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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![## Problem Statement
Find a polynomial that represents the area of the sign when \( a = 4 \). (Simplify your answer completely.)
The yield sign is shaped like a triangle. The diagram shows the height of the sign as \( h \) inches and the base of the sign as \( (h - a) \) inches. We are given the value \( a = 4 \).
## Steps to Solve
1. **Identify the Polynomial Expression for Area**:
Since the yield sign is a triangle, the formula to find the area of a triangle is:
\[
\text{Area (A)} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Here, the base of the triangle is \( (h - a) \) and the height is \( h \).
2. **Substitute the Base and Height into the Formula**:
Substitute \((h - a)\) for the base and \( h \) for the height in the formula:
\[
A = \frac{1}{2} \times (h - a) \times h
\]
3. **Substitute \( a = 4 \) into the Polynomial**:
Replace \( a \) with 4 in the formula:
\[
A = \frac{1}{2} \times (h - 4) \times h
\]
4. **Simplify the Expression**:
Expand and simplify the expression:
\[
A = \frac{1}{2} \times (h - 4) \times h = \frac{1}{2} \times (h^2 - 4h) = \frac{1}{2} h^2 - 2h
\]
## Solution
The polynomial representing the area of the sign when \( a = 4 \) is:
\[
\boxed{\frac{1}{2} h^2 - 2h}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcfa510ce-a779-4198-b3d3-c9e941c192c9%2Fc67ab62a-3034-4672-9121-235360749900%2Fhbx66j_processed.png&w=3840&q=75)
Transcribed Image Text:## Problem Statement
Find a polynomial that represents the area of the sign when \( a = 4 \). (Simplify your answer completely.)
The yield sign is shaped like a triangle. The diagram shows the height of the sign as \( h \) inches and the base of the sign as \( (h - a) \) inches. We are given the value \( a = 4 \).
## Steps to Solve
1. **Identify the Polynomial Expression for Area**:
Since the yield sign is a triangle, the formula to find the area of a triangle is:
\[
\text{Area (A)} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Here, the base of the triangle is \( (h - a) \) and the height is \( h \).
2. **Substitute the Base and Height into the Formula**:
Substitute \((h - a)\) for the base and \( h \) for the height in the formula:
\[
A = \frac{1}{2} \times (h - a) \times h
\]
3. **Substitute \( a = 4 \) into the Polynomial**:
Replace \( a \) with 4 in the formula:
\[
A = \frac{1}{2} \times (h - 4) \times h
\]
4. **Simplify the Expression**:
Expand and simplify the expression:
\[
A = \frac{1}{2} \times (h - 4) \times h = \frac{1}{2} \times (h^2 - 4h) = \frac{1}{2} h^2 - 2h
\]
## Solution
The polynomial representing the area of the sign when \( a = 4 \) is:
\[
\boxed{\frac{1}{2} h^2 - 2h}
\]
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