High School Math 2012 Common-core Algebra 1 Practice And Problem Solvingworkbook Grade 8/9

1st Edition

ISBN: 9780133185614

Author: Prentice Hall

Publisher: Prentice Hall

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Textbook Question

Chapter 8.3, Problem 41P

Multi Step The height of a painting is twice its width x. You want a 3 inch wide wooden frame for the painting. The area of the frame alone is 216 square inches.

a. Draw a diagram that represents this situation.

b. Write a variable expression for the area of the frame alone.

c. What are the dimensions of the frame?

Expert Solution

To determine

To graph: The height of a painting is twice of its width $x$ . You want 3 inch wide wooden frame for the painting. The area of the frame alone is 216 square inches. Draw a diagram that represents this situation.

Explanation of Solution

Given:

The height of a painting is twice of its width $x$ and there is 3 inch wide wooden frame for the painting.

Calculation:

It is given that width of the painting is $x$ and height of painting is twice of its width so height of the painting is $2x$ .

High School Math 2012 Common-core Algebra 1 Practice And Problem Solvingworkbook Grade 8/9, Chapter 8.3, Problem 41P

ii.

Expert Solution

To determine

To calculate: The height of a painting is twice of its width $x$ . You want 3 inch wide wooden frame for the painting. The area of the frame alone is 216 square inches. Write a variable expression for the area of the frame alone.

Answer to Problem 41P

The expression for the area of frame alone is $18x−36$

Explanation of Solution

Given:

To find the area of frame alone we should subtract the area of smaller rectangle from the area of larger rectangle from the figure shown in above part.

Calculation:

Let $A$ be the area of frame alone, so

$A=$ Area of Larger Rectangle $−$ Area of Smaller Rectangle

$A=2x*x−(2x−6)(x−6)$

$A=2x2−(2x2−12x−6x+36)$

$A=2x2−2x2+18x−36$

$A=18x−36$

Conclusion:

The expression for the area of frame alone is $18x−36$

iii.

Expert Solution

To determine

To calculate: The height of a painting is twice of its width $x$ . You want 3 inch wide wooden frame for the painting. The area of the frame alone is 216 square inches. What are the dimensions of the frame?

Answer to Problem 41P

The length of frame is 28 inches and the width of frame is 14 inches

Explanation of Solution

Given:

The area of the frame alone is 216 square inches

Calculation:

From the above part we know the expression of the area of frame alone is $18x−36$ and its area is given as 216 square inches.

Now we know the expression for the area of frame alone and its area also so by equating them we get

$A=18x−36$

$216=18x−36$

$216+36=18x$

$252=18x$

$x=25218=14$

Width of frame is 14 inches and its length is twice of width, so

length $=2*14=28$ inches

Conclusion:

The length of frame is 28 inches and the width of frame is 14 inches.

Chapter 8.3, Problem 40P

Chapter 8.3, Problem 1STP

Chapter 8 Solutions

High School Math 2012 Common-core Algebra 1 Practice And Problem Solvingworkbook Grade 8/9

Ch. 8.1 - Find the degree of each monomial. 2b2c2 Ch. 8.1 - Find the degree of each monomial. 5x Ch. 8.1 - Find the degree of each monomial. 3.7y5 Ch. 8.1 - Find the degree of each monomial. 19ab Ch. 8.1 - Find the degree of each monomial. 12 Ch. 8.1 - Find the degree of each monomial. 12z2 Ch. 8.1 - Find the degree of each monomial. t Ch. 8.1 - Find the degree of each monomial. 4d4e Ch. 8.1 - Simplify. 2a3b+4a3b Ch. 8.1 - Simplify. 5x34x3

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