Algebra 1
1st Edition
ISBN: 9780078884801
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Question
Chapter 5, Problem 2STP
(a)
To determine
Draw a picture to represent this situation.
(a)
Expert Solution
Answer to Problem 2STP
The right side must be down than the right side
Explanation of Solution
Given:
In a balance have 12 pounds on the left side and 18 pounds on the right side.
Concept Used:
As 12 lbs is less than 18 lbs. So the right side must be down than the right side.
Thus, the right side must be down than the right side as 12 pounds on the left side and 18 pounds on the right side
(b)
To determine
Write an inequality.
(b)
Expert Solution
Answer to Problem 2STP
Explanation of Solution
Given:
In a balance have 12 pounds on the left side and 18 pounds on the tight side.
Concept Used:
Left side 12 lbs is less than the right side 18 lbs.
Inequality:
Calculation:
Inequality:
Thus, we can write the inequality
(c)
To determine
Create a table showing the result of doubling, tripling or quadrupling the weight of each side of the balance.
Create a second table showing the result of reducing the weight on each side of the balance by a factor of
(c)
Expert Solution
Answer to Problem 2STP
Explanation of Solution
Given: In a balance have 12 pounds on the left side and 18 pounds on the tight side.
Concept Used:
Make two tables to represent the situation doubling, tripling or quadrupling the weight of each side of the balance and by a factor of
Calculation:
Create a table showing the result of doubling, tripling or quadrupling the weight of each side of the balance.
| x | Original | 12 Pound | 18 Pound | |
| x2 | Doubling | 24 Pound | < | 36 Pound |
| x3 | Tripling | 36 Pound | < | 54 Pound |
| x4 | Quadrupling | 48 Pound | < | 72 Pound |
Create a second table showing the result of reducing the weight on each side of the balance by a factor of
| x | Original | 12 Pound | < | 18 Pound |
| by a factor of | 6 Pound | < | 9 Pound | |
| by a factor of | 4 Pound | < | 6 Pound | |
| by a factor of | 3 Pound | < | 4.5 Pound |
Thus, the two tables represent the situations.
(d)
To determine
Describe the effect multiplying or dividing each side of an inequality by the same positive value has on the inequality.
(d)
Expert Solution
Explanation of Solution
Given: In a balance have 12 pounds on the left side and 18 pounds on the tight side.
Concept Used:
If a true inequality is multiplied by a positive number, the resulting inequality is also true.
If a true inequality is divided by a positive number, the resulting inequality is also true.
Thus, if a true inequality is multiplied by a positive number, the resulting inequality is also true and if a true inequality is divided by a positive number, the resulting inequality is also true.
Chapter 5 Solutions
Algebra 1
Ch. 5.1 - Prob. 1ACYPCh. 5.1 - Prob. 1BCYPCh. 5.1 - Prob. 2CYPCh. 5.1 - Prob. 3ACYPCh. 5.1 - Prob. 3BCYPCh. 5.1 - Prob. 4CYPCh. 5.1 - Prob. 1CYUCh. 5.1 - Prob. 2CYUCh. 5.1 - Prob. 3CYUCh. 5.1 - Prob. 4CYU
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- Listen ANALYZING RELATIONSHIPS Describe the x-values for which (a) f is increasing or decreasing, (b) f(x) > 0 and (c) f(x) <0. y Af -2 1 2 4x a. The function is increasing when and decreasing whenarrow_forwardBy forming the augmented matrix corresponding to this system of equations and usingGaussian elimination, find the values of t and u that imply the system:(i) is inconsistent.(ii) has infinitely many solutions.(iii) has a unique solutiona=2 b=1arrow_forwardif a=2 and b=1 1) Calculate 49(B-1)2+7B−1AT+7ATB−1+(AT)2 2)Find a matrix C such that (B − 2C)-1=A 3) Find a non-diagonal matrix E ̸= B such that det(AB) = det(AE)arrow_forwardWrite the equation line shown on the graph in slope, intercept form.arrow_forward1.2.15. (!) Let W be a closed walk of length at least 1 that does not contain a cycle. Prove that some edge of W repeats immediately (once in each direction).arrow_forward1.2.18. (!) Let G be the graph whose vertex set is the set of k-tuples with elements in (0, 1), with x adjacent to y if x and y differ in exactly two positions. Determine the number of components of G.arrow_forward1.2.17. (!) Let G,, be the graph whose vertices are the permutations of (1,..., n}, with two permutations a₁, ..., a,, and b₁, ..., b, adjacent if they differ by interchanging a pair of adjacent entries (G3 shown below). Prove that G,, is connected. 132 123 213 312 321 231arrow_forward1.2.19. Let and s be natural numbers. Let G be the simple graph with vertex set Vo... V„−1 such that v; ↔ v; if and only if |ji| Є (r,s). Prove that S has exactly k components, where k is the greatest common divisor of {n, r,s}.arrow_forward1.2.20. (!) Let u be a cut-vertex of a simple graph G. Prove that G - v is connected. עarrow_forward1.2.12. (-) Convert the proof at 1.2.32 to an procedure for finding an Eulerian circuit in a connected even graph.arrow_forward1.2.16. Let e be an edge appearing an odd number of times in a closed walk W. Prove that W contains the edges of a cycle through c.arrow_forward1.2.11. (−) Prove or disprove: If G is an Eulerian graph with edges e, f that share vertex, then G has an Eulerian circuit in which e, f appear consecutively. aarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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