Answer The area of the triangle is 24 . Explanation Given: The given equations are, 2 x + y = 5 y = x − 4 y = 5 Calculation: Consider the given equations is, 2 x + y = 5 y = x − 4 y = 5 The graph for the equations is shown in Figure 1 Figure 1 The intersection points of the line is at x = 0 and x = 9 . Thus, the base of the triangle is 9 . The intersections of the y axis is at y = − 1 .Then the height of the triangle is, 5 − ( − 1 ) = 6 . Thus, the area of the triangle is, 1 2 ( 8 ) ( 6 ) = 24

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ISBN: 9780395977224

Author: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher: McDougal Littell

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Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 9.1, Problem 24WE

To determine

To find: The area of the region whose vertices are the point of the intersection of the given equations.

Expert Solution & Answer

Answer to Problem 24WE

The area of the triangle is 24 .

Explanation of Solution

Given:

The given equations are,

2x+y=5y=x−4y=5

Calculation:

Consider the given equations is,

2x+y=5y=x−4y=5

The graph for the equations is shown in Figure 1

Algebra: Structure And Method, Book 1, Chapter 9.1, Problem 24WE

Figure 1

The intersection points of the line is at x=0 and x=9 . Thus, the base of the triangle is 9 .

The intersections of the y axis is at y=−1 .Then the height of the triangle is,

5−(−1)=6 .

Thus, the area of the triangle is,

12(8)(6)=24

Chapter 9.1, Problem 23WE

Chapter 9.1, Problem 1MRE

Chapter 9 Solutions

Algebra: Structure And Method, Book 1

Ch. 9.1 - Prob. 1OE Ch. 9.1 - Prob. 2OE Ch. 9.1 - Prob. 3OE Ch. 9.1 - Prob. 4OE Ch. 9.1 - Prob. 5OE Ch. 9.1 - Prob. 6OE Ch. 9.1 - Prob. 7OE Ch. 9.1 - Prob. 8OE Ch. 9.1 - Prob. 9OE Ch. 9.1 - Prob. 1WE

Ch. 9.1 - Prob. 2WE Ch. 9.1 - Prob. 3WE Ch. 9.1 - Prob. 4WE Ch. 9.1 - Prob. 5WE Ch. 9.1 - Prob. 6WE Ch. 9.1 - Prob. 7WE Ch. 9.1 - Prob. 8WE Ch. 9.1 - Prob. 9WE Ch. 9.1 - Prob. 10WE Ch. 9.1 - Prob. 11WE Ch. 9.1 - Prob. 12WE Ch. 9.1 - Prob. 13WE Ch. 9.1 - Prob. 14WE Ch. 9.1 - Prob. 15WE Ch. 9.1 - Prob. 16WE Ch. 9.1 - Prob. 17WE Ch. 9.1 - Prob. 18WE Ch. 9.1 - Prob. 19WE Ch. 9.1 - Prob. 20WE Ch. 9.1 - Prob. 21WE Ch. 9.1 - Prob. 22WE Ch. 9.1 - Prob. 23WE Ch. 9.1 - Prob. 24WE Ch. 9.1 - Prob. 1MRE Ch. 9.1 - Prob. 2MRE Ch. 9.1 - Prob. 3MRE Ch. 9.1 - Prob. 4MRE Ch. 9.1 - Prob. 5MRE Ch. 9.1 - Prob. 6MRE Ch. 9.1 - Prob. 1CE Ch. 9.1 - Prob. 2CE Ch. 9.1 - Prob. 3CE Ch. 9.1 - Prob. 4CE Ch. 9.2 - Prob. 1OE Ch. 9.2 - Prob. 2OE Ch. 9.2 - Prob. 3OE Ch. 9.2 - Prob. 4OE Ch. 9.2 - Prob. 5OE Ch. 9.2 - Prob. 6OE Ch. 9.2 - Prob. 7OE Ch. 9.2 - Prob. 8OE Ch. 9.2 - Prob. 9OE Ch. 9.2 - Prob. 10OE Ch. 9.2 - Prob. 11OE Ch. 9.2 - Prob. 12OE Ch. 9.2 - Prob. 1WE Ch. 9.2 - Prob. 2WE Ch. 9.2 - Prob. 3WE Ch. 9.2 - Prob. 4WE Ch. 9.2 - Prob. 5WE Ch. 9.2 - Prob. 6WE Ch. 9.2 - Prob. 7WE Ch. 9.2 - Prob. 8WE Ch. 9.2 - Prob. 9WE Ch. 9.2 - Prob. 10WE Ch. 9.2 - Prob. 11WE Ch. 9.2 - Prob. 12WE Ch. 9.2 - Prob. 13WE Ch. 9.2 - Prob. 14WE Ch. 9.2 - Prob. 15WE Ch. 9.2 - Prob. 16WE Ch. 9.2 - Prob. 17WE Ch. 9.2 - Prob. 18WE Ch. 9.2 - Prob. 19WE Ch. 9.2 - Prob. 20WE Ch. 9.2 - Prob. 21WE Ch. 9.2 - Prob. 22WE Ch. 9.2 - Prob. 23WE Ch. 9.2 - Prob. 24WE Ch. 9.2 - Prob. 25WE Ch. 9.2 - Prob. 26WE Ch. 9.2 - Prob. 27WE Ch. 9.2 - Prob. 28WE Ch. 9.2 - Prob. 29WE Ch. 9.2 - Prob. 30WE Ch. 9.2 - Prob. 31WE Ch. 9.2 - Prob. 32WE Ch. 9.2 - Prob. 33WE Ch. 9.2 - Prob. 34WE Ch. 9.2 - Prob. 35WE Ch. 9.2 - Prob. 36WE Ch. 9.2 - Prob. 37WE Ch. 9.2 - Prob. 38WE Ch. 9.2 - Prob. 39WE Ch. 9.2 - Prob. 40WE Ch. 9.2 - Prob. 41WE Ch. 9.2 - Prob. 1MRE Ch. 9.2 - Prob. 2MRE Ch. 9.2 - Prob. 3MRE Ch. 9.2 - Prob. 4MRE Ch. 9.2 - Prob. 5MRE Ch. 9.2 - Prob. 6MRE Ch. 9.2 - Prob. 7MRE Ch. 9.2 - Prob. 8MRE Ch. 9.2 - Prob. 9MRE Ch. 9.2 - Prob. 10MRE Ch. 9.2 - Prob. 11MRE Ch. 9.2 - 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