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Chapter 5: Problem 84

Evaluate each expression for \(x=6, y=0.3,\) and \(z=-2.4 .\) $$ y^{2} $$

Short Answer

Expert verified
The expression evaluates to 0.09.

Step by step solution

01

Identify the Expression

The given expression is \( y^2 \). This means we need to square the value of \( y \) to evaluate the expression.
02

Substitute the Given Value

We are provided with the value of \( y = 0.3 \). Substitute this value into the expression to get \( (0.3)^2 \).
03

Calculate the Square

Calculate \( (0.3)^2 \). The square of 0.3 is calculated by multiplying 0.3 by itself. \( 0.3 \times 0.3 = 0.09 \).
04

Final Result

The evaluated expression for \( y^2 \) when \( y = 0.3 \) is \( 0.09 \).

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Key Concepts

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

Substitution
Substitution in mathematics refers to the process of replacing the variables in an expression with given numerical values. This method helps in evaluating expressions by transforming them into numerical calculations.
For instance, if we have an expression with a variable like \( y^2 \) and we know that \( y = 0.3 \), we substitute the value for \( y \) in the expression.
By doing so, the expression becomes simply \( (0.3)^2 \), which can then be easily calculated.
  • Identify the expression and the variable involved.
  • Find the given value for the variable.
  • Replace the variable with this value in the expression.

This method is particularly useful as it simplifies complex algebraic expressions into simple arithmetic tasks.
Powers and Exponents
Powers and exponents are mathematical concepts used to express repeated multiplication of the same number. An expression like \( y^2 \) means \( y \) is multiplied by itself once.
In general, \( a^n \) means \( a \) is multiplied by itself \( n \) times. Here, the number \( a \) is called the base, and \( n \) is the exponent. To evaluate the expression \( y^2 \) given \( y = 0.3 \):
  • Start by interpreting the expression. \( y^2 \) indicates squaring \( y \).
  • Use the substitution to transform \( y^2 \) into \( (0.3)^2 \).
  • Finally, compute by multiplying \( 0.3 \times 0.3 \) to get the result, \( 0.09 \).
The concept of powers and exponents simplifies handling repeated multiplications, making complex calculations easier.
Prealgebra Concepts
Prealgebra is the foundational level of algebra that introduces basic arithmetic and symbolic reasoning. It covers basic operations, variables, and the initial understanding of algebraic expressions.
Evaluating expressions is an essential skill in prealgebra that involves substituting values and performing arithmetic operations.
  • Learn how to handle variables and understand expressions.
  • Focus on operations like addition, subtraction, multiplication, and division.
  • Build skills in recognizing and calculating powers and exponents.

For example, when given the task to evaluate \( y^2 \) for \( y = 0.3 \), you use your prealgebra concepts to substitute the value and then calculate the square. This simple exercise highlights the importance of understanding and applying basic algebraic techniques.

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