Problem 46 Evaluate each expression for \(x... [FREE SOLUTION]

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Chapter 5: Problem 46

Evaluate each expression for $x=3, y=-0.2,$ and $z=5.7 .$ See Example $12 .$ $$y z$$

Short Answer

Expert verified

The expression evaluates to -1.14.

Step by step solution

Substitute Values into the Expression

The given expression is $ yz $. We need to substitute $ y = -0.2 $ and $ z = 5.7 $ into the expression.

Calculate the Product

Substitute the values to get the expression $ (-0.2)(5.7) $. Now, multiply these two numbers together. Calculate $-0.2 \times 5.7$.

Simplify the Result

Perform the multiplication: $ -0.2 \times 5.7 = -1.14 $. Write down the simplified result.

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Key Concepts

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

Substitution

In Prealgebra, substitution is a technique where you replace variables in an expression with their numerical values. This allows you to evaluate expressions easily. For example, in the exercise provided, we are asked to evaluate the expression $ yz $ by substituting $ y = -0.2 $ and $ z = 5.7 $. To perform substitution:

Take the variable in the expression.
Replace it with its corresponding numerical value.

After substitution, you end up with numbers instead of variables, making it possible to perform calculations and find a numerical answer. Think of substitution like plugging numbers into a formula to see what outcome you get.

Expressions

Expressions in mathematics are combinations of numbers, variables, and operations (like addition, subtraction, multiplication, and division). They do not have an equal sign, unlike equations. The expression given in the exercise is $ yz $, where $ y $ and $ z $ are variables that can be replaced with numbers. Evaluating an expression involves substituting these variables and performing the necessary mathematical operations to simplify the expression into a single number.When handling expressions:

Identify the variables and what values they take.
Use operations according to the expression's structure (like multiplication in $ yz $).

Expressions are like simple recipes where variables are ingredients, and you figure out the result by adding, subtracting, multiplying, or dividing those ingredients.

Multiplication

Multiplication is one of the basic arithmetic operations used to find the total number of items when you have groups of the same size. In the context of our exercise, multiplication helps us find the product of two numbers, $-0.2$ and $5.7$, which were substituted in place of $ y $ and $ z $ respectively.During multiplication:

You multiply a negative number by a positive number, resulting in a negative product.
Simplify the multiplication result to get your final answer.

In our example:

$-0.2$ and $5.7$ get multiplied to give $-1.14$.

Remember that multiplication is repetitive addition. You're basically adding $5.7$ together $-0.2$ times, which gives a negative total because one of the numbers is negative.

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91影视

Evaluate each expression for \(x=3, y=-0.2,\) and \(z=5.7 .\) See Example \(12 .\) $$y z$$

Short Answer

Step by step solution

Substitute Values into the Expression

Calculate the Product

Simplify the Result

Key Concepts

Substitution

Expressions

Multiplication

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