/*! 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 29 For Problems \(21-40\), simplify... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 29

For Problems \(21-40\), simplify each numerical expression. $$ -7^{2}-6^{2}+5^{2} $$

Short Answer

Expert verified
The simplified expression is \(-60\).

Step by step solution

01

Evaluate the square of each number

First, calculate the square of each individual number. The problem is \(-7^{2} - 6^{2} + 5^{2}\).Calculate: - \(-7^{2} = -(7 imes 7) = -49\)- \(-6^{2} = -(6 imes 6) = -36\)- \(5^{2} = 5 imes 5 = 25\)
02

Combine the evaluated values

Next, substitute the evaluated values back into the expression and perform the arithmetic operations: - \(-49 - 36 + 25\).
03

Perform the subtraction

Perform the subtraction from left to right:- First, calculate \(-49 - 36\): \(-49 - 36 = -85\).
04

Perform the addition

Now add the last value: - Calculate \(-85 + 25\): \(-85 + 25 = -60\).

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.

Understanding Arithmetic Operations
Arithmetic operations form the backbone of simplifying expressions. They include addition, subtraction, multiplication, and division. In our example expression, we need to perform both addition and subtraction:
  • Addition: For this operation, you combine numbers to get their sum. If you add negative and positive numbers, think of it as finding the difference between their absolute values and keeping the sign of the larger absolute value.
  • Subtraction: This involves taking away one number from another. When subtracting negative numbers, you could think of it as adding the opposite number.
Break down the expression into simpler calculations like step by step subtraction and addition. By mastering these operations, simplifying complex expressions becomes manageable.
Applying the Order of Operations
The order of operations is crucial in math as it dictates the correct sequence of activities to simplify expressions. Often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition, and Subtraction), it ensures that everyone follows the same rules. Not following these rules can lead to incorrect answers.In the expression \(-7^{2} - 6^{2} + 5^{2}\), exponents are tackled before any addition or subtraction.
  • Exponents: Always resolve them first. Handle any numbers raised to a power before moving on to other operations.
  • Left to Right: After solving exponents, go from left to right when performing addition and subtraction.
In this way, you can effectively simplify expressions without any confusion.
The Concept of Squaring Numbers
Squaring a number is multiplying the number by itself. It is denoted as a power of 2 and is a fundamental concept in mathematics. When you square a number, you emphasize its magnitude by increasing its value rapidly.For instance, in the expression:\(-7^{2}, -6^{2}, \) and\(5^{2}\):
  • Square the Numbers: Calculate \(7 \times 7 = 49\), \(6 \times 6 = 36\), and \(5 \times 5 = 25\).
  • Negative Outcomes: Notice that the squared values for negative numbers like \(-7\) and \(-6\) appear as positive before the negative sign takes effect, thus resulting in \(-49\) and \(-36\).
Understanding squaring helps you grasp how numbers grow rapidly and affects the values in an expression, crucial for accurate simplification.

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

Mindy takes a daily walk of \(2 \frac{1}{2}\) miles. One day a thunderstorm forced her to stop her walk after \(\frac{3}{4}\) of a mile. By hov much was her walk shortened that day?

Simplify each algebraic expression by combinang similar terms. $$\frac{5}{6} x+\frac{3}{4} y+\frac{4}{9} x+\frac{7}{10} y$$

For her exercise program, Laian jogs for \(2 \frac{1}{2}\) miles, then walks for \(\frac{3}{4}\) of a mile, and finally jogs for another \(1 \frac{1}{4}\) miles. Find the total distance that Lian covers.

Simplify each algebraic expression by combining similar terms. $$0.3(x-4)+0.4(x+6)-0.6 x$$

Perform the indicated operations. $$(0.4)(2.9)$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Statistics

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.