The area of the desktop shown below is given by the expression (4x + 16x - 9) in.2. Factor this expression to find the expressions that represent its length and width. in (larger value) in (smaller value) Determine the difference in the length and width of the desktop. in
The area of the desktop shown below is given by the expression (4x + 16x - 9) in.2. Factor this expression to find the expressions that represent its length and width. in (larger value) in (smaller value) Determine the difference in the length and width of the desktop. in
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
#### Steps to Solve:
1. **Factor the given quadratic expression**:
\[ 4x^2 + 16x - 9 \]
2. **Identify the dimensions (Length and Width)** by analyzing the factored form.
3. **Calculate the difference between the length and width** of the desktop.
#### Input Fields:
- **Larger value (Length)**:
\[
\_\_\_\_\_\_
\]
- **Smaller value (Width)**:
\[
\_\_\_\_\_\_
\]
#### Determining the Difference:
- **Difference in the length and width of the desktop**:
\[
\_\_\_\_\_\_\ \text{in}
\]
This exercise involves algebraic manipulation and understanding quadratic expressions to find the physical dimensions of a given object. Users are to input their calculated dimensions in the provided fields and determine the difference between these dimensions.
**Note**: The visual representation (image of the desk) aids in contextualizing the problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b91f986-cff4-42a8-8faf-14c1255b04a2%2F775e61dc-6e39-4cc1-81bb-e07213c69b72%2F6ikxq6_processed.png&w=3840&q=75)
Transcribed Image Text:### Determining the Dimensions of a Desktop from its Area Expression
#### Problem Statement:
The area of the desktop shown below is given by the expression \( (4x^2 + 16x - 9) \text{ in}^2 \). Factor this expression to find the expressions that represent its length and width.
#### Steps to Solve:
1. **Factor the given quadratic expression**:
\[ 4x^2 + 16x - 9 \]
2. **Identify the dimensions (Length and Width)** by analyzing the factored form.
3. **Calculate the difference between the length and width** of the desktop.
#### Input Fields:
- **Larger value (Length)**:
\[
\_\_\_\_\_\_
\]
- **Smaller value (Width)**:
\[
\_\_\_\_\_\_
\]
#### Determining the Difference:
- **Difference in the length and width of the desktop**:
\[
\_\_\_\_\_\_\ \text{in}
\]
This exercise involves algebraic manipulation and understanding quadratic expressions to find the physical dimensions of a given object. Users are to input their calculated dimensions in the provided fields and determine the difference between these dimensions.
**Note**: The visual representation (image of the desk) aids in contextualizing the problem.
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