Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Concept explainers

Minimization
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Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
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Question
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Chapter 5.3, Problem 82HP
To determine

To calculate: The quadratic equation in standard form provided two random roots and when the signs of roots are switched.

Expert Solution & Answer
Check Mark

Answer to Problem 82HP

Only the term with coefficient of x has changed its sign when sign of roots are switched.

Explanation of Solution

Given information:

The two random roots of the quadratic equation.

Formula used:

The standard form of the quadratic equation is ax2+bx+c and its factored form is (x−p)(x−q)=0 where p and q are its roots.

Calculation:

Consider the roots of the quadratic equation that are 1 and 5.

Recall that standard form of the quadratic equation is ax2+bx+c and its factored form is (x−p)(x−q)=0 where p and q are its roots.

Apply it,

  (x−1)(x−5)=0x2−5x−x+5=0x2−6x+5=0

When sign of roots are switched,

Consider the roots of the quadratic equation that are −1 and -5.

Recall that standard form of the quadratic equation is ax2+bx+c and its factored form is (x−p)(x−q)=0 where p and q are its roots.

Apply it,

  (x−(−1))(x−(−5))=0(x+1)(x+5)=0x2+5x+x+5=0x2+6x+5=0

Thus, only the term with coefficient of x has changed its sign when sign of roots are switched.

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Chapter 5.3, Problem 81HP
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Chapter 5 Solutions

Algebra 2

Ch. 5.1 - Prob. 1ACYPCh. 5.1 - Prob. 1BCYPCh. 5.1 - Prob. 2ACYPCh. 5.1 - Prob. 2BCYPCh. 5.1 - Prob. 2CCYPCh. 5.1 - Prob. 3ACYPCh. 5.1 - Prob. 3BCYPCh. 5.1 - Prob. 3CCYPCh. 5.1 - Prob. 4CYPCh. 5.1 - Prob. 1CYU
Ch. 5.1 - Prob. 2CYUCh. 5.1 - Prob. 3CYUCh. 5.1 - Prob. 4CYUCh. 5.1 - Prob. 5CYUCh. 5.1 - Prob. 6CYUCh. 5.1 - Prob. 7CYUCh. 5.1 - Prob. 8CYUCh. 5.1 - Prob. 9CYUCh. 5.1 - Prob. 10CYUCh. 5.1 - Prob. 11CYUCh. 5.1 - Prob. 12PPSCh. 5.1 - Prob. 13PPSCh. 5.1 - Prob. 14PPSCh. 5.1 - Prob. 15PPSCh. 5.1 - Prob. 16PPSCh. 5.1 - Prob. 17PPSCh. 5.1 - Prob. 18PPSCh. 5.1 - Prob. 19PPSCh. 5.1 - Prob. 20PPSCh. 5.1 - Prob. 21PPSCh. 5.1 - Prob. 22PPSCh. 5.1 - Prob. 23PPSCh. 5.1 - Prob. 24PPSCh. 5.1 - Prob. 25PPSCh. 5.1 - Prob. 26PPSCh. 5.1 - Prob. 27PPSCh. 5.1 - Prob. 28PPSCh. 5.1 - Prob. 29PPSCh. 5.1 - Prob. 30PPSCh. 5.1 - Prob. 31PPSCh. 5.1 - Prob. 32PPSCh. 5.1 - Prob. 33PPSCh. 5.1 - Prob. 34PPSCh. 5.1 - Prob. 35PPSCh. 5.1 - Prob. 36PPSCh. 5.1 - Prob. 37PPSCh. 5.1 - Prob. 38PPSCh. 5.1 - Prob. 39PPSCh. 5.1 - Prob. 40PPSCh. 5.1 - Prob. 41PPSCh. 5.1 - Prob. 42PPSCh. 5.1 - Prob. 43PPSCh. 5.1 - Prob. 44PPSCh. 5.1 - Prob. 45PPSCh. 5.1 - Prob. 46PPSCh. 5.1 - Prob. 47PPSCh. 5.1 - Prob. 48PPSCh. 5.1 - Prob. 49PPSCh. 5.1 - 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Prob. 1BCYPCh. 5.4 - Prob. 2ACYPCh. 5.4 - Prob. 2BCYPCh. 5.4 - Prob. 2CCYPCh. 5.4 - Prob. 3ACYPCh. 5.4 - Prob. 3BCYPCh. 5.4 - Prob. 4CYPCh. 5.4 - Prob. 5ACYPCh. 5.4 - Prob. 5BCYPCh. 5.4 - Prob. 6CYPCh. 5.4 - Prob. 7ACYPCh. 5.4 - Prob. 7BCYPCh. 5.4 - Prob. 1CYUCh. 5.4 - Prob. 2CYUCh. 5.4 - Prob. 3CYUCh. 5.4 - Prob. 4CYUCh. 5.4 - Prob. 5CYUCh. 5.4 - Prob. 6CYUCh. 5.4 - Prob. 7CYUCh. 5.4 - Prob. 8CYUCh. 5.4 - Prob. 9CYUCh. 5.4 - Prob. 10CYUCh. 5.4 - Prob. 11CYUCh. 5.4 - Prob. 12CYUCh. 5.4 - Prob. 13CYUCh. 5.4 - Prob. 14CYUCh. 5.4 - Prob. 15CYUCh. 5.4 - Prob. 16CYUCh. 5.4 - Prob. 17CYUCh. 5.4 - Prob. 18PPSCh. 5.4 - Prob. 19PPSCh. 5.4 - Prob. 20PPSCh. 5.4 - Prob. 21PPSCh. 5.4 - Prob. 22PPSCh. 5.4 - Prob. 23PPSCh. 5.4 - Prob. 24PPSCh. 5.4 - Prob. 25PPSCh. 5.4 - Prob. 26PPSCh. 5.4 - Prob. 27PPSCh. 5.4 - Prob. 28PPSCh. 5.4 - Prob. 29PPSCh. 5.4 - Prob. 30PPSCh. 5.4 - Prob. 31PPSCh. 5.4 - Prob. 32PPSCh. 5.4 - Prob. 33PPSCh. 5.4 - Prob. 34PPSCh. 5.4 - Prob. 35PPSCh. 5.4 - Prob. 36PPSCh. 5.4 - Prob. 37PPSCh. 5.4 - 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Prob. 87SCh. 5.4 - Prob. 88SCh. 5.4 - Prob. 89SCh. 5.5 - Prob. 1ACYPCh. 5.5 - Prob. 1BCYPCh. 5.5 - Prob. 2ACYPCh. 5.5 - Prob. 2BCYPCh. 5.5 - Prob. 3CYPCh. 5.5 - Prob. 4ACYPCh. 5.5 - Prob. 4BCYPCh. 5.5 - Prob. 5ACYPCh. 5.5 - Prob. 5BCYPCh. 5.5 - Prob. 6ACYPCh. 5.5 - Prob. 6BCYPCh. 5.5 - Prob. 1CYUCh. 5.5 - Prob. 2CYUCh. 5.5 - Prob. 3CYUCh. 5.5 - Prob. 4CYUCh. 5.5 - Prob. 5CYUCh. 5.5 - Prob. 6CYUCh. 5.5 - Prob. 7CYUCh. 5.5 - Prob. 8CYUCh. 5.5 - Prob. 9CYUCh. 5.5 - Prob. 10CYUCh. 5.5 - Prob. 11CYUCh. 5.5 - Prob. 12CYUCh. 5.5 - Prob. 13CYUCh. 5.5 - Prob. 14PPSCh. 5.5 - Prob. 15PPSCh. 5.5 - Prob. 16PPSCh. 5.5 - Prob. 17PPSCh. 5.5 - Prob. 18PPSCh. 5.5 - Prob. 19PPSCh. 5.5 - Prob. 20PPSCh. 5.5 - Prob. 21PPSCh. 5.5 - Prob. 22PPSCh. 5.5 - Prob. 23PPSCh. 5.5 - Prob. 24PPSCh. 5.5 - Prob. 25PPSCh. 5.5 - Prob. 26PPSCh. 5.5 - Prob. 27PPSCh. 5.5 - Prob. 28PPSCh. 5.5 - Prob. 29PPSCh. 5.5 - Prob. 30PPSCh. 5.5 - Prob. 31PPSCh. 5.5 - Prob. 32PPSCh. 5.5 - Prob. 33PPSCh. 5.5 - Prob. 34PPSCh. 5.5 - Prob. 35PPSCh. 5.5 - 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Prob. 2ECh. 5.5 - Prob. 3ECh. 5.5 - Prob. 4ECh. 5.5 - Prob. 5ECh. 5.5 - Prob. 6ECh. 5.5 - Prob. 7ECh. 5.5 - Prob. 8ECh. 5.5 - Prob. 9ECh. 5.6 - Prob. 1ACYPCh. 5.6 - Prob. 1BCYPCh. 5.6 - Prob. 2ACYPCh. 5.6 - Prob. 2BCYPCh. 5.6 - Prob. 3ACYPCh. 5.6 - Prob. 3BCYPCh. 5.6 - Prob. 4ACYPCh. 5.6 - Prob. 4BCYPCh. 5.6 - Prob. 5ACYPCh. 5.6 - Prob. 5BCYPCh. 5.6 - Prob. 1CYUCh. 5.6 - Prob. 2CYUCh. 5.6 - Prob. 3CYUCh. 5.6 - Prob. 4CYUCh. 5.6 - Prob. 5CYUCh. 5.6 - Prob. 6CYUCh. 5.6 - Prob. 7CYUCh. 5.6 - Prob. 8CYUCh. 5.6 - Prob. 9CYUCh. 5.6 - Prob. 10CYUCh. 5.6 - Prob. 11CYUCh. 5.6 - Prob. 12CYUCh. 5.6 - Prob. 13CYUCh. 5.6 - Prob. 14PPSCh. 5.6 - Prob. 15PPSCh. 5.6 - Prob. 16PPSCh. 5.6 - Prob. 17PPSCh. 5.6 - Prob. 18PPSCh. 5.6 - Prob. 19PPSCh. 5.6 - Prob. 20PPSCh. 5.6 - Prob. 21PPSCh. 5.6 - Prob. 22PPSCh. 5.6 - Prob. 23PPSCh. 5.6 - Prob. 24PPSCh. 5.6 - Prob. 25PPSCh. 5.6 - Prob. 26PPSCh. 5.6 - Prob. 27PPSCh. 5.6 - Prob. 28PPSCh. 5.6 - Prob. 29PPSCh. 5.6 - Prob. 30PPSCh. 5.6 - Prob. 31PPSCh. 5.6 - Prob. 32PPSCh. 5.6 - Prob. 33PPSCh. 5.6 - Prob. 34PPSCh. 5.6 - Prob. 35PPSCh. 5.6 - Prob. 36PPSCh. 5.6 - Prob. 37PPSCh. 5.6 - Prob. 38PPSCh. 5.6 - Prob. 39PPSCh. 5.6 - Prob. 40PPSCh. 5.6 - Prob. 41PPSCh. 5.6 - Prob. 42PPSCh. 5.6 - Prob. 43HPCh. 5.6 - Prob. 44HPCh. 5.6 - Prob. 45HPCh. 5.6 - Prob. 46HPCh. 5.6 - Prob. 47HPCh. 5.6 - Prob. 48HPCh. 5.6 - Prob. 49HPCh. 5.6 - Prob. 50HPCh. 5.6 - Prob. 51HPCh. 5.6 - Prob. 52HPCh. 5.6 - Prob. 53STPCh. 5.6 - Prob. 54STPCh. 5.6 - Prob. 55STPCh. 5.6 - Prob. 56STPCh. 5.6 - Prob. 57STPCh. 5.6 - Prob. 58STPCh. 5.6 - Prob. 59STPCh. 5.6 - Prob. 60STPCh. 5.6 - Prob. 61SCh. 5.6 - Prob. 62SCh. 5.6 - Prob. 63SCh. 5.6 - Prob. 1ECh. 5.6 - Prob. 2ECh. 5.6 - Prob. 3ECh. 5.6 - Prob. 4ECh. 5.6 - Prob. 5ECh. 5.6 - Prob. 6ECh. 5.6 - Prob. 7ECh. 5.6 - Prob. 8ECh. 5.6 - Prob. 9ECh. 5.6 - Prob. 10ECh. 5.7 - Prob. 1ACYPCh. 5.7 - Prob. 1BCYPCh. 5.7 - Prob. 2CYPCh. 5.7 - Prob. 3ACYPCh. 5.7 - Prob. 3BCYPCh. 5.7 - Prob. 1CYUCh. 5.7 - Prob. 2CYUCh. 5.7 - Prob. 3CYUCh. 5.7 - Prob. 4CYUCh. 5.7 - Prob. 5CYUCh. 5.7 - Prob. 6CYUCh. 5.7 - Prob. 7CYUCh. 5.7 - Prob. 8PPSCh. 5.7 - Prob. 9PPSCh. 5.7 - Prob. 10PPSCh. 5.7 - Prob. 11PPSCh. 5.7 - Prob. 12PPSCh. 5.7 - Prob. 13PPSCh. 5.7 - Prob. 14PPSCh. 5.7 - Prob. 15PPSCh. 5.7 - Prob. 16PPSCh. 5.7 - Prob. 17PPSCh. 5.7 - Prob. 18PPSCh. 5.7 - Prob. 19PPSCh. 5.7 - Prob. 20PPSCh. 5.7 - Prob. 21PPSCh. 5.7 - Prob. 22PPSCh. 5.7 - Prob. 23PPSCh. 5.7 - Prob. 24PPSCh. 5.7 - Prob. 25PPSCh. 5.7 - Prob. 26PPSCh. 5.7 - Prob. 27PPSCh. 5.7 - Prob. 28PPSCh. 5.7 - Prob. 29PPSCh. 5.7 - Prob. 30PPSCh. 5.7 - Prob. 31PPSCh. 5.7 - Prob. 32PPSCh. 5.7 - Prob. 33PPSCh. 5.7 - Prob. 34PPSCh. 5.7 - Prob. 35PPSCh. 5.7 - Prob. 36PPSCh. 5.7 - Prob. 37PPSCh. 5.7 - Prob. 38PPSCh. 5.7 - Prob. 39PPSCh. 5.7 - Prob. 40PPSCh. 5.7 - Prob. 41PPSCh. 5.7 - Prob. 42PPSCh. 5.7 - Prob. 43PPSCh. 5.7 - Prob. 44PPSCh. 5.7 - Prob. 45PPSCh. 5.7 - Prob. 46PPSCh. 5.7 - Prob. 47PPSCh. 5.7 - Prob. 48HPCh. 5.7 - Prob. 49HPCh. 5.7 - Prob. 50HPCh. 5.7 - Prob. 51HPCh. 5.7 - Prob. 52HPCh. 5.7 - Prob. 53HPCh. 5.7 - Prob. 54HPCh. 5.7 - Prob. 55HPCh. 5.7 - Prob. 56HPCh. 5.7 - Prob. 57STPCh. 5.7 - Prob. 58STPCh. 5.7 - Prob. 59STPCh. 5.7 - Prob. 60STPCh. 5.7 - Prob. 61STPCh. 5.7 - Prob. 62STPCh. 5.7 - Prob. 63STPCh. 5.7 - Prob. 64STPCh. 5.7 - Prob. 65STPCh. 5.7 - Prob. 66STPCh. 5.7 - Prob. 67STPCh. 5.7 - Prob. 68STPCh. 5.7 - Prob. 69STPCh. 5.7 - Prob. 70STPCh. 5.7 - Prob. 71STPCh. 5.7 - Prob. 72STPCh. 5.7 - Prob. 73STPCh. 5.7 - Prob. 74SCh. 5.7 - Prob. 75SCh. 5.7 - Prob. 76SCh. 5.7 - Prob. 1ECh. 5.7 - Prob. 2ECh. 5.7 - Prob. 3ECh. 5.7 - Prob. 4ECh. 5.8 - Prob. 1ACYPCh. 5.8 - Prob. 1BCYPCh. 5.8 - Prob. 2ACYPCh. 5.8 - Prob. 2BCYPCh. 5.8 - Prob. 3ACYPCh. 5.8 - Prob. 3BCYPCh. 5.8 - Prob. 4CYPCh. 5.8 - Prob. 5ACYPCh. 5.8 - Prob. 5BCYPCh. 5.8 - Prob. 1CYUCh. 5.8 - Prob. 2CYUCh. 5.8 - Prob. 3CYUCh. 5.8 - Prob. 4CYUCh. 5.8 - Prob. 5CYUCh. 5.8 - Prob. 6CYUCh. 5.8 - Prob. 7CYUCh. 5.8 - Prob. 8CYUCh. 5.8 - Prob. 9CYUCh. 5.8 - Prob. 10CYUCh. 5.8 - Prob. 11CYUCh. 5.8 - Prob. 12CYUCh. 5.8 - Prob. 13PPSCh. 5.8 - Prob. 14PPSCh. 5.8 - Prob. 15PPSCh. 5.8 - Prob. 16PPSCh. 5.8 - Prob. 17PPSCh. 5.8 - Prob. 18PPSCh. 5.8 - Prob. 19PPSCh. 5.8 - Prob. 20PPSCh. 5.8 - Prob. 21PPSCh. 5.8 - Prob. 22PPSCh. 5.8 - Prob. 23PPSCh. 5.8 - Prob. 24PPSCh. 5.8 - Prob. 25PPSCh. 5.8 - Prob. 26PPSCh. 5.8 - Prob. 27PPSCh. 5.8 - Prob. 28PPSCh. 5.8 - Prob. 29PPSCh. 5.8 - Prob. 30PPSCh. 5.8 - Prob. 31PPSCh. 5.8 - Prob. 32PPSCh. 5.8 - Prob. 33PPSCh. 5.8 - Prob. 34PPSCh. 5.8 - Prob. 35PPSCh. 5.8 - Prob. 36PPSCh. 5.8 - Prob. 37PPSCh. 5.8 - Prob. 38PPSCh. 5.8 - Prob. 39PPSCh. 5.8 - Prob. 40PPSCh. 5.8 - Prob. 41PPSCh. 5.8 - Prob. 42PPSCh. 5.8 - Prob. 43PPSCh. 5.8 - Prob. 44PPSCh. 5.8 - Prob. 45PPSCh. 5.8 - Prob. 46PPSCh. 5.8 - Prob. 47PPSCh. 5.8 - Prob. 48PPSCh. 5.8 - Prob. 49PPSCh. 5.8 - Prob. 50PPSCh. 5.8 - Prob. 51PPSCh. 5.8 - Prob. 52PPSCh. 5.8 - Prob. 53PPSCh. 5.8 - Prob. 54PPSCh. 5.8 - Prob. 55PPSCh. 5.8 - Prob. 56PPSCh. 5.8 - Prob. 57HPCh. 5.8 - Prob. 58HPCh. 5.8 - Prob. 59HPCh. 5.8 - Prob. 60HPCh. 5.8 - Prob. 61HPCh. 5.8 - Prob. 62HPCh. 5.8 - Prob. 63HPCh. 5.8 - Prob. 64HPCh. 5.8 - Prob. 65HPCh. 5.8 - Prob. 66HPCh. 5.8 - Prob. 67STPCh. 5.8 - Prob. 68STPCh. 5.8 - Prob. 69STPCh. 5.8 - Prob. 70STPCh. 5.8 - Prob. 71STPCh. 5.8 - Prob. 72STPCh. 5.8 - Prob. 73STPCh. 5.8 - Prob. 74STPCh. 5.8 - Prob. 75STPCh. 5.8 - Prob. 76STPCh. 5.8 - Prob. 77SCh. 5.8 - Prob. 78SCh. 5.8 - Prob. 79SCh. 5.8 - Prob. 80SCh. 5.8 - Prob. 81SCh. 5.8 - Prob. 82SCh. 5 - Prob. 1QCCh. 5 - Prob. 2QCCh. 5 - Prob. 3QCCh. 5 - Prob. 4QCCh. 5 - Prob. 5QCCh. 5 - Prob. 6QCCh. 5 - Prob. 7QCCh. 5 - Prob. 8QCCh. 5 - Prob. 9QCCh. 5 - Prob. 10QCCh. 5 - Prob. 11QCCh. 5 - Prob. 12QCCh. 5 - Prob. 13QCCh. 5 - Prob. 14QCCh. 5 - Prob. 15QCCh. 5 - Prob. 1MCQCh. 5 - Prob. 2MCQCh. 5 - Prob. 3MCQCh. 5 - Prob. 4MCQCh. 5 - Prob. 5MCQCh. 5 - Prob. 6MCQCh. 5 - Prob. 7MCQCh. 5 - Prob. 8MCQCh. 5 - Prob. 9MCQCh. 5 - Prob. 10MCQCh. 5 - Prob. 11MCQCh. 5 - Prob. 12MCQCh. 5 - Prob. 13MCQCh. 5 - Prob. 14MCQCh. 5 - Prob. 15MCQCh. 5 - Prob. 16MCQCh. 5 - Prob. 17MCQCh. 5 - Prob. 18MCQCh. 5 - Prob. 19MCQCh. 5 - Prob. 20MCQCh. 5 - Prob. 21MCQCh. 5 - Prob. 22MCQCh. 5 - Prob. 23MCQCh. 5 - Prob. 1SGRCh. 5 - Prob. 2SGRCh. 5 - Prob. 3SGRCh. 5 - Prob. 4SGRCh. 5 - Prob. 5SGRCh. 5 - Prob. 6SGRCh. 5 - Prob. 7SGRCh. 5 - Prob. 8SGRCh. 5 - Prob. 9SGRCh. 5 - Prob. 10SGRCh. 5 - Prob. 11SGRCh. 5 - Prob. 12SGRCh. 5 - Prob. 13SGRCh. 5 - Prob. 14SGRCh. 5 - Prob. 15SGRCh. 5 - Prob. 16SGRCh. 5 - Prob. 17SGRCh. 5 - Prob. 18SGRCh. 5 - Prob. 19SGRCh. 5 - Prob. 20SGRCh. 5 - Prob. 21SGRCh. 5 - Prob. 22SGRCh. 5 - Prob. 23SGRCh. 5 - Prob. 24SGRCh. 5 - Prob. 25SGRCh. 5 - Prob. 26SGRCh. 5 - Prob. 27SGRCh. 5 - Prob. 28SGRCh. 5 - Prob. 29SGRCh. 5 - Prob. 30SGRCh. 5 - Prob. 31SGRCh. 5 - Prob. 32SGRCh. 5 - Prob. 33SGRCh. 5 - Prob. 34SGRCh. 5 - Prob. 35SGRCh. 5 - Prob. 36SGRCh. 5 - Prob. 37SGRCh. 5 - Prob. 38SGRCh. 5 - Prob. 39SGRCh. 5 - Prob. 40SGRCh. 5 - Prob. 41SGRCh. 5 - Prob. 42SGRCh. 5 - Prob. 43SGRCh. 5 - Prob. 44SGRCh. 5 - Prob. 45SGRCh. 5 - Prob. 46SGRCh. 5 - Prob. 47SGRCh. 5 - Prob. 48SGRCh. 5 - Prob. 49SGRCh. 5 - Prob. 50SGRCh. 5 - Prob. 51SGRCh. 5 - Prob. 52SGRCh. 5 - Prob. 53SGRCh. 5 - Prob. 54SGRCh. 5 - Prob. 55SGRCh. 5 - Prob. 56SGRCh. 5 - Prob. 57SGRCh. 5 - Prob. 58SGRCh. 5 - Prob. 59SGRCh. 5 - Prob. 60SGRCh. 5 - Prob. 61SGRCh. 5 - Prob. 62SGRCh. 5 - Prob. 63SGRCh. 5 - Prob. 64SGRCh. 5 - Prob. 65SGRCh. 5 - Prob. 66SGRCh. 5 - Prob. 67SGRCh. 5 - Prob. 68SGRCh. 5 - Prob. 69SGRCh. 5 - Prob. 70SGRCh. 5 - Prob. 71SGRCh. 5 - Prob. 72SGRCh. 5 - Prob. 73SGRCh. 5 - Prob. 1PTCh. 5 - Prob. 2PTCh. 5 - Prob. 3PTCh. 5 - Prob. 4PTCh. 5 - Prob. 5PTCh. 5 - Prob. 6PTCh. 5 - Prob. 7PTCh. 5 - Prob. 8PTCh. 5 - Prob. 9PTCh. 5 - Prob. 10PTCh. 5 - Prob. 11PTCh. 5 - Prob. 12PTCh. 5 - Prob. 13PTCh. 5 - Prob. 14PTCh. 5 - Prob. 15PTCh. 5 - Prob. 16PTCh. 5 - Prob. 17PTCh. 5 - Prob. 18PTCh. 5 - Prob. 19PTCh. 5 - Prob. 20PTCh. 5 - Prob. 21PTCh. 5 - Prob. 22PTCh. 5 - Prob. 23PTCh. 5 - Prob. 24PTCh. 5 - Prob. 25PTCh. 5 - Prob. 26PTCh. 5 - Prob. 1ECh. 5 - Prob. 2ECh. 5 - Prob. 3ECh. 5 - Prob. 4ECh. 5 - Prob. 5ECh. 5 - Prob. 6ECh. 5 - Prob. 1STPCh. 5 - Prob. 2STPCh. 5 - Prob. 3STPCh. 5 - Prob. 4STPCh. 5 - Prob. 5STPCh. 5 - Prob. 6STPCh. 5 - Prob. 7STPCh. 5 - Prob. 8STPCh. 5 - Prob. 9STPCh. 5 - Prob. 10STPCh. 5 - Prob. 11STPCh. 5 - Prob. 12STPCh. 5 - Prob. 13STPCh. 5 - Prob. 14STPCh. 5 - Prob. 15STPCh. 5 - Prob. 16STP

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