/*! 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 83 Evaluate each expression for \(x... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 83

Evaluate each expression for \(x=6, y=0.3,\) and \(z=-2.4 .\) $$ z^{2} $$

Short Answer

Expert verified
\(z^2 = 5.76\) for \(z = -2.4\).

Step by step solution

01

Identify the Expression

The expression we need to evaluate is \(z^2\). This means we need to square the value of \(z\).
02

Substitute the Value of z

Replace \(z\) in the expression with its given value: \(-2.4\). So the expression becomes \((-2.4)^2\).
03

Square the Number

Calculate \((-2.4)^2\). To square a number, multiply it by itself: \((-2.4) \times (-2.4) = 5.76\).

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.

Evaluating Expressions
Evaluating expressions is like solving a puzzle. You start with an equation that has numbers and variables, and your job is to find out what it's worth when you substitute the given numbers into it. This makes your expression easier to understand and solve.
This process is essential in mathematics because it helps in determining the actual value of the expression, not just in algebra but in many areas of math and real life. When evaluating expressions, you follow these steps:
  • Identify the expression given. Understand what operations need to be performed.
  • Substitute any given values for the variables in the expression. This transforms the variables into numbers.
  • Perform the necessary calculations step by step, following the order of operations.
By mastering the evaluation of expressions, you build a strong foundation for further mathematical studies.
Substitution
Substitution in mathematics is like replacing a placeholder with a real object. In terms of expressions, it is the process of replacing variables with given numbers. This is crucial for evaluating expressions because it allows us to work with actual numbers instead of just variables.
Here's how substitution works:
  • Identify all variables in the expression that need to be replaced.
  • Look at the values provided for each variable. Just like in our exercise, where we replaced \(z\) with \(-2.4\).
  • Carefully insert these values in place of the variables within the expression, ensuring accuracy so you don't make errors when calculating.
Substitution transforms an abstract expression into something tangible, so you can proceed to solve it confidently.
Squaring Numbers
Squaring a number means multiplying the number by itself. It is a fundamental arithmetic operation that often appears in algebraic expressions and equations. When you see a term like \(z^2\), it means you need the square of \(z\).
  • First, note the base number; this is the number being squared. For instance, in our exercise, \(-2.4\) is the base.
  • Next, multiply the base by itself. Remember that when squaring a negative number, such as \(-2.4\), the result is positive because multiplying two negative signs gives a positive outcome: \((-2.4) \times (-2.4)\).
  • The final product is the squared value. For example, \((-2.4)\) squared equals \(5.76\). This is because you multiply \(-2.4\) by itself to arrive at this positive result.
Understanding squaring is crucial because it's a common operation in both simple arithmetic and more complex algebraic problems.

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

Americans ages \(16-19\) drive, on average, 7624 miles per year. About how many miles each week is that? Round to the nearest tenth. (Note: There are 52 weeks in a year.)

There are 2.54 centimeters in 1 inch. How many inches are there in 50 centimeters? Round to the nearest tenth.

Divide. \(\frac{456.25}{10,000}\)

Divide. \(9 \overline{) 1 3 0 . 5 }\)

Solve. $$ 7.68 y=-114.98496 $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Decision Maths

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.