/*! 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 67 Evaluate the given expression fo... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 67

Evaluate the given expression for \(x=2, y=-3,\) and \(z=-4.\) $$(z-3 x)^{2}$$

Short Answer

Expert verified
The evaluated value is 100.

Step by step solution

01

- Substitute given values

Identify the given values for the variables and substitute them into the expression. Here, substitute \( x = 2 \), \( y = -3 \), and \( z = -4 \) into the expression \((z - 3x)^{2}\).
02

- Simplify the expression inside the parentheses

Calculate the expression inside the parentheses after substitution. Substituting the given values, we get: \( z - 3x = -4 - 3(2) \).
03

- Perform the multiplication

Now perform the multiplication within the parentheses: \( -4 - 3 \times 2 = -4 - 6 \).
04

- Calculate the result inside the parentheses

Simplify the result: \(-4 - 6 = -10\).
05

- Square the result

Finally, square the result to complete the evaluation: \((-10)^{2} = 100\).

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 in Algebra
Substitution in algebra involves replacing the variables in an expression with the values given. In this exercise, we replaced the variables \(x\), \(y\), and \(z\) with the values 2, -3, and -4 respectively. To replace variables correctly:
- Identify all the variables in the expression.
- Look at the given values for each variable.
- Insert these values in place of the variables.

For our example, the expression \( (z-3x)^{2} \) becomes \( (-4-3 \times 2)^{2} \) after substitution. It鈥檚 like putting puzzle pieces in the right spots!
Simplifying Expressions
Simplifying expressions is crucial to solving algebra problems efficiently. It involves combining like terms and calculating arithmetic operations in the correct order. Here鈥檚 how we simplified the expression step-by-step:
- After substituting the values, we had \( -4-3 \times 2 \).
- Next, we performed the multiplication: \( 3 \times 2 \) which gave us 6.
- Then, we combined the terms by following the order of operations, moving from left to right: \( -4 - 6 = -10 \).

Simplifying the expression inside the parentheses helps us understand what we need to square next.
Squaring Numbers
Squaring a number means multiplying it by itself. In this exercise, it was the final step to find the solution. Let鈥檚 break it down:
- Once we simplified the expression inside the parentheses to \( -10 \), our task was to square this value.
- Squaring \(-10\) is \( (-10)^{2} = -10 \times -10 \). Since multiplying two negative numbers results in a positive number, the answer is 100.

Squaring is essential for various problems, especially when dealing with quadratic expressions. Understanding squaring will help you solve a range of algebra problems more confidently!

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 the given expression for \(x=0.24\) and \(y=-0.5 .\) Round off to the nearest thousandth where necessary. $$(x+y)^{2}$$

Simplify each expression as completely as possible. $$7(a-1)-6[2 a-4(a-3)]$$

Evaluate the given expression for \(x=2, y=-3,\) and \(z=-4.\) $$x^{2}+3 x^{2} y-3 x y^{2}+y^{3}$$

Simplify by combining like terms whenever possible. $$-5 s^{2}+3 s t-s^{2}+6 s^{2}$$

Evaluate the given expression for \(x=2, y=-3,\) and \(z=-4.\) $$(y-2 z)(y+3 z)$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

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.