Problem 75 Evaluate each expression for \(x... [FREE SOLUTION]

Chapter 2: Problem 75

Evaluate each expression for $x=-3$ and $z=-4$ $$ 10-x^{2} $$

Short Answer

Expert verified

The expression evaluates to 1 for $x = -3$ and $z = -4$.

Step by step solution

Substitute the Value of x

First, substitute the given value of $x = -3$ into the expression. The expression is $10 - x^2$, so substituting gives us $10 - (-3)^2$.

Evaluate the Power of x

Calculate $(-3)^2$. We know that $-3$ squared is $(-3) \times (-3) = 9$. So, replace $(-3)^2$ with 9 in the expression.

Complete the Calculation

Now, substitute the value from Step 2 back into the expression: $10 - 9$. Finally, calculate the expression to get the result: $10 - 9 = 1$.

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Key Concepts

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

Substituting Values

In algebra, one of the first steps in solving expressions like this is substituting given values for variables. You might encounter expressions with variables such as $x$ or $z$, and the key to simplifying these expressions is to replace these variables with the specific numbers provided in the problem. In our example, we're working with the variable $x$ and its given value of $-3$.

Substituting turns $10 - x^2$ into $10 - (-3)^2$.
This replacement step makes it much easier to work with real numbers rather than variables.

The goal of substitution is to create simpler calculations that lead to a numerical answer. Remember, it's vital to accurately follow the instructions and replace each variable as indicated by the problem statement.

Exponents

Exponents are essentially a way to represent repeated multiplication. In our provided problem, we have the expression $(-3)^2$. An exponent tells us how many times to multiply a number by itself. So in this case, the exponent of 2 tells us to multiply $-3$ by itself one more time:

Calculate $(-3) \times (-3)$.
This results in $9$ because multiplying two negative numbers results in a positive product.

Understanding exponents is crucial because they appear frequently in mathematical problems. Make sure to remember the rule that any negative number squared will result in a positive number.

Arithmetic Operations

Arithmetic operations include basic mathematical operations like addition, subtraction, multiplication, and division. These operations form the foundation of most algebraic tasks. In this exercise, we are asked to calculate the expression $10 - 9$ once the exponent has been evaluated.

First, you conduct the operation inside the substitution: calculate the exponent to get $9$.
Then, you perform the subtraction: $10 - 9$.
The result is $1$, which completes the evaluation of the expression.

Being adept with arithmetic operations ensures that you can confidently solve expressions step by step, leading to the correct solution.

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91影视

Evaluate each expression for \(x=-3\) and \(z=-4\) $$ 10-x^{2} $$

Short Answer

Step by step solution

Substitute the Value of x

Evaluate the Power of x

Complete the Calculation

Key Concepts

Substituting Values

Exponents

Arithmetic Operations

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