/*! 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 111 \([10-3(2+7)+20]^{2}\)... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 111

\([10-3(2+7)+20]^{2}\)

Short Answer

Expert verified
9

Step by step solution

01

- Simplify Inside the Parentheses

First, solve the expression inside the parentheses: \(2 + 7 = 9\)
02

- Multiply Inside the Brackets

Next, substitute the result from Step 1 into the expression and multiply: \(3 \cdot 9 = 27\)
03

- Subtract and Add Inside the Brackets

Now, continue simplifying inside the brackets: \(10 - 27 + 20\). Perform the subtraction first: \(10 - 27 = -17\), then add 20: \(-17 + 20 = 3\)
04

- Raise to the Power

Finally, raise the result to the power of 2: \(3^{2} = 9\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

parentheses in math
Understanding parentheses in math is crucial since they determine the order in which operations are performed. Parentheses are used to group parts of a mathematical expression that should be solved first.
For example, in the given exercise, we start with the innermost parentheses: \(2 + 7\).
Within these parentheses, we perform the addition first, giving us 9. Parentheses help clarify the sequence of operations and ensure we follow the correct order.
This is key to avoiding mistakes in more complex equations.
exponents
Exponents, also known as powers, are used to express repeated multiplication. When you see a number raised to a power, such as \(3^{2}\), it means that the number is multiplied by itself.
In the exercise, after simplifying the expression inside the brackets, we encounter \(3^{2}\).
This means we multiply 3 by itself: \(3 \times 3 = 9\). Exponents hugely simplify expressions, making it easier to work with large numbers or repeated multiplication.
basic arithmetic operations
Basic arithmetic operations are the foundation of math and include addition, subtraction, multiplication, and division.
In this exercise, we use these operations in conjunction with parentheses and exponents. Here鈥檚 how:
  • Addition: Inside the parentheses, we add 2 and 7 to get 9.
  • Multiplication: Next, we multiply 3 by 9.
  • Subtraction: We subtract 27 from 10.
  • Addition (again): Finally, we add 20 to -17.
Understanding how to correctly apply these operations step-by-step ensures accurate results in any math problem.
Breaking down each operation helps to avoid mistakes and clearly see each part of the equation.

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Most popular questions from this chapter

An employee works for 8 hours at \(\$ 9.75\) per hour. The employer withholds \(7.65 \%\) of her gross wages for Social Security and Medicare taxes. Find the amount of wages after with holding.

The International Basketball Federation rules (2006) state, "For all men's competitions in all categories, the circumference of the ball shall be no less than \(749 \mathrm{~mm}\) and no more than \(780 \mathrm{~mm}\) (size 7)." Find the maximum volume of the ball in cubic millimeters. Round to the nearest whole number. (Source: www.fiba.com)

\( 3^{3}\)

The shape of a table top is a trapezoid with bases that measure \(25 \mathrm{in}\). and \(60 \mathrm{in}\). The height is \(30 \mathrm{in}\). Find the area of this table.

Find the volume of a sphere with a diameter of \(15 \mathrm{in}\).
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