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Chapter 8: Problem 39

Evaluate the given expression for \(x=-3\) and \(y=5\) $$-x^{2}$$

Short Answer

Expert verified
-9

Step by step solution

01

Substitute the value for x

First, replace the variable x with the given value \(-3\) in the expression. The expression becomes \(-(-3)^{2}\).
02

Calculate the exponent

Next, calculate \(-3\) squared. \((-3)^{2} = 9\). So, the expression now is \(-9\).
03

Apply the negative sign

Finally, we apply the negative sign, so \(-9\) remains \(-9\).

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Key Concepts

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

substituting variables
In algebra, we often work with variables, which are symbols representing numbers that can change. To evaluate an algebraic expression, we must substitute these variables with actual numbers.
Let's see how this works with our example. Our expression is \(-x^{2}\) and we need to evaluate it for \(x = -3\).

  • Start by replacing the x in the expression with -3.

  • The expression \(-x^{2}\) becomes \(-(-3)^{2}\).

    • Practicing substitution with different numbers can help you better understand the values and how they influence the expression.
exponentiation
Exponentiation is a mathematical operation involving two numbers: the base and the exponent. The exponent tells how many times the base is multiplied by itself.
For instance, in the expression \(-(-3)^{2}\), -3 is the base, and 2 is the exponent.
When we calculate \((-3)^{2}\), we multiply -3 by itself:
\((-3) \times (-3) = 9\).

Some important points to remember:
  • Any number raised to the power of 0 is 1.

  • Any number raised to the power of 1 is itself.

    • It's always crucial to perform exponentiation before other operations, following the order of operations (PEMDAS/BODMAS).
negative numbers
Negative numbers are numbers less than zero, often used to represent loss, debt, or temperature below freezing.
When handling negative numbers, it's important to pay attention to their signs, especially in operations like multiplication and addition.
In our example \(-(-3)^{2}\), we see that:
  • First, by squaring -3, we get a positive 9.

  • Then, applying the negative sign from the original expression gives us -9.

    • When multiplying two negative numbers, the result is positive. But when multiplying a negative and a positive number, the result is negative.

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Most popular questions from this chapter

Simplify the expression and express your final answer with positive exponents only. $$\left(x^{3}\right)^{4}$$

In a basketball league of \(n\) teams in which each team plays every other team twice, the total number of games played is \(n^{2}-n .\) How many teams are there in a league that plays a total of 90 games?

Look at the following and discuss what is happening at each step. $$\begin{array}{l}x^{2}-x-20 \\\\\quad=x^{2}-5 x+4 x-20 \\\\\quad=x(x-5)+4(x-5) \\\\\quad=(x+4)(x-5)\end{array}$$

Factor each of the following expressions as completely as possible. If an expression is not factorable, say so. $$6 s^{2}-6 s-72$$

Factor each of the following as completely as possible. If the expression is not factorable, say so. Try factoring by grouping where it might help. $$x(x-5)+4(x-5)$$
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