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Chapter 1: Problem 2

Check Choose the letter(s) of the correct response. If \(x=2\) and \(y=1,\) then the value of \(x y\) is A. \(\frac{1}{2}\) \(\mathbf{B} .1\) C. 2 D. 3

Short Answer

Expert verified
C. 2

Step by step solution

01

- Identify the values of x and y

In the given problem, the values are provided: \( x = 2 \) \( y = 1 \)
02

- Calculate the value of xy

To find the value of \( xy \), multiply the given values of \( x \) and \( y \): \( x \cdot y = 2 \cdot 1 = 2 \)
03

- Choose the correct answer

The calculated value of \( xy \) is 2. From the given choices, the correct answer is: C. 2

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Key Concepts

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

Multiplication
Multiplication is a basic arithmetic operation where you combine groups of numbers to find a total. It is often seen as repeated addition. For example, if you have 2 groups of 1 item, you can add them: 1 + 1, which equals 2.
But to simplify, we use multiplication, so 2 times 1 is just written as 2.
In the given exercise, you multiplied the variables x and y to find their product.

If we break down the multiplication of the given variables:
  • We have x = 2 and y = 1
  • We multiply these two values:
    for a better illustration:
    \[ x \times y = 2 \times 1 = 2 \]
Variable Substitution
Variable substitution is a technique in algebra where you replace a variable with a given value. This helps in simplifying the equation or expression you're working with.
In algebra, variables represent unknown values. Here, you substitute known values for the variables x and y.

For the current exercise, you were given the specific values:
  • \( x = 2 \)
  • \( y = 1 \)
By substituting x and y with these values, you simplify the expression meant to solve:
  • So, replacing x and y in \( xy \) with the given values, it becomes \( 2 \times 1 \).
Solving for Products
Solving for products means finding the result of multiplying two or more numbers together. It's a crucial concept in algebra and basic arithmetic. To solve for a product, follow these steps:
  • Identify the numbers or variables involved.
  • Substitute any given values for the variables.
  • Multiply the numbers to find the product.

In the given exercise:
  • We identified the values of x and y as 2 and 1, respectively.
  • Substituted these values into the multiplication equation.
  • Performed the multiplication to obtain the final answer.
Therefore, \(2 \times 1 = 2 \), leading us to conclude the product is 2. This matches option C from the given choices.

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Most popular questions from this chapter

Perform each indicated operation. $$ \left(-\frac{3}{8}-\frac{2}{3}\right)-\left(-\frac{9}{8}-3\right) $$

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. See Example \(9 .\) 7 less than a number is 2

Write a numerical expression for each phrase and simplify. 9 less than \(-13\)

To find the average (mean) of a group of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. \(18,12,0,-4,\) and \(-10\)

Write a numerical expression for each phrase and simplify. The sum of \(-7\) and \(-13,\) increased by 14
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