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 58WE
To determine
To find: the coordinate of a point located between two given points on a number line.
Expert Solution & Answer
Answer to Problem 58WE
The coordinate of the point between C and D with the given condition is 2
Explanation of Solution
Given Information: Point C and D are located on the number line with coordinates -2 and 4 respectively. An unknown point is located between C and D such that its distance from C is twice its distance from D
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 C and D which are located at - 2 and 4 respectively. The number line and the given numbers marked on it are as shown below.
1. Let the distance between the point D and the unknown point be x.
2. Then the distance between the unknown point and the point C is 2x.
3. Also, the sum of the distance x and 2 x forms the distance between the points C and D. The distance between C and D has to be calculated considering the magnitude only. Here, it is the sum of 2 units corresponding to distance from point C to origin and then 4 units corresponding to distance between origin and point D..
Thus, the distance between C and D can be represented as,
The above value of x implies that, the unknown point is located at a distance of 2 units from point D towards C and 4 units from point D towards C. Thus the coordinate of the desired point is at 2. 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
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- 1. For the following subsets of R3, explain whether or not they are a subspace of R³. (a) (b) 1.1 0.65 U = span -3.4 0.23 0.4 -0.44 0 (})} a V {(2) | ER (c) Z= the points in the z-axisarrow_forwardSolve the following equation forx. leave answer in Simplified radical form. 5x²-4x-3=6arrow_forwardMATCHING LIST Question 6 Listen Use the given equations and their discriminants to match them to the type and number of solutions. 00 ed two irrational solutions a. x²+10x-2=-24 two rational solutions b. 8x²+11x-3=7 one rational solution c. 3x²+2x+7=2 two non-real solutions d. x²+12x+45 = 9 DELL FLOWER CHILD 10/20 All Changes S $681 22991arrow_forward
- 88 MULTIPLE CHOICE Question 7 Listen The following irrational expression is given in unsimplified form with four op- tions in simplified form. Select the correct simplified form. Select only one option. A 2±3√√2 B 4±√3 2±√ √3 D 1±√√3 DELL FLOWER CHILD 11/200 4 ± √48 4 ✓ All Changes Saved 165arrow_forwardUse the graph of y = f(x) to answer the following. 3- 2 -4 -2 -1 1 2 3 4 -1 2 m -3- + (d) Find all x for which f(x) = -2. If there is more than one value, separate them with commas or write your answer in interval notation, if necessary. Select "None", if applicable. Value(s) of x for which f(x)=-2: | (0,0) (0,0) (0,0) (0,0) 0,0... -00 None (h) Determine the range of f. The range is (0,0) Garrow_forwardWhat is g(f(4))arrow_forward
- 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
- 1) Find the partial feraction decomposition for each of 5- X 2 2x+x-1 The following: 3 B) 3 X + 3xarrow_forwardT={(−7,1),(1,−1),(6,−8),(2,8)} Find the domain and range of the inverse. Express your answer as a set of numbers.arrow_forwardT={(−7,1),(1,−1),(6,−8),(2,8)}. Find the inverse. Express your answer as a set of ordered pairs.arrow_forward
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