Pre-Algebra Student Edition
Pre-Algebra Student Edition
1st Edition
ISBN: 9780078957734
Author: Glencoe/McGraw-Hill
Publisher: MCG
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Coordinate Geometry
Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on …
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Chapter 2.7, Problem 3PPS
To determine

To find:The coordinate of the vertices of the image of given triangle XYZ in coordinate plane after each given coordinates is translated 4 units right and 5 units down.

Expert Solution & Answer
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Answer to Problem 3PPS

The coordinates of the vertices of the image of triangle XYZ i.e. of triangle X`Y`Z` will be  X`(4,−1),Y`(2,−5),Z`(6,−5) .

Explanation of Solution

Given information: 

The triangle XYZ is shown in XY plane, with its vertices as X(0,4),Y(−2,0),Z(2,0) .

Formula used: 

By rule, when a point is shifted few units in right side, these units are added in its x coordinate and when it is shifted few units in down direction, these units are subtracted in given y coordinates. So, to get the coordinates of imaged triangle, we add 4 in each corresponding x coordinate and subtract 5 in each corresponding original y coordinate.

Calculation : So, based on above concept or formula used, the coordinates of vertices of imaged triangle X`Y`Z` be,

  X`=(0+4,4−5)=(4,−1)Y`=(−2+4,0−5)=(2,−5) Z` =(2+4,0−5)=(6,−5)

Conclusion:

Thus, the required coordinates of image of triangle XYZ will be  X`(4,−1),Y`(2,−5),Z`(6,−5) .

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Chapter 2.7, Problem 2CYU
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Chapter 2.7, Problem 4PPS

Chapter 2 Solutions

Pre-Algebra Student Edition

Ch. 2.1 - Prob. 1AGPCh. 2.1 - Prob. 1BGPCh. 2.1 - Prob. 2AGPCh. 2.1 - Prob. 2BGPCh. 2.1 - Prob. 3GPCh. 2.1 - Prob. 4AGPCh. 2.1 - Prob. 4BGPCh. 2.1 - Prob. 5GPCh. 2.1 - Prob. 1CYUCh. 2.1 - Prob. 2CYU
Ch. 2.1 - Prob. 3CYUCh. 2.1 - Prob. 4CYUCh. 2.1 - Prob. 5CYUCh. 2.1 - Prob. 6CYUCh. 2.1 - Prob. 7CYUCh. 2.1 - Prob. 8CYUCh. 2.1 - Prob. 9CYUCh. 2.1 - Prob. 10CYUCh. 2.1 - Prob. 11CYUCh. 2.1 - Prob. 12CYUCh. 2.1 - Prob. 13CYUCh. 2.1 - Prob. 14CYUCh. 2.1 - Prob. 15CYUCh. 2.1 - Prob. 16PPSCh. 2.1 - Prob. 17PPSCh. 2.1 - Prob. 18PPSCh. 2.1 - Prob. 19PPSCh. 2.1 - Prob. 20PPSCh. 2.1 - Prob. 21PPSCh. 2.1 - Prob. 22PPSCh. 2.1 - Prob. 23PPSCh. 2.1 - Prob. 24PPSCh. 2.1 - Prob. 25PPSCh. 2.1 - Prob. 26PPSCh. 2.1 - Prob. 27PPSCh. 2.1 - Prob. 28PPSCh. 2.1 - Prob. 29PPSCh. 2.1 - Prob. 30PPSCh. 2.1 - Prob. 31PPSCh. 2.1 - Prob. 32PPSCh. 2.1 - Prob. 33PPSCh. 2.1 - Prob. 34PPSCh. 2.1 - Prob. 35PPSCh. 2.1 - Prob. 36PPSCh. 2.1 - Prob. 37PPSCh. 2.1 - Prob. 38PPSCh. 2.1 - Prob. 39PPSCh. 2.1 - Prob. 40PPSCh. 2.1 - Prob. 41PPSCh. 2.1 - Prob. 42PPSCh. 2.1 - Prob. 43PPSCh. 2.1 - Prob. 44PPSCh. 2.1 - Prob. 45PPSCh. 2.1 - Prob. 46PPSCh. 2.1 - Prob. 47PPSCh. 2.1 - Prob. 48PPSCh. 2.1 - Prob. 49PPSCh. 2.1 - Prob. 50PPSCh. 2.1 - Prob. 51PPSCh. 2.1 - Prob. 52PPSCh. 2.1 - Prob. 53PPSCh. 2.1 - Prob. 54PPSCh. 2.1 - Prob. 55PPSCh. 2.1 - Prob. 56PPSCh. 2.1 - Prob. 57PPSCh. 2.1 - Prob. 58PPSCh. 2.1 - Prob. 59PPSCh. 2.1 - Prob. 60PPSCh. 2.1 - Prob. 61PPSCh. 2.1 - Prob. 62PPSCh. 2.1 - Prob. 63PPSCh. 2.1 - Prob. 64HPCh. 2.1 - Prob. 65HPCh. 2.1 - Prob. 66HPCh. 2.1 - Prob. 67HPCh. 2.1 - Prob. 68HPCh. 2.1 - Prob. 69HPCh. 2.1 - Prob. 70HPCh. 2.1 - Prob. 71STPCh. 2.1 - Prob. 72STPCh. 2.1 - Prob. 73STPCh. 2.1 - Prob. 74STPCh. 2.1 - Prob. 75SRCh. 2.1 - Prob. 76SRCh. 2.1 - Prob. 77SRCh. 2.1 - Prob. 78SCh. 2.1 - Prob. 79SCh. 2.1 - Prob. 80SCh. 2.1 - Prob. 81SCh. 2.1 - Prob. 82SCh. 2.1 - Prob. 83SCh. 2.2 - Prob. 1AGPCh. 2.2 - Prob. 1BGPCh. 2.2 - Prob. 1CGPCh. 2.2 - Prob. 2AGPCh. 2.2 - Prob. 2BGPCh. 2.2 - Prob. 3AGPCh. 2.2 - Prob. 3BGPCh. 2.2 - Prob. 4AGPCh. 2.2 - Prob. 4BGPCh. 2.2 - Prob. 5GPCh. 2.2 - Prob. 6AGPCh. 2.2 - Prob. 6BGPCh. 2.2 - Prob. 1CYUCh. 2.2 - Prob. 2CYUCh. 2.2 - Prob. 3CYUCh. 2.2 - Prob. 4CYUCh. 2.2 - Prob. 5CYUCh. 2.2 - Prob. 6CYUCh. 2.2 - Prob. 7CYUCh. 2.2 - Prob. 8CYUCh. 2.2 - Prob. 9PPSCh. 2.2 - Prob. 10PPSCh. 2.2 - Prob. 11PPSCh. 2.2 - Prob. 12PPSCh. 2.2 - Prob. 13PPSCh. 2.2 - Prob. 14PPSCh. 2.2 - Prob. 15PPSCh. 2.2 - Prob. 16PPSCh. 2.2 - Prob. 17PPSCh. 2.2 - Prob. 18PPSCh. 2.2 - Prob. 19PPSCh. 2.2 - Prob. 20PPSCh. 2.2 - Prob. 21PPSCh. 2.2 - Prob. 22PPSCh. 2.2 - Prob. 23PPSCh. 2.2 - Prob. 24PPSCh. 2.2 - Prob. 25PPSCh. 2.2 - Prob. 26PPSCh. 2.2 - Prob. 27PPSCh. 2.2 - Prob. 28PPSCh. 2.2 - Prob. 29PPSCh. 2.2 - Prob. 30PPSCh. 2.2 - Prob. 31PPSCh. 2.2 - Prob. 32PPSCh. 2.2 - Prob. 33PPSCh. 2.2 - Prob. 34PPSCh. 2.2 - Prob. 35PPSCh. 2.2 - Prob. 36HPCh. 2.2 - Prob. 37HPCh. 2.2 - Prob. 38HPCh. 2.2 - Prob. 39HPCh. 2.2 - Prob. 40HPCh. 2.2 - Prob. 41HPCh. 2.2 - Prob. 42HPCh. 2.2 - Prob. 43HPCh. 2.2 - Prob. 44HPCh. 2.2 - Prob. 45STPCh. 2.2 - Prob. 46STPCh. 2.2 - Prob. 47STPCh. 2.2 - Prob. 48STPCh. 2.2 - Prob. 49SRCh. 2.2 - Prob. 50SRCh. 2.2 - Prob. 51SRCh. 2.2 - Prob. 52SRCh. 2.2 - Prob. 53SRCh. 2.2 - Prob. 54SRCh. 2.2 - Prob. 55SRCh. 2.2 - Prob. 56SRCh. 2.2 - Prob. 57SRCh. 2.2 - Prob. 58SRCh. 2.2 - Prob. 59SRCh. 2.2 - Prob. 60SRCh. 2.2 - Prob. 61SCh. 2.2 - Prob. 62SCh. 2.2 - Prob. 63SCh. 2.2 - Prob. 64SCh. 2.3 - Prob. 1AGPCh. 2.3 - Prob. 1BGPCh. 2.3 - Prob. 2AGPCh. 2.3 - Prob. 2BGPCh. 2.3 - Prob. 3GPCh. 2.3 - Prob. 4AGPCh. 2.3 - Prob. 4BGPCh. 2.3 - Prob. 1CYUCh. 2.3 - Prob. 2CYUCh. 2.3 - Prob. 3CYUCh. 2.3 - Prob. 4CYUCh. 2.3 - Prob. 5CYUCh. 2.3 - Prob. 6CYUCh. 2.3 - Prob. 7CYUCh. 2.3 - Prob. 8CYUCh. 2.3 - Prob. 9CYUCh. 2.3 - Prob. 10CYUCh. 2.3 - Prob. 11CYUCh. 2.3 - Prob. 12CYUCh. 2.3 - Prob. 13PPSCh. 2.3 - Prob. 14PPSCh. 2.3 - Prob. 15PPSCh. 2.3 - Prob. 16PPSCh. 2.3 - Prob. 17PPSCh. 2.3 - Prob. 18PPSCh. 2.3 - Prob. 19PPSCh. 2.3 - Prob. 20PPSCh. 2.3 - Prob. 21PPSCh. 2.3 - Prob. 22PPSCh. 2.3 - Prob. 23PPSCh. 2.3 - Prob. 24PPSCh. 2.3 - Prob. 25PPSCh. 2.3 - Prob. 26PPSCh. 2.3 - Prob. 27PPSCh. 2.3 - Prob. 28PPSCh. 2.3 - Prob. 29PPSCh. 2.3 - Prob. 30PPSCh. 2.3 - Prob. 31PPSCh. 2.3 - Prob. 32PPSCh. 2.3 - Prob. 33PPSCh. 2.3 - Prob. 34PPSCh. 2.3 - Prob. 35PPSCh. 2.3 - Prob. 36PPSCh. 2.3 - Prob. 37PPSCh. 2.3 - Prob. 38PPSCh. 2.3 - Prob. 39PPSCh. 2.3 - Prob. 40PPSCh. 2.3 - Prob. 41HPCh. 2.3 - Prob. 42HPCh. 2.3 - Prob. 43HPCh. 2.3 - Prob. 44HPCh. 2.3 - Prob. 45STPCh. 2.3 - Prob. 46STPCh. 2.3 - Prob. 47STPCh. 2.3 - Prob. 48STPCh. 2.3 - Prob. 49SRCh. 2.3 - Prob. 50SRCh. 2.3 - Prob. 51SRCh. 2.3 - Prob. 52SRCh. 2.3 - Prob. 53SRCh. 2.3 - Prob. 54SRCh. 2.3 - Prob. 55SRCh. 2.3 - Prob. 56SRCh. 2.3 - Prob. 57SRCh. 2.3 - Prob. 58SCh. 2.3 - Prob. 59SCh. 2.3 - Prob. 60SCh. 2.3 - Prob. 61SCh. 2.4 - Prob. 1AGPCh. 2.4 - Prob. 1BGPCh. 2.4 - Prob. 2AGPCh. 2.4 - Prob. 2BGPCh. 2.4 - Prob. 3GPCh. 2.4 - Prob. A4GPCh. 2.4 - Prob. 4BGPCh. 2.4 - Prob. 5AGPCh. 2.4 - Prob. 5BGPCh. 2.4 - Prob. 6AGPCh. 2.4 - Prob. 6BGPCh. 2.4 - Prob. 1CYUCh. 2.4 - Prob. 2CYUCh. 2.4 - Prob. 3CYUCh. 2.4 - Prob. 4CYUCh. 2.4 - Prob. 5CYUCh. 2.4 - Prob. 6CYUCh. 2.4 - Prob. 7CYUCh. 2.4 - Prob. 8CYUCh. 2.4 - Prob. 9CYUCh. 2.4 - Prob. 10CYUCh. 2.4 - Prob. 11PPSCh. 2.4 - Prob. 12PPSCh. 2.4 - Prob. 13PPSCh. 2.4 - Prob. 14PPSCh. 2.4 - Prob. 15PPSCh. 2.4 - Prob. 16PPSCh. 2.4 - Prob. 17PPSCh. 2.4 - Prob. 18PPSCh. 2.4 - Prob. 19PPSCh. 2.4 - Prob. 20PPSCh. 2.4 - Prob. 21PPSCh. 2.4 - Prob. 22PPSCh. 2.4 - Prob. 23PPSCh. 2.4 - Prob. 24PPSCh. 2.4 - Prob. 25PPSCh. 2.4 - Prob. 26PPSCh. 2.4 - Prob. 27PPSCh. 2.4 - Prob. 28PPSCh. 2.4 - Prob. 29PPSCh. 2.4 - Prob. 30PPSCh. 2.4 - Prob. 31PPSCh. 2.4 - Prob. 32PPSCh. 2.4 - Prob. 33PPSCh. 2.4 - Prob. 34PPSCh. 2.4 - Prob. 35PPSCh. 2.4 - Prob. 36PPSCh. 2.4 - Prob. 37PPSCh. 2.4 - Prob. 38PPSCh. 2.4 - Prob. 39PPSCh. 2.4 - Prob. 40PPSCh. 2.4 - Prob. 41PPSCh. 2.4 - Prob. 42PPSCh. 2.4 - Prob. 43HPCh. 2.4 - Prob. 44HPCh. 2.4 - Prob. 45HPCh. 2.4 - Prob. 46HPCh. 2.4 - Prob. 47HPCh. 2.4 - Prob. 48HPCh. 2.4 - Prob. 49HPCh. 2.4 - Prob. 50STPCh. 2.4 - Prob. 51STPCh. 2.4 - Prob. 52STPCh. 2.4 - Prob. 53STPCh. 2.4 - Prob. 54SRCh. 2.4 - Prob. 55SRCh. 2.4 - Prob. 56SRCh. 2.4 - Prob. 57SRCh. 2.4 - Prob. 58SRCh. 2.4 - Prob. 59SRCh. 2.4 - Prob. 60SCh. 2.4 - Prob. 61SCh. 2.4 - Prob. 62SCh. 2.4 - Prob. 63SCh. 2.5 - Prob. 1AGPCh. 2.5 - Prob. 1BGPCh. 2.5 - Prob. 2AGPCh. 2.5 - Prob. 2BGPCh. 2.5 - Prob. 3AGPCh. 2.5 - Prob. 3BGPCh. 2.5 - Prob. 4GPCh. 2.5 - Prob. 1CYUCh. 2.5 - Prob. 2CYUCh. 2.5 - Prob. 3CYUCh. 2.5 - Prob. 4CYUCh. 2.5 - Prob. 5CYUCh. 2.5 - Prob. 6CYUCh. 2.5 - Prob. 7CYUCh. 2.5 - Prob. 8CYUCh. 2.5 - Prob. 9CYUCh. 2.5 - Prob. 10CYUCh. 2.5 - Prob. 11CYUCh. 2.5 - Prob. 12CYUCh. 2.5 - Prob. 13PPSCh. 2.5 - Prob. 14PPSCh. 2.5 - Prob. 15PPSCh. 2.5 - Prob. 16PPSCh. 2.5 - Prob. 17PPSCh. 2.5 - Prob. 18PPSCh. 2.5 - Prob. 19PPSCh. 2.5 - Prob. 20PPSCh. 2.5 - Prob. 21PPSCh. 2.5 - Prob. 22PPSCh. 2.5 - Prob. 23PPSCh. 2.5 - Prob. 24PPSCh. 2.5 - Prob. 25PPSCh. 2.5 - Prob. 26PPSCh. 2.5 - Prob. 27PPSCh. 2.5 - Prob. 28PPSCh. 2.5 - Prob. 29PPSCh. 2.5 - Prob. 30PPSCh. 2.5 - Prob. 31PPSCh. 2.5 - Prob. 32PPSCh. 2.5 - Prob. 33PPSCh. 2.5 - Prob. 34PPSCh. 2.5 - Prob. 35PPSCh. 2.5 - Prob. 36PPSCh. 2.5 - Prob. 37PPSCh. 2.5 - Prob. 38PPSCh. 2.5 - Prob. 39PPSCh. 2.5 - Prob. 40PPSCh. 2.5 - Prob. 41PPSCh. 2.5 - Prob. 42PPSCh. 2.5 - Prob. 43PPSCh. 2.5 - Prob. 44PPSCh. 2.5 - Prob. 45PPSCh. 2.5 - Prob. 46PPSCh. 2.5 - Prob. 47PPSCh. 2.5 - Prob. 48PPSCh. 2.5 - Prob. 49HPCh. 2.5 - Prob. 50HPCh. 2.5 - Prob. 51HPCh. 2.5 - Prob. 52HPCh. 2.5 - Prob. 53HPCh. 2.5 - Prob. 54STPCh. 2.5 - Prob. 55STPCh. 2.5 - Prob. 56STPCh. 2.5 - Prob. 57STPCh. 2.5 - Prob. 58SRCh. 2.5 - Prob. 59SRCh. 2.5 - Prob. 60SRCh. 2.5 - Prob. 61SRCh. 2.5 - Prob. 62SRCh. 2.5 - Prob. 63SRCh. 2.5 - Prob. 64SRCh. 2.5 - Prob. 65SRCh. 2.5 - Prob. 66SCh. 2.5 - Prob. 67SCh. 2.5 - Prob. 68SCh. 2.5 - Prob. 69SCh. 2.6 - Prob. 1AGPCh. 2.6 - Prob. 1BGPCh. 2.6 - Prob. 2AGPCh. 2.6 - Prob. 2BGPCh. 2.6 - Prob. 2CGPCh. 2.6 - Prob. 3GPCh. 2.6 - Prob. 1CYUCh. 2.6 - Prob. 2CYUCh. 2.6 - Prob. 3CYUCh. 2.6 - Prob. 4CYUCh. 2.6 - Prob. 5CYUCh. 2.6 - Prob. 6CYUCh. 2.6 - Prob. 7CYUCh. 2.6 - Prob. 8CYUCh. 2.6 - Prob. 9CYUCh. 2.6 - Prob. 10PPSCh. 2.6 - Prob. 11PPSCh. 2.6 - Prob. 12PPSCh. 2.6 - Prob. 13PPSCh. 2.6 - Prob. 14PPSCh. 2.6 - Prob. 15PPSCh. 2.6 - Prob. 16PPSCh. 2.6 - Prob. 17PPSCh. 2.6 - Prob. 18PPSCh. 2.6 - Prob. 19PPSCh. 2.6 - Prob. 20PPSCh. 2.6 - Prob. 21PPSCh. 2.6 - Prob. 22PPSCh. 2.6 - Prob. 23PPSCh. 2.6 - Prob. 24PPSCh. 2.6 - Prob. 25PPSCh. 2.6 - Prob. 26PPSCh. 2.6 - Prob. 27PPSCh. 2.6 - Prob. 28PPSCh. 2.6 - Prob. 29PPSCh. 2.6 - Prob. 30PPSCh. 2.6 - Prob. 31PPSCh. 2.6 - Prob. 32PPSCh. 2.6 - Prob. 33PPSCh. 2.6 - Prob. 34PPSCh. 2.6 - Prob. 35PPSCh. 2.6 - Prob. 36PPSCh. 2.6 - Prob. 37PPSCh. 2.6 - Prob. 38PPSCh. 2.6 - Prob. 39PPSCh. 2.6 - Prob. 40PPSCh. 2.6 - Prob. 41PPSCh. 2.6 - Prob. 42PPSCh. 2.6 - Prob. 43PPSCh. 2.6 - Prob. 44PPSCh. 2.6 - Prob. 45PPSCh. 2.6 - Prob. 46PPSCh. 2.6 - Prob. 47HPCh. 2.6 - Prob. 48HPCh. 2.6 - Prob. 49HPCh. 2.6 - Prob. 50HPCh. 2.6 - Prob. 51STPCh. 2.6 - Prob. 52STPCh. 2.6 - Prob. 53STPCh. 2.6 - Prob. 54STPCh. 2.6 - Prob. 55SRCh. 2.6 - Prob. 56SRCh. 2.6 - Prob. 57SRCh. 2.6 - Prob. 58SRCh. 2.6 - Prob. 59SRCh. 2.6 - Prob. 60SRCh. 2.6 - Prob. 61SRCh. 2.6 - Prob. 62SRCh. 2.6 - Prob. 63SCh. 2.6 - Prob. 64SCh. 2.6 - Prob. 65SCh. 2.6 - Prob. 66SCh. 2.6 - Prob. 67SCh. 2.6 - Prob. 68SCh. 2.7 - Prob. 1GPCh. 2.7 - Prob. 2AGPCh. 2.7 - Prob. 2BGPCh. 2.7 - Prob. 1CYUCh. 2.7 - Prob. 2CYUCh. 2.7 - Prob. 3PPSCh. 2.7 - Prob. 4PPSCh. 2.7 - Prob. 5PPSCh. 2.7 - Prob. 6PPSCh. 2.7 - Prob. 7PPSCh. 2.7 - Prob. 8PPSCh. 2.7 - Prob. 9PPSCh. 2.7 - Prob. 10PPSCh. 2.7 - Prob. 11PPSCh. 2.7 - Prob. 12PPSCh. 2.7 - Prob. 13PPSCh. 2.7 - Prob. 14PPSCh. 2.7 - Prob. 15PPSCh. 2.7 - Prob. 16PPSCh. 2.7 - Prob. 17PPSCh. 2.7 - Prob. 18HPCh. 2.7 - Prob. 19HPCh. 2.7 - Prob. 20HPCh. 2.7 - Prob. 21HPCh. 2.7 - Prob. 22HPCh. 2.7 - Prob. 23STPCh. 2.7 - Prob. 24STPCh. 2.7 - Prob. 25STPCh. 2.7 - Prob. 26STPCh. 2.7 - Prob. 27SRCh. 2.7 - Prob. 28SRCh. 2.7 - Prob. 29SRCh. 2.7 - Prob. 30SRCh. 2.7 - Prob. 31SRCh. 2.7 - Prob. 32SRCh. 2.7 - Prob. 33SRCh. 2.7 - Prob. 34SCh. 2.7 - Prob. 35SCh. 2.7 - Prob. 36SCh. 2.7 - Prob. 37SCh. 2 - Prob. 1QCCh. 2 - Prob. 2QCCh. 2 - Prob. 3QCCh. 2 - Prob. 4QCCh. 2 - Prob. 5QCCh. 2 - Prob. 6QCCh. 2 - Prob. 7QCCh. 2 - Prob. 8QCCh. 2 - Prob. 9QCCh. 2 - Prob. 10QCCh. 2 - Prob. 11QCCh. 2 - Prob. 12QCCh. 2 - Prob. 13QCCh. 2 - Prob. 14QCCh. 2 - Prob. 15QCCh. 2 - Prob. 16QCCh. 2 - Prob. 1MCQCh. 2 - Prob. 2MCQCh. 2 - Prob. 3MCQCh. 2 - Prob. 4MCQCh. 2 - Prob. 5MCQCh. 2 - Prob. 6MCQCh. 2 - Prob. 7MCQCh. 2 - Prob. 8MCQCh. 2 - Prob. 9MCQCh. 2 - Prob. 10MCQCh. 2 - Prob. 11MCQCh. 2 - Prob. 12MCQCh. 2 - Prob. 13MCQCh. 2 - Prob. 14MCQCh. 2 - Prob. 15MCQCh. 2 - Prob. 16MCQCh. 2 - Prob. 17MCQCh. 2 - Prob. 18MCQCh. 2 - Prob. 19MCQCh. 2 - Prob. 20MCQCh. 2 - Prob. 21MCQCh. 2 - Prob. 22MCQCh. 2 - Prob. 23MCQCh. 2 - Prob. 24MCQCh. 2 - Prob. 25MCQCh. 2 - Prob. 1SGRCh. 2 - Prob. 2SGRCh. 2 - Prob. 3SGRCh. 2 - Prob. 4SGRCh. 2 - Prob. 5SGRCh. 2 - Prob. 6SGRCh. 2 - Prob. 7SGRCh. 2 - Prob. 8SGRCh. 2 - Prob. 9SGRCh. 2 - Prob. 10SGRCh. 2 - Prob. 11SGRCh. 2 - Prob. 12SGRCh. 2 - Prob. 13SGRCh. 2 - Prob. 14SGRCh. 2 - Prob. 15SGRCh. 2 - Prob. 16SGRCh. 2 - Prob. 17SGRCh. 2 - Prob. 18SGRCh. 2 - Prob. 19SGRCh. 2 - Prob. 20SGRCh. 2 - Prob. 21SGRCh. 2 - Prob. 22SGRCh. 2 - Prob. 23SGRCh. 2 - Prob. 24SGRCh. 2 - Prob. 25SGRCh. 2 - Prob. 26SGRCh. 2 - Prob. 27SGRCh. 2 - Prob. 28SGRCh. 2 - Prob. 29SGRCh. 2 - Prob. 30SGRCh. 2 - Prob. 31SGRCh. 2 - Prob. 32SGRCh. 2 - Prob. 33SGRCh. 2 - Prob. 34SGRCh. 2 - Prob. 35SGRCh. 2 - Prob. 36SGRCh. 2 - Prob. 37SGRCh. 2 - Prob. 38SGRCh. 2 - Prob. 39SGRCh. 2 - Prob. 40SGRCh. 2 - Prob. 41SGRCh. 2 - Prob. 42SGRCh. 2 - Prob. 43SGRCh. 2 - Prob. 44SGRCh. 2 - Prob. 45SGRCh. 2 - Prob. 46SGRCh. 2 - Prob. 47SGRCh. 2 - Prob. 48SGRCh. 2 - Prob. 49SGRCh. 2 - Prob. 50SGRCh. 2 - Prob. 51SGRCh. 2 - Prob. 52SGRCh. 2 - Prob. 53SGRCh. 2 - Prob. 54SGRCh. 2 - Prob. 55SGRCh. 2 - Prob. 56SGRCh. 2 - Prob. 57SGRCh. 2 - Prob. 58SGRCh. 2 - Prob. 59SGRCh. 2 - Prob. 60SGRCh. 2 - Prob. 61SGRCh. 2 - Prob. 1PTCh. 2 - Prob. 2PTCh. 2 - Prob. 3PTCh. 2 - Prob. 4PTCh. 2 - Prob. 5PTCh. 2 - Prob. 6PTCh. 2 - Prob. 7PTCh. 2 - Prob. 8PTCh. 2 - Prob. 9PTCh. 2 - Prob. 10PTCh. 2 - Prob. 11PTCh. 2 - Prob. 12PTCh. 2 - Prob. 13PTCh. 2 - Prob. 14PTCh. 2 - Prob. 15PTCh. 2 - Prob. 16PTCh. 2 - Prob. 17PTCh. 2 - Prob. 18PTCh. 2 - Prob. 19PTCh. 2 - Prob. 20PTCh. 2 - Prob. 21PTCh. 2 - Prob. 22PTCh. 2 - Prob. 23PTCh. 2 - Prob. 24PTCh. 2 - Prob. 25PTCh. 2 - Prob. 26PTCh. 2 - Prob. 27PTCh. 2 - Prob. 28PTCh. 2 - Prob. 29PTCh. 2 - Prob. 30PTCh. 2 - Prob. 31PTCh. 2 - Prob. 32PTCh. 2 - Prob. 33PTCh. 2 - Prob. 1ECh. 2 - Prob. 2ECh. 2 - Prob. 3ECh. 2 - Prob. 4ECh. 2 - Prob. 5ECh. 2 - Prob. 1STPCh. 2 - Prob. 2STPCh. 2 - Prob. 3STPCh. 2 - Prob. 4STPCh. 2 - Prob. 5STPCh. 2 - Prob. 6STPCh. 2 - Prob. 7STPCh. 2 - Prob. 8STPCh. 2 - Prob. 9STPCh. 2 - Prob. 10STPCh. 2 - Prob. 11STPCh. 2 - Prob. 12STPCh. 2 - Prob. 13STPCh. 2 - Prob. 14STP

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