Algebra: Structure And Method, Book 1
(REV)00 Edition
ISBN: 9780395977224
Author: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher: McDougal Littell
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Question
Chapter 1.8, Problem 57WE
To determine
To find: the coordinate of a point located between two given points on a number line.
Expert Solution & Answer
Answer to Problem 57WE
The coordinate of the point between M and T with the given condition is 3
Explanation of Solution
Given Information: Point M and T are located on the number line with coordinates 2 and 5 respectively. An unknown point is located between M and T such that its distance from M is half its distance from T .
A number line is used to graphically represent numbers along a line. It consists of 0 as the center point. The positive numbers are marked to the right and negative numbers are marked to the left side of the center point.
The given points are M and T which are located at 2 and 5 respectively. The number line and the given numbers marked on it are as shown below.
1. Let the distance between the point M and the unknown point X be x.
2. Then the distance between the unknown point and the point T is 2x.
3. Also, the sum of the distance x and 2 x forms the distance between the points M and T. The distance between M and T is 3 units.
Thus, the distance between M and T can be represented as,
The above value of x implies that, the unknown point X is located at a distance of 1 unit from point M and two units from point T. Thus the coordinate of X is at 3. This is shown in Figure 2.
Chapter 1 Solutions
Algebra: Structure And Method, Book 1
Ch. 1.1 - Prob. 1OECh. 1.1 - Prob. 2OECh. 1.1 - Prob. 3OECh. 1.1 - Prob. 4OECh. 1.1 - Prob. 5OECh. 1.1 - Prob. 6OECh. 1.1 - Prob. 7OECh. 1.1 - Prob. 8OECh. 1.1 - Prob. 9OECh. 1.1 - Prob. 10OE
Ch. 1.1 - Prob. 11OECh. 1.1 - Prob. 12OECh. 1.1 - Prob. 13OECh. 1.1 - Prob. 14OECh. 1.1 - Prob. 15OECh. 1.1 - Prob. 16OECh. 1.1 - Prob. 17OECh. 1.1 - Prob. 18OECh. 1.1 - Prob. 19OECh. 1.1 - Prob. 20OECh. 1.1 - Prob. 21OECh. 1.1 - Prob. 22OECh. 1.1 - Prob. 23OECh. 1.1 - Prob. 24OECh. 1.1 - Prob. 25OECh. 1.1 - Prob. 26OECh. 1.1 - Prob. 1WECh. 1.1 - Prob. 2WECh. 1.1 - Prob. 3WECh. 1.1 - Prob. 4WECh. 1.1 - Prob. 5WECh. 1.1 - Prob. 6WECh. 1.1 - Prob. 7WECh. 1.1 - Prob. 8WECh. 1.1 - Prob. 9WECh. 1.1 - Prob. 10WECh. 1.1 - Prob. 11WECh. 1.1 - Prob. 12WECh. 1.1 - Prob. 13WECh. 1.1 - Prob. 14WECh. 1.1 - Prob. 15WECh. 1.1 - Prob. 16WECh. 1.1 - Prob. 17WECh. 1.1 - Prob. 18WECh. 1.1 - Prob. 19WECh. 1.1 - Prob. 20WECh. 1.1 - Prob. 21WECh. 1.1 - Prob. 22WECh. 1.1 - Prob. 23WECh. 1.1 - Prob. 24WECh. 1.1 - Prob. 25WECh. 1.1 - Prob. 26WECh. 1.1 - Prob. 27WECh. 1.1 - Prob. 28WECh. 1.1 - Prob. 29WECh. 1.1 - Prob. 30WECh. 1.1 - Prob. 31WECh. 1.1 - Prob. 32WECh. 1.1 - Prob. 33WECh. 1.1 - Prob. 34WECh. 1.1 - Prob. 35WECh. 1.1 - Prob. 36WECh. 1.1 - Prob. 37WECh. 1.1 - Prob. 38WECh. 1.1 - Prob. 39WECh. 1.1 - Prob. 40WECh. 1.1 - Prob. 41WECh. 1.1 - Prob. 42WECh. 1.1 - Prob. 43WECh. 1.1 - Prob. 44WECh. 1.1 - Prob. 45WECh. 1.1 - Prob. 46WECh. 1.1 - Prob. 47WECh. 1.1 - Prob. 48WECh. 1.1 - Prob. 49WECh. 1.1 - Prob. 1MRECh. 1.1 - Prob. 2MRECh. 1.1 - Prob. 3MRECh. 1.1 - Prob. 4MRECh. 1.1 - Prob. 5MRECh. 1.1 - Prob. 6MRECh. 1.1 - Prob. 7MRECh. 1.1 - Prob. 8MRECh. 1.1 - Prob. 9MRECh. 1.1 - Prob. 10MRECh. 1.1 - Prob. 11MRECh. 1.1 - Prob. 12MRECh. 1.1 - Prob. 13MRECh. 1.1 - Prob. 14MRECh. 1.1 - Prob. 15MRECh. 1.1 - Prob. 16MRECh. 1.1 - Prob. 1ECh. 1.1 - Prob. 2ECh. 1.2 - Prob. 1OECh. 1.2 - Prob. 2OECh. 1.2 - Prob. 3OECh. 1.2 - Prob. 4OECh. 1.2 - Prob. 5OECh. 1.2 - Prob. 6OECh. 1.2 - Prob. 7OECh. 1.2 - Prob. 8OECh. 1.2 - Prob. 9OECh. 1.2 - Prob. 10OECh. 1.2 - Prob. 11OECh. 1.2 - Prob. 12OECh. 1.2 - Prob. 13OECh. 1.2 - Prob. 14OECh. 1.2 - Prob. 15OECh. 1.2 - Prob. 16OECh. 1.2 - Prob. 17OECh. 1.2 - Prob. 18OECh. 1.2 - Prob. 19OECh. 1.2 - Prob. 20OECh. 1.2 - Prob. 1WECh. 1.2 - Prob. 2WECh. 1.2 - Prob. 3WECh. 1.2 - Prob. 4WECh. 1.2 - Prob. 5WECh. 1.2 - Prob. 6WECh. 1.2 - Prob. 7WECh. 1.2 - Prob. 8WECh. 1.2 - Prob. 9WECh. 1.2 - Prob. 10WECh. 1.2 - Prob. 11WECh. 1.2 - Prob. 12WECh. 1.2 - Prob. 13WECh. 1.2 - Prob. 14WECh. 1.2 - Prob. 15WECh. 1.2 - Prob. 16WECh. 1.2 - Prob. 17WECh. 1.2 - Prob. 18WECh. 1.2 - Prob. 19WECh. 1.2 - Prob. 20WECh. 1.2 - Prob. 21WECh. 1.2 - Prob. 22WECh. 1.2 - Prob. 23WECh. 1.2 - Prob. 24WECh. 1.2 - Prob. 25WECh. 1.2 - Prob. 26WECh. 1.2 - Prob. 27WECh. 1.2 - Prob. 28WECh. 1.2 - Prob. 29WECh. 1.2 - Prob. 30WECh. 1.2 - Prob. 31WECh. 1.2 - Prob. 32WECh. 1.2 - Prob. 33WECh. 1.2 - Prob. 34WECh. 1.2 - Prob. 35WECh. 1.2 - Prob. 36WECh. 1.2 - Prob. 37WECh. 1.2 - Prob. 38WECh. 1.2 - Prob. 39WECh. 1.2 - Prob. 40WECh. 1.2 - Prob. 41WECh. 1.2 - Prob. 42WECh. 1.2 - Prob. 43WECh. 1.2 - Prob. 44WECh. 1.2 - Prob. 45WECh. 1.2 - Prob. 46WECh. 1.2 - Prob. 1MRECh. 1.2 - Prob. 2MRECh. 1.2 - Prob. 3MRECh. 1.2 - 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Prob. 51WECh. 1.4 - Prob. 52WECh. 1.4 - Prob. 53WECh. 1.4 - Prob. 54WECh. 1.4 - Prob. 1MRECh. 1.4 - Prob. 2MRECh. 1.4 - Prob. 3MRECh. 1.4 - Prob. 4MRECh. 1.4 - Prob. 5MRECh. 1.4 - Prob. 6MRECh. 1.4 - Prob. 7MRECh. 1.4 - Prob. 8MRECh. 1.4 - Prob. 9MRECh. 1.4 - Prob. 10MRECh. 1.4 - Prob. 11MRECh. 1.4 - Prob. 12MRECh. 1.4 - Prob. 13MRECh. 1.4 - Prob. 14MRECh. 1.5 - Prob. 1OECh. 1.5 - Prob. 2OECh. 1.5 - Prob. 3OECh. 1.5 - Prob. 4OECh. 1.5 - Prob. 5OECh. 1.5 - Prob. 6OECh. 1.5 - Prob. 7OECh. 1.5 - Prob. 8OECh. 1.5 - Prob. 9OECh. 1.5 - Prob. 10OECh. 1.5 - Prob. 11OECh. 1.5 - Prob. 12OECh. 1.5 - Prob. 13OECh. 1.5 - Prob. 1WECh. 1.5 - Prob. 2WECh. 1.5 - Prob. 3WECh. 1.5 - Prob. 4WECh. 1.5 - Prob. 5WECh. 1.5 - Prob. 6WECh. 1.5 - Prob. 7WECh. 1.5 - Prob. 8WECh. 1.5 - Prob. 9WECh. 1.5 - Prob. 10WECh. 1.5 - Prob. 11WECh. 1.5 - Prob. 12WECh. 1.5 - Prob. 13WECh. 1.5 - Prob. 14WECh. 1.5 - Prob. 15WECh. 1.5 - Prob. 16WECh. 1.5 - Prob. 17WECh. 1.5 - Prob. 18WECh. 1.5 - Prob. 19WECh. 1.5 - Prob. 20WECh. 1.5 - Prob. 21WECh. 1.5 - Prob. 22WECh. 1.5 - Prob. 23WECh. 1.5 - Prob. 24WECh. 1.5 - Prob. 25WECh. 1.5 - Prob. 26WECh. 1.5 - Prob. 27WECh. 1.5 - Prob. 28WECh. 1.5 - Prob. 29WECh. 1.5 - Prob. 30WECh. 1.5 - Prob. 31WECh. 1.5 - Prob. 32WECh. 1.5 - Prob. 33WECh. 1.5 - Prob. 34WECh. 1.5 - Prob. 35WECh. 1.5 - Prob. 36WECh. 1.5 - Prob. 1MRECh. 1.5 - Prob. 2MRECh. 1.5 - Prob. 3MRECh. 1.5 - Prob. 4MRECh. 1.5 - Prob. 5MRECh. 1.5 - Prob. 6MRECh. 1.5 - Prob. 7MRECh. 1.5 - Prob. 8MRECh. 1.5 - Prob. 9MRECh. 1.5 - Prob. 10MRECh. 1.5 - Prob. 11MRECh. 1.5 - Prob. 12MRECh. 1.6 - Prob. 1PCh. 1.6 - Prob. 2PCh. 1.6 - Prob. 3PCh. 1.6 - Prob. 4PCh. 1.6 - Prob. 5PCh. 1.6 - Prob. 6PCh. 1.6 - Prob. 7PCh. 1.6 - Prob. 8PCh. 1.6 - Prob. 9PCh. 1.6 - Prob. 10PCh. 1.6 - Prob. 11PCh. 1.6 - Prob. 12PCh. 1.6 - Prob. 13PCh. 1.6 - Prob. 14PCh. 1.6 - Prob. 15PCh. 1.6 - Prob. 16PCh. 1.6 - Prob. 17PCh. 1.6 - Prob. 18PCh. 1.6 - Prob. 19PCh. 1.6 - Prob. 20PCh. 1.6 - Prob. 21PCh. 1.6 - Prob. 22PCh. 1.6 - Prob. 1MRECh. 1.6 - Prob. 2MRECh. 1.6 - Prob. 3MRECh. 1.6 - Prob. 4MRECh. 1.6 - Prob. 5MRECh. 1.6 - Prob. 6MRECh. 1.6 - Prob. 7MRECh. 1.6 - Prob. 8MRECh. 1.6 - Prob. 9MRECh. 1.6 - Prob. 10MRECh. 1.6 - Prob. 11MRECh. 1.6 - Prob. 12MRECh. 1.6 - Prob. 1ECh. 1.6 - Prob. 2ECh. 1.6 - Prob. 3ECh. 1.7 - Prob. 1PCh. 1.7 - Prob. 2PCh. 1.7 - Prob. 3PCh. 1.7 - Prob. 4PCh. 1.7 - Prob. 5PCh. 1.7 - Prob. 6PCh. 1.7 - Prob. 7PCh. 1.7 - Prob. 8PCh. 1.7 - Prob. 9PCh. 1.7 - Prob. 10PCh. 1.7 - Prob. 11PCh. 1.7 - Prob. 12PCh. 1.7 - Prob. 13PCh. 1.7 - Prob. 14PCh. 1.7 - Prob. 15PCh. 1.7 - Prob. 16PCh. 1.7 - Prob. 17PCh. 1.7 - Prob. 18PCh. 1.7 - Prob. 1MRECh. 1.7 - Prob. 2MRECh. 1.7 - Prob. 3MRECh. 1.7 - Prob. 4MRECh. 1.7 - Prob. 5MRECh. 1.7 - Prob. 6MRECh. 1.7 - Prob. 7MRECh. 1.7 - Prob. 8MRECh. 1.7 - Prob. 1STCh. 1.7 - Prob. 2STCh. 1.7 - Prob. 3STCh. 1.7 - Prob. 4STCh. 1.8 - Prob. 1OECh. 1.8 - Prob. 2OECh. 1.8 - Prob. 3OECh. 1.8 - Prob. 4OECh. 1.8 - Prob. 5OECh. 1.8 - Prob. 6OECh. 1.8 - Prob. 7OECh. 1.8 - Prob. 8OECh. 1.8 - Prob. 9OECh. 1.8 - Prob. 10OECh. 1.8 - Prob. 11OECh. 1.8 - Prob. 12OECh. 1.8 - Prob. 13OECh. 1.8 - Prob. 14OECh. 1.8 - Prob. 15OECh. 1.8 - Prob. 16OECh. 1.8 - Prob. 17OECh. 1.8 - Prob. 18OECh. 1.8 - Prob. 19OECh. 1.8 - Prob. 20OECh. 1.8 - Prob. 21OECh. 1.8 - Prob. 22OECh. 1.8 - Prob. 23OECh. 1.8 - Prob. 24OECh. 1.8 - Prob. 1WECh. 1.8 - Prob. 2WECh. 1.8 - Prob. 3WECh. 1.8 - Prob. 4WECh. 1.8 - Prob. 5WECh. 1.8 - Prob. 6WECh. 1.8 - Prob. 7WECh. 1.8 - Prob. 8WECh. 1.8 - Prob. 9WECh. 1.8 - Prob. 10WECh. 1.8 - Prob. 11WECh. 1.8 - Prob. 12WECh. 1.8 - Prob. 13WECh. 1.8 - Prob. 14WECh. 1.8 - Prob. 15WECh. 1.8 - Prob. 16WECh. 1.8 - Prob. 17WECh. 1.8 - Prob. 18WECh. 1.8 - Prob. 19WECh. 1.8 - Prob. 20WECh. 1.8 - Prob. 21WECh. 1.8 - Prob. 22WECh. 1.8 - Prob. 23WECh. 1.8 - Prob. 24WECh. 1.8 - Prob. 25WECh. 1.8 - Prob. 26WECh. 1.8 - Prob. 27WECh. 1.8 - Prob. 28WECh. 1.8 - Prob. 29WECh. 1.8 - Prob. 30WECh. 1.8 - Prob. 31WECh. 1.8 - Prob. 32WECh. 1.8 - Prob. 33WECh. 1.8 - Prob. 34WECh. 1.8 - Prob. 35WECh. 1.8 - Prob. 36WECh. 1.8 - Prob. 37WECh. 1.8 - Prob. 38WECh. 1.8 - Prob. 39WECh. 1.8 - Prob. 40WECh. 1.8 - Prob. 41WECh. 1.8 - Prob. 42WECh. 1.8 - Prob. 43WECh. 1.8 - Prob. 44WECh. 1.8 - Prob. 45WECh. 1.8 - Prob. 46WECh. 1.8 - Prob. 47WECh. 1.8 - Prob. 48WECh. 1.8 - Prob. 49WECh. 1.8 - Prob. 50WECh. 1.8 - Prob. 51WECh. 1.8 - Prob. 52WECh. 1.8 - Prob. 53WECh. 1.8 - Prob. 54WECh. 1.8 - Prob. 55WECh. 1.8 - Prob. 56WECh. 1.8 - Prob. 57WECh. 1.8 - Prob. 58WECh. 1.8 - Prob. 1MRECh. 1.8 - Prob. 2MRECh. 1.8 - Prob. 3MRECh. 1.8 - Prob. 4MRECh. 1.8 - Prob. 5MRECh. 1.8 - Prob. 6MRECh. 1.8 - Prob. 7MRECh. 1.8 - Prob. 8MRECh. 1.8 - Prob. 9MRECh. 1.8 - Prob. 10MRECh. 1.9 - Prob. 1OECh. 1.9 - Prob. 2OECh. 1.9 - Prob. 3OECh. 1.9 - Prob. 4OECh. 1.9 - Prob. 5OECh. 1.9 - Prob. 6OECh. 1.9 - Prob. 7OECh. 1.9 - Prob. 8OECh. 1.9 - Prob. 9OECh. 1.9 - Prob. 10OECh. 1.9 - Prob. 11OECh. 1.9 - Prob. 12OECh. 1.9 - Prob. 13OECh. 1.9 - Prob. 14OECh. 1.9 - Prob. 15OECh. 1.9 - Prob. 16OECh. 1.9 - Prob. 17OECh. 1.9 - Prob. 18OECh. 1.9 - Prob. 19OECh. 1.9 - Prob. 20OECh. 1.9 - 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Prob. 45WECh. 1.9 - Prob. 1MRECh. 1.9 - Prob. 2MRECh. 1.9 - Prob. 3MRECh. 1.9 - Prob. 4MRECh. 1.9 - Prob. 5MRECh. 1.9 - Prob. 6MRECh. 1.9 - Prob. 7MRECh. 1.9 - Prob. 8MRECh. 1.9 - Prob. 9MRECh. 1.9 - Prob. 10MRECh. 1.9 - Prob. 1STCh. 1.9 - Prob. 2STCh. 1.9 - Prob. 3STCh. 1.9 - Prob. 4STCh. 1.9 - Prob. 5STCh. 1 - Prob. 1CRCh. 1 - Prob. 2CRCh. 1 - Prob. 3CRCh. 1 - Prob. 4CRCh. 1 - Prob. 5CRCh. 1 - Prob. 6CRCh. 1 - Prob. 7CRCh. 1 - Prob. 8CRCh. 1 - Prob. 9CRCh. 1 - Prob. 10CRCh. 1 - Prob. 11CRCh. 1 - Prob. 12CRCh. 1 - Prob. 1CTCh. 1 - Prob. 2CTCh. 1 - Prob. 3CTCh. 1 - Prob. 4CTCh. 1 - Prob. 5CTCh. 1 - Prob. 6CTCh. 1 - Prob. 7CTCh. 1 - Prob. 8CTCh. 1 - Prob. 9CTCh. 1 - Prob. 10CTCh. 1 - Prob. 11CTCh. 1 - Prob. 12CTCh. 1 - Prob. 13CTCh. 1 - Prob. 14CTCh. 1 - Prob. 15CTCh. 1 - Prob. 16CTCh. 1 - Prob. 17CTCh. 1 - Prob. 18CTCh. 1 - Prob. 19CTCh. 1 - Prob. 20CTCh. 1 - Prob. 1MSCh. 1 - Prob. 2MSCh. 1 - Prob. 3MSCh. 1 - Prob. 4MSCh. 1 - Prob. 5MSCh. 1 - Prob. 6MSCh. 1 - Prob. 7MSCh. 1 - Prob. 8MSCh. 1 - Prob. 9MSCh. 1 - Prob. 10MSCh. 1 - Prob. 11MSCh. 1 - Prob. 12MSCh. 1 - Prob. 13MSCh. 1 - Prob. 14MSCh. 1 - Prob. 15MSCh. 1 - Prob. 16MSCh. 1 - Prob. 17MSCh. 1 - Prob. 18MSCh. 1 - Prob. 19MSCh. 1 - Prob. 20MSCh. 1 - Prob. 21MSCh. 1 - Prob. 22MSCh. 1 - Prob. 23MSCh. 1 - Prob. 24MSCh. 1 - Prob. 25MSCh. 1 - Prob. 26MSCh. 1 - Prob. 27MSCh. 1 - Prob. 28MS
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- 10) Multiply (8m + 3)² A) 8m²+11m+6 B) m² + 48m+9 C) 64m²+48m+9 D) 16m²+11m+6arrow_forwardLet R be field and X= R³/s Vector space over R M=(a,b,c)labic, e Rra+b= 3- <3 Show that Ms and why with proof. 1) is convexset and affine set of botost ii) is blanced set and symmetirs set of x iii) is hy per space and hyper plane ofx or hot iii) find f:MR st kerf = M 18/103 and finnd fiM→R/{0} st M= {xEX, f(t) = x, texiαER? jiii) show that Mis Maxsubspace or not and Mis a max. affine set or not.arrow_forwardFind The partial fraction decomposition for each The following 2× B) (x+3) a 3 6 X-3x+2x-6arrow_forward
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- 2.8.1arrow_forwardKate, Luke, Mary and Nancy are sharing a cake. The cake had previously been divided into four slices (s1, s2, s3 and s4). The following table shows the values of the slices in the eyes of each player. What is fair share to nancy? S1 S2 S3 S4 Kate $4.00 $6.00 $6.00 $4.00 Luke $5.30 $5.00 $5.25 $5.45 Mary $4.25 $4.50 $3.50 $3.75 Nancy $6.00 $4.00 $4.00 $6.00arrow_forwardKate, Luke, Mary and Nancy are sharing a cake. The cake had previously been divided into four slices (s1, s2, s3 and s4). The following table shows the values of the slices in the eyes of each player. S1 S2 S3 S4 Kate $4.00 $6.00 $6.00 $4.00 Luke $5.30 $5.00 $5.25 $5.45 Mary $4.25 $4.50 $3.50 $3.75 Nancy $6.00 $4.00 $4.00 $6.00 how much is the cak worth to maryarrow_forward
- Kate, Luke, Mary and Nancy are sharing a cake. The cake had previously been divided into four slices (s1, s2, s3 and s4). The following table shows the values of the slices in the eyes of each player. What is the threshold of fair share for Luke? S1 S2 S3 S4 Kate $4.00 $6.00 $6.00 $4.00 Luke $5.30 $5.00 $5.25 $5.45 Mary $4.25 $4.50 $3.50 $3.75 Nancy $6.00 $4.00 $4.00 $6.00arrow_forward2. A microwave manufacturing firm has determined that their profit function is P(x)=-0.0014x+0.3x²+6x-355 , where is the number of microwaves sold annually. a. Graph the profit function using a calculator. b. Determine a reasonable viewing window for the function. c. Approximate all of the zeros of the function using the CALC menu of your calculator. d. What must be the range of microwaves sold in order for the firm to profit?arrow_forwardA clothing manufacturer's profitability can be modeled by p (x)=-x4 + 40x² - 144, where .x is the number of items sold in thousands and p (x) is the company's profit in thousands of dollars. a. Sketch the function on your calculator and describe the end behavior. b. Determine the zeros of the function. c. Between what two values should the company sell in order to be profitable? d. Explain why only two of the zeros are considered in part c.arrow_forward
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