The dimensions of the three rearview mirrors on an automobile are given in the illustration below. (Assume a(x) = 4x, b(x) = 3x2, c(x) = 3x, and d(x) = 6x.) a(x) cm Windshield b(x) cm d(x) cm d(x) cm с(x) сп с (х) ст Driver side door Passenger side door (a) Write an algebraic expression that gives the area of the rearview mirror mounted on the windshield. cm2 (b) Write an algebraic expression that gives the total area of the two side mirrors. cm2 (c) Write an algebraic expression that gives the total area of all three mirrors. Express the result in factored form. cm2

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Rearview Mirror Dimensions

The dimensions of the three rearview mirrors on an automobile are given in the illustration below. Assume the following expressions for the dimensions:
- \( a(x) = 4x \)
- \( b(x) = 3x^2 \)
- \( c(x) = 3x \)
- \( d(x) = 6x \)

#### Illustration Description

1. **Windshield Mirror:**
    - Dimensions are labeled as \( a(x) \) cm (horizontal) and \( b(x) \) cm (vertical).

2. **Driver Side Door Mirror:**
    - Dimensions are labeled as \( c(x) \) cm (vertical) and \( d(x) \) cm (horizontal).

3. **Passenger Side Door Mirror:**
    - Dimensions are similarly labeled as \( c(x) \) cm (vertical) and \( d(x) \) cm (horizontal).

### Problems

(a) Write an algebraic expression that gives the area of the rearview mirror mounted on the windshield.
   \[
   \text{Area} = \_\_\_\_\_\_ \text{ cm}^2
   \]

(b) Write an algebraic expression that gives the total area of the two side mirrors.
   \[
   \text{Total Area} = \_\_\_\_\_\_ \text{ cm}^2
   \]

(c) Write an algebraic expression that gives the total area of all three mirrors. Express the result in factored form.
   \[
   \text{Total Area} = \_\_\_\_\_\_ \text{ cm}^2
   \]

#### Solutions

Let's solve each part step by step.

**(a) Area of the Windshield Mirror**

The area of the windshield mirror is calculated as:
\[
\text{Area} = a(x) \cdot b(x) = 4x \cdot 3x^2 = 12x^3 \text{ cm}^2 
\]

**(b) Total Area of the Two Side Mirrors**

Each side mirror area is calculated as:
\[
\text{Area of one side mirror} = c(x) \cdot d(x) = 3x \cdot 6x = 18x^2 \text{ cm}^2
\]

Since there are two side mirrors:
\[
\text{Total
Transcribed Image Text:### Rearview Mirror Dimensions The dimensions of the three rearview mirrors on an automobile are given in the illustration below. Assume the following expressions for the dimensions: - \( a(x) = 4x \) - \( b(x) = 3x^2 \) - \( c(x) = 3x \) - \( d(x) = 6x \) #### Illustration Description 1. **Windshield Mirror:** - Dimensions are labeled as \( a(x) \) cm (horizontal) and \( b(x) \) cm (vertical). 2. **Driver Side Door Mirror:** - Dimensions are labeled as \( c(x) \) cm (vertical) and \( d(x) \) cm (horizontal). 3. **Passenger Side Door Mirror:** - Dimensions are similarly labeled as \( c(x) \) cm (vertical) and \( d(x) \) cm (horizontal). ### Problems (a) Write an algebraic expression that gives the area of the rearview mirror mounted on the windshield. \[ \text{Area} = \_\_\_\_\_\_ \text{ cm}^2 \] (b) Write an algebraic expression that gives the total area of the two side mirrors. \[ \text{Total Area} = \_\_\_\_\_\_ \text{ cm}^2 \] (c) Write an algebraic expression that gives the total area of all three mirrors. Express the result in factored form. \[ \text{Total Area} = \_\_\_\_\_\_ \text{ cm}^2 \] #### Solutions Let's solve each part step by step. **(a) Area of the Windshield Mirror** The area of the windshield mirror is calculated as: \[ \text{Area} = a(x) \cdot b(x) = 4x \cdot 3x^2 = 12x^3 \text{ cm}^2 \] **(b) Total Area of the Two Side Mirrors** Each side mirror area is calculated as: \[ \text{Area of one side mirror} = c(x) \cdot d(x) = 3x \cdot 6x = 18x^2 \text{ cm}^2 \] Since there are two side mirrors: \[ \text{Total
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