Problem 69 Evaluate each expression for \(x... [FREE SOLUTION]

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Chapter 2: Problem 69

Evaluate each expression for $x=-3$ and $z=-4$ $$ x^{2} $$

Short Answer

Expert verified

The value of $x^2$ for $x=-3$ is 9.

Step by step solution

Understand the Expression

The expression given is $x^2$. This indicates that you are expected to square the value of $x$.

Substitute the Given Value of x

We need to replace $x$ with its given value, which is $-3$. So the expression becomes $(-3)^2$.

Calculate the Square

Now, calculate the square of $-3$. Recall that squaring a negative number results in a positive number: $(-3) \times (-3) = 9$.

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Key Concepts

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

Substitution in Math

Substitution in math is a process where you replace a variable with a specific value. This technique is fundamental when evaluating expressions. By substituting, you change an algebraic expression into a numerical one, which you can easily solve.
To substitute correctly:

Identify the variable in the expression.
Use the given value for that variable.
Replace the variable with its numerical value.

In our example, you are given the expression $x^2$. You need to replace $x$ with $-3$. This action transforms $x^2$ into $(-3)^2$. Once substitution is done, you can move on to the next steps of evaluation.

Exponents

Exponents are used in mathematics to indicate how many times a number (called the base) is multiplied by itself. Learning to work with exponents can simplify complex multiplication arithmetic.
Some important facts about exponents are:

The exponent "2" means "square" or multiply the base by itself once.
If an exponent is a negative number, it can change the direction of multiplication or make numbers smaller.
Zero as an exponent means the base is equal to 1 (when not undefined).

In our example of $x^2$, the exponent is $2$, which means you multiply $x$ by itself one time. For $x = -3$, you calculate $(-3) \times (-3)$. This results in the next concept: squaring numbers.

Squaring Numbers

Squaring numbers involves multiplying a number by itself. This concept is straightforward yet extremely useful in algebra, providing the foundation for more complex operations.
Key points about squaring numbers:

Squaring a positive number always gives a positive result.
Squaring a negative number also results in a positive number because a negative times a negative equals a positive.
Zero squared is zero.

In the problem at hand, we need to square $-3$. The calculation is straightforward: $(-3) \times (-3) = 9$. This is because the negatives cancel out, resulting in a positive outcome. It's important to have a clear understanding of this, as it affects the result of evaluating expressions with square terms.

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91影视

Evaluate each expression for \(x=-3\) and \(z=-4\) $$ x^{2} $$

Short Answer

Step by step solution

Understand the Expression

Substitute the Given Value of x

Calculate the Square

Key Concepts

Substitution in Math

Exponents

Squaring Numbers

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