/*! 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 64 Use the order of operations to s... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 64

Use the order of operations to simplify each expression. $$-3^{2}+2[20 \div(7-11)]$$

Short Answer

Expert verified
The simplified form of the expression \(-3^{2}+2[20 \div(7 - 11)]\) is -1.

Step by step solution

01

Evaluate the Exponent

Start with evaluating the expression \(-3^{2}\). In mathematics, the exponent operation is performed before the negation operation. Therefore, it would be \( (-3)^{2} = 9 \).
02

Evaluate the Parentheses

Next, evaluate the expression within the parentheses (7-11). So, it should be \( 7-11 = -4 \).
03

Perform Multiplication and Division

Now perform the division operation \( 20 \div -4 \) which equals to -5. Also, multiply the result by 2 which is \(-5*2 = -10\)
04

Perform Addition

Finally, add the result from step one with the result from step three, which is \(9 + (-10) = -1 \).

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.

Exponentiation
Exponentiation involves raising a number to the power of another. It's a shortcut for multiplying a number by itself a specific number of times. In this expression, we see \(-3^{2}\).
  • First, focus on the base, which is \(-3\).
  • The exponent is 2. This means you multiply \(-3\) by itself once.
  • Calculate \((-3) \times (-3)\), which equals 9.
So, the result of \((-3)^2\) is 9. Note that exponents come before negative signs unless parentheses indicate otherwise.
Remember, understanding the order here is crucial to avoid mistakes!
Parentheses
Parentheses indicate which operations should be performed first. They help group parts of mathematical expressions, bringing clarity. In our exercise, we must focus on \((7-11)\).
  • Calculate the expression inside the parentheses: \(7 - 11\) yields \(-4\).
By doing this, we respect the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Keep the parentheses in mind for clarity and correctness!
Multiplication and Division
Multiplication and division are operations of equal precedence. This means you solve them from left to right as they appear. In this problem, they occur with \(20 \div (-4)\).
  • First, perform the division: \(20 \div (-4)\) equals \(-5\).
  • Next, the multiplication follows: multiply \(-5\) by 2 to get \(-10\).
By handling multiplication and division this way, you ensure accuracy in your math problems. Keep practicing, and this will become second nature!
Addition and Subtraction
Addition and subtraction are the final steps to complete in the order of operations. They should be applied left to right. Let's look at our problem: we need to add \(9\) and \(-10\).
  • Start by looking at your simplified results from earlier steps.
  • Next, calculate: \(9 + (-10)\).
  • This results in \(-1\).
Remember, adding a negative number is the same as subtracting its positive equivalent. Keeping this in mind helps simplify complex 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

The bar graph shows that in 2000 and 2001 , the U.S. government collected more in taxes than it spent, so there was a budget surplus for each of these years. By contrast, in 2002 through \(2009,\) the government spent more than it collected, resulting in budget deficits. Exercises \(79-80\) involve these deficits. (GRAPH CANT COPY) a. In \(2006,\) the government collected \(\$ 2407\) billion and spent \(\$ 2655\) billion. Find \(2407+(-2655)\) and determine the deficit, in billions of dollars, for 2006 b. In \(2007,\) the government collected \(\$ 2568\) billion and spent \(\$ 2730\) billion. Find the deficit, in billions of dollars, for 2007 . c. Use your answers from part (a) and (b) to determine the combined deficit, in billions of dollars, for 2006 and 2007

In Exercises \(139-142\), write an algebraic expression for the given English phrase. The distance covered by a car traveling at 50 miles per hour for \(x\) hours

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The value of \(\frac{|3-7|-2^{3}}{(-2)(-3)}\) is the fraction that results when \(\frac{1}{3}\) is subtracted from \(-\frac{1}{3}\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Some integers are not rational numbers.

In Palo Alto, California, a government agency ordered computer-related companies to contribute to a pool of money to clean up underground water supplies. (The companies had stored toxic chemicals in leaking underground containers.) The mathematical model $$ C=\frac{200 x}{100-x} $$ describes the cost, \(C,\) in tens of thousands of dollars, for removing \(x\) percent of the contaminants. Use this formula to solve. a. Find the cost, in tens of thousands of dollars, for removing \(60 \%\) of the contaminants. b. Find the cost, in tens of thousands of dollars, for removing \(90 \%\) of the contaminants. c. Describe what is happening to the cost of the cleanup as the percentage of contaminants removed increases.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

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.