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Find a polynomial that represents the area of the sign when a = 4. (Simplify your answer completely.) in? (h – a) in. YIELD h in.

Find a polynomial that represents the area of the sign when a = 4. (Simplify your answer completely.) in? (h – a) in. YIELD h in.

Algebra and Trigonometry (6th Edition)
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: \[ \boxed{\frac{1}{2} h^2 - 2h} \]
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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