pendulum whose length is 64 feet.

Simplify each expression. $$\left(\frac{8}{27}\right)^{-2 / 3}$$

Rationalize the denominator of each expression. Assume that all variables are positive when they appear. $$\frac{-2}{\sqrt[3]{9}}$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

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.