/*! 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 72 Evaluate \(-p^{2}\) for \(p=-1\)... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 72

Evaluate \(-p^{2}\) for \(p=-1\) $$ [1.6] $$

Short Answer

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Step by step solution

01

Substitute the value of p

Replace the variable \( p \) with \( -1 \) in the expression \( -p^{2} \). This gives us: \( -(-1)^{2} \).
02

Evaluate the exponent

Calculate \( (-1)^{2} \). When raising \(-1\) to the power of 2, you get: \( (-1) \times (-1) = 1\).
03

Apply the negative sign

Apply the negative sign to the result obtained in Step 2. This results in: \( -1 \).

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Key Concepts

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

substitution in algebra
Substitution in algebra is a fundamental technique used to simplify expressions and solve equations. It involves replacing a variable with a specific value. In our exercise, we substitute the variable \( p \) with \( -1 \). Let's break this down further:

This is what happens when we substitute:
  • The original expression is \( -p^{2} \).
  • We replace \( p \) with \( -1 \), so it becomes \( -(-1)^{2} \).
By carrying out substitution, we make it easier to evaluate the expression. Always remember to carefully substitute the variable with its given value to avoid mistakes.
evaluating exponents
Evaluating exponents involves calculating the result of raising a number to a power. In our exercise, we need to find \( (-1)^{2} \). Here鈥檚 a step-by-step breakdown:

Understanding exponents:
  • When you see \( a^{b} \), it means you multiply \( a \) by itself \( b \) times.
For our specific example:
  • (-1)^{2} means multiplying -1 by itself twice.
  • This calculation can be written as: \( (-1) \times (-1) \).
  • Since multiplying two negative numbers results in a positive number, \( (-1) \times (-1) = 1 \).
Understanding how to evaluate exponents is crucial for solving algebraic expressions correctly.
negative numbers
Dealing with negative numbers can sometimes be confusing, but it is essential to understand their properties. In the given exercise, negative numbers play a key role. Let鈥檚 break down what happens:

When we substitute \( p \) with \( -1 \) and evaluate \( (-1)^{2} \), we need to know that:
  • Multiplying two negative numbers results in a positive number \( (-1 \times -1 = 1) \).


Finally, we apply the negative sign from the original expression to our result:
  • We started with the expression \( -p^{2} \).
  • Since \( (-1)^{2} = 1 \), the expression becomes \( -1 \).
Understanding the behavior of negative numbers helps you avoid mistakes and correctly simplify algebraic expressions.

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Most popular questions from this chapter

Solve each system. If a system's equations are dependent or if there is no solution, state this. $$ \begin{aligned} x+y+z &=57 \\ -2 x+y &=3 \\ x-& z=6 \end{aligned} $$

Solve \(C=\frac{2}{3}(x-y)\) for \(y\)

Determine whether each pair of lines is parallel, perpendicular, or neither. [ 2.4] $$ \begin{aligned} &3 x-y=12\\\ &y=3 x+7 \end{aligned} $$

Gold used to make jewelry is often a blend of gold, silver, and copper. The relative amounts of the metals determine the color of the alloy. Red gold is \(75 \%\) gold, \(5 \%\) silver, and \(20 \%\) copper. Yellow gold is \(75 \%\) gold, \(12.5 \%\) silver, and \(12.5 \%\) copper. White gold is \(37.5 \%\) gold and \(62.5 \%\) silver. If 100 g of red gold costs 4177.15,100 dollars g of yellow gold costs 4185.25 dollars, and \(100 \mathrm{g}\) of white gold costs 2153.875 dollars, how much do gold, silver, and copper cost per gram?

The sum of the digits in a four-digit number is \(10 .\) Twice the sum of the thousands digit and the tens digit is 1 less than the sum of the other two digits. The tens digit is twice the thousands digit. The ones digit equals the sum of the thousands digit and the hundreds digit. Find the four-digit number.
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