/*! 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 12 Evaluate each expression if \(x=... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 12

Evaluate each expression if \(x=-2\) and \(y=4\) $$x^{2}+y^{2}$$

Short Answer

Expert verified
The expression evaluates to 20.

Step by step solution

01

Substitute the values of x and y

Substitute the given values of \(x = -2\) and \(y = 4\) into the expression \(x^2 + y^2\). This gives us \((-2)^2 + (4)^2\).
02

Calculate the squares

Calculate the square of each term independently: \((-2)^2\) is \(4\), and \((4)^2\) is \(16\).
03

Add the results

Add the results from the previous step: \(4 + 16 = 20\).

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.

Expressions Evaluation
In prealgebra, evaluating expressions is a fundamental skill. It involves replacing variables in an expression with given numbers and performing the necessary calculations to find the answer. This process helps us analyze and simplify problems to find specific numerical results. In our example, we evaluated the expression \(x^2 + y^2\) when \(x = -2\) and \(y = 4\). Evaluating expressions requires focusing on:
  • Identifying the variables in the expression.
  • Knowing the values assigned to these variables.
  • Substituting the variables with their given values.
  • Performing mathematical operations like addition or multiplication.
Remember, following a consistent order of operations is crucial to get the correct result. Expressions evaluation is a powerful tool for solving a range of math problems efficiently.
Substitution in Expressions
Substitution is the process of replacing variables in an algebraic expression with specific numbers. This method transforms an abstract expression into a concrete numerical problem, making it easier to solve. Let's take a closer look at how this works:
  • Identify Variables: Begin by determining which letters (variables) you need to substitute. In our exercise, these are \(x\) and \(y\).
  • Insert Values: Replace each variable with the provided number. Using our example, substitute \(x = -2\) and \(y = 4\) into \(x^2 + y^2\), which will become \((-2)^2 + 4^2\).
  • Rewrite Expression: Once substituted, rewrite the expression with the numbers in place of variables for clarity.
Substitution might seem straightforward, but it requires attention to detail to ensure nothing is missed. This skill is foundational in solving algebraic expressions and can simplify complex problems into manageable computations.
Square Calculation
Calculating squares of numbers is a basic yet essential math skill, especially in algebra. A square of a number is simply that number multiplied by itself. Here's how you perform square calculations:
  • Understand the Concept: Squaring a number, written as \(n^2\), means multiplying the number by itself. So, \((-2)^2\) means multiplying \(-2\) by \(-2\), which is \(4\).
  • Positive Results: When you square negative numbers, the result is always positive because a negative times a negative equals a positive.
  • Practice with Positive Numbers: For any positive number like \(4\), \(4^2\) equals \(16\) because \(4 \times 4 = 16\).
Mastering square calculations helps in solving a variety of problems, from simple arithmetic to more complex algebraic equations. It's crucial for students to become comfortable with squares to prepare for more advanced math concepts.

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

Evaluate each expression if \(s=-2\) and \(t=3\). $$s^{-5}$$

Simplify each fraction. If the fraction is already in simplest form, write simplified. $$\frac{y^{3}}{y}$$

Find each equivalent measure. $$1 \mathrm{yd}=\underline{?} \text { in. }$$

Determine whether the statement is true or false. If true, explain your reasoning. If false, give a counterexample. $$\text { For any integer } a,(-a)^{2}=-a^{2}$$

OPEN ENDED Write a numerical fraction and an algebraic fraction in simplest form and a numerical fraction and an algebraic fraction not in simplest form.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure 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.