/*! 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 21 Evaluate the expression when \(x... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 21

Evaluate the expression when \(x=3, y=-2\), and \(z=4$$\frac{x-y}{5 z}\)

Short Answer

Expert verified
The evaluated expression is 0.25

Step by step solution

01

Substitute the variables

First, substitute the provided values into the expression. This gives: \(\frac{3-(-2)}{5*4}\)
02

Perform the operations in the numerator

Subtract -2 from 3 in the numerator, which results in: \(\frac{3+2}{5*4}\)
03

Simplify the numerator

Simplify the addition in the numerator, which results in: \(\frac{5}{5*4}\)
04

Perform the operation in the denominator

Multiply 5 by 4 in the denominator, resulting in: \(\frac{5}{20}\)
05

Simplify the expression

Simplifying the fraction \(\frac{5}{20}\) gives the final answer of \(0.25\)

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.

Substitution
When evaluating expressions, substitution is a key step. It involves replacing variables with provided values. For example, in the expression \(\frac{x-y}{5z}\), we substitute \(x\), \(y\), and \(z\) with their given values: 3, -2, and 4 respectively. This transforms our expression into \(\frac{3-(-2)}{5 \times 4}\).
Substitution makes an abstract expression concrete, allowing us to perform calculations. It is crucial to do this accurately, ensuring each variable is replaced with its correct corresponding value. Pay attention to signs, especially when dealing with negative numbers like \(-2\). Proper substitution lays the groundwork for further steps, like simplifying.
Numerator and Denominator
The terms numerator and denominator are fundamental in understanding fractions. In a fraction \(\frac{a}{b}\), \(a\) is the numerator, located above the fraction line, and \(b\) is the denominator, which is positioned below the line.
  • The numerator represents how many parts of the whole are being considered.
  • The denominator shows how many equal parts the whole is divided into.
In our exercise, after substitution, we have \(\frac{5}{20}\). Here, 5 is the result of subtracting \(-2\) from 3, and it becomes the numerator. The multiplication of \(5 \times 4\) gives us 20 in the denominator. Keep track of these operations separately to avoid confusion.
Simplifying Fractions
Now comes simplifying fractions, a process made to make expressions more digestible. Simplification aims to write the fraction in its simplest form, where the numerator and denominator share no common divisors besides 1.
To simplify \(\frac{5}{20}\):
  • Identify the greatest common divisor (GCD) of 5 and 20, which is 5.
  • Divide both the numerator and denominator by the GCD.
  • This gives \(\frac{5 \div 5}{20 \div 5} = \frac{1}{4}\).
As a decimal, this fraction is equivalent to 0.25. Simplifying helps because it presents the solution in the easiest, most understandable way.

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

Write the number in scientific notation.Land Area of Earth: \(57,300,000\) square miles

Factor the perfect square trinomial.\(x^{2}-4 x+4\)

Simplify the expression.\(\frac{x^{2} \cdot x^{n}}{x^{3} \cdot x^{n}}\)

Factor out the common factor.\(4 x^{3}-6 x^{2}+12 x\)

Electron Microscopes Electron microscopes provide greater magnification than traditional light microscopes by using focused beams of electrons instead of visible light. It is the extremely short wavelengths of the electron beams that make electron microscopes so powerful. The wavelength \(\lambda\) (in meters) of any object in motion is given by \(\lambda=\frac{6.626 \times 10^{-34}}{m v}\), where \(m\) is the mass (in kilograms) of the object and \(v\) is its velocity (in meters per second). Find the wavelength of an electron with a mass of \(9.11 \times 10^{-31}\) kilogram and a velocity of \(5.9 \times 10^{6}\) meters per second. (Submitted by Brian McIntyre, Senior Laboratory Engineer for the Optics Electron Microscopy Facility at the University of Rochester.)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Statistics

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.