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<h1>
Overview&#x00A0;&#x000D;of&#x00A0;&#x000D;math&#x00A0;&#x000D;topics&#x00A0;&#x000D;in&#x00A0;&#x000D;examples - EMTeachline mathematics software contents -  algebraic equations  
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This&#x00A0;&#x000D;page&#x00A0;&#x000D;was&#x00A0;&#x000D;created&#x00A0;&#x000D;by&#x00A0;&#x000D; <a href="../../../" target="_parent">EMMentor_algebra_equations</a>
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These pages show a small sample - about 6500 examples - of math problems from EMTeachline mathematics software. Together with demonstration of thematic contents, these examples also demonstrate two functions available in all EMTeachline programs - the function of preparation of variant tests and the function of answer. For each math topic, shown are 80 math tests. Even- and odd-numbered tests are similar, so that pairs 1-2, 3-4, 5-6, ...79-80 represent similar variant tests. All EMTeachline programs  - including very cheap ones - enable you to easily create hundreds of tests like these and generate numerous similar variants; the number of generated variants is indicated in the description of each program. In addition, all programs provide dozens of ready variant tests and solutions to all math problems. At the bottom of this page we offer you to try examples of learning techniques available in the programs EMSolution and EMMentor and see examples of performance/error analysis available in the program EMMentor. 
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<a href="../../../arithmetic_1_/base/28/v0.xml" target="_parent"><b>
1
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2
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<font color="FF9900">
3
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</b>
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<a href="../../../algebra_equations_1_/base/28/v0.xml" target="_parent"><b>
4
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<td width="14" valgin="top" class="tabsheet1">
<a href="../../../algebra_equations_d_1_/base/28/v0.xml" target="_parent"><b>
5
</b></a>
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<td width="14" valgin="top" class="tabsheet1">
<a href="../../../algebra_inequalities_l_1_/base/28/v0.xml" target="_parent"><b>
6
</b></a>
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<td width="14" valgin="top" class="tabsheet1">
<a href="../../../algebra_inequalities_1_/base/28/v0.xml" target="_parent"><b>
7
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<a href="../../../algebra_inequalities_d_1_/base/28/v0.xml" target="_parent"><b>
8
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<a href="../../../trigonometry_1_/base/28/v0.xml" target="_parent"><b>
9
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<a href="../../../trigonometry_equations_l_1_/base/28/v0.xml" target="_parent"><b>
10
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<td width="14" valgin="top" class="tabsheet1">
<a href="../../../trigonometry_equations_1_/base/28/v0.xml" target="_parent"><b>
11
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<a href="../../../trigonometry_equations_d_1_/base/28/v0.xml" target="_parent"><b>
12
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13
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14
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15
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 algebraic equations  
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<b>Test I</b>
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1
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3
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<a href="../../../algebra_equations_l_1_/base/2/v0.xml" target="_parent">
<b>
5
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<a href="../../../algebra_equations_l_1_/base/3/v0.xml" target="_parent">
<b>
7
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<a href="../../../algebra_equations_l_1_/base/4/v0.xml" target="_parent">
<b>
9
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<a href="../../../algebra_equations_l_1_/base/5/v0.xml" target="_parent">
<b>
11
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<a href="../../../algebra_equations_l_1_/base/6/v0.xml" target="_parent">
<b>
13
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<a href="../../../algebra_equations_l_1_/base/7/v0.xml" target="_parent">
<b>
15
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<a href="../../../algebra_equations_l_1_/base/8/v0.xml" target="_parent">
<b>
17
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<a href="../../../algebra_equations_l_1_/base/9/v0.xml" target="_parent">
<b>
19
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<a href="../../../algebra_equations_l_1_/base/10/v0.xml" target="_parent">
<b>
21
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<a href="../../../algebra_equations_l_1_/base/11/v0.xml" target="_parent">
<b>
23
</b>
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<a href="../../../algebra_equations_l_1_/base/12/v0.xml" target="_parent">
<b>
25
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<b>
27
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<a href="../../../algebra_equations_l_1_/base/14/v0.xml" target="_parent">
<b>
29
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<a href="../../../algebra_equations_l_1_/base/15/v0.xml" target="_parent">
<b>
31
</b>
</a>
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<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/16/v0.xml" target="_parent">
<b>
33
</b>
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<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/17/v0.xml" target="_parent">
<b>
35
</b>
</a>
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<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/18/v0.xml" target="_parent">
<b>
37
</b>
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<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/19/v0.xml" target="_parent">
<b>
39
</b>
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<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/20/v0.xml" target="_parent">
<b>
41
</b>
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<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/21/v0.xml" target="_parent">
<b>
43
</b>
</a>
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<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/22/v0.xml" target="_parent">
<b>
45
</b>
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<a href="../../../algebra_equations_l_1_/base/23/v0.xml" target="_parent">
<b>
47
</b>
</a>
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<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/24/v0.xml" target="_parent">
<b>
49
</b>
</a>
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<a href="../../../algebra_equations_l_1_/base/25/v0.xml" target="_parent">
<b>
51
</b>
</a>
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<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/26/v0.xml" target="_parent">
<b>
53
</b>
</a>
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<a href="../../../algebra_equations_l_1_/base/27/v0.xml" target="_parent">
<b>
55
</b>
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<b>57</b>
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<a href="../../../algebra_equations_l_1_/base/29/v0.xml" target="_parent">
<b>
59
</b>
</a>
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<a href="../../../algebra_equations_l_1_/base/30/v0.xml" target="_parent">
<b>
61
</b>
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<a href="../../../algebra_equations_l_1_/base/31/v0.xml" target="_parent">
<b>
63
</b>
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<a href="../../../algebra_equations_l_1_/base/32/v0.xml" target="_parent">
<b>
65
</b>
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<a href="../../../algebra_equations_l_1_/base/33/v0.xml" target="_parent">
<b>
67
</b>
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<a href="../../../algebra_equations_l_1_/base/34/v0.xml" target="_parent">
<b>
69
</b>
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<a href="../../../algebra_equations_l_1_/base/35/v0.xml" target="_parent">
<b>
71
</b>
</a>
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<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/36/v0.xml" target="_parent">
<b>
73
</b>
</a>
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<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/37/v0.xml" target="_parent">
<b>
75
</b>
</a>
</div>
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<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/38/v0.xml" target="_parent">
<b>
77
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/39/v0.xml" target="_parent">
<b>
79
</b>
</a>
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<b>Test II</b>
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<a href="../../../algebra_equations_l_1_/base/0/v1.xml" target="_parent">
<b>
2
</b>
</a>
</div>
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<a href="../../../algebra_equations_l_1_/base/1/v1.xml" target="_parent">
<b>
4
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/2/v1.xml" target="_parent">
<b>
6
</b>
</a>
</div>
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<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/3/v1.xml" target="_parent">
<b>
8
</b>
</a>
</div>
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<a href="../../../algebra_equations_l_1_/base/4/v1.xml" target="_parent">
<b>
10
</b>
</a>
</div>
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<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/5/v1.xml" target="_parent">
<b>
12
</b>
</a>
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<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/6/v1.xml" target="_parent">
<b>
14
</b>
</a>
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<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/7/v1.xml" target="_parent">
<b>
16
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/8/v1.xml" target="_parent">
<b>
18
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/9/v1.xml" target="_parent">
<b>
20
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/10/v1.xml" target="_parent">
<b>
22
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/11/v1.xml" target="_parent">
<b>
24
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/12/v1.xml" target="_parent">
<b>
26
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/13/v1.xml" target="_parent">
<b>
28
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/14/v1.xml" target="_parent">
<b>
30
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/15/v1.xml" target="_parent">
<b>
32
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/16/v1.xml" target="_parent">
<b>
34
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/17/v1.xml" target="_parent">
<b>
36
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/18/v1.xml" target="_parent">
<b>
38
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/19/v1.xml" target="_parent">
<b>
40
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/20/v1.xml" target="_parent">
<b>
42
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/21/v1.xml" target="_parent">
<b>
44
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/22/v1.xml" target="_parent">
<b>
46
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/23/v1.xml" target="_parent">
<b>
48
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/24/v1.xml" target="_parent">
<b>
50
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/25/v1.xml" target="_parent">
<b>
52
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/26/v1.xml" target="_parent">
<b>
54
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/27/v1.xml" target="_parent">
<b>
56
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/28/v1.xml" target="_parent">
<b>
58
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/29/v1.xml" target="_parent">
<b>
60
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/30/v1.xml" target="_parent">
<b>
62
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/31/v1.xml" target="_parent">
<b>
64
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/32/v1.xml" target="_parent">
<b>
66
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/33/v1.xml" target="_parent">
<b>
68
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/34/v1.xml" target="_parent">
<b>
70
</b>
</a>
</div>
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<a href="../../../algebra_equations_l_1_/base/35/v1.xml" target="_parent">
<b>
72
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/36/v1.xml" target="_parent">
<b>
74
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
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<a href="../../../algebra_equations_l_1_/base/37/v1.xml" target="_parent">
<b>
76
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/38/v1.xml" target="_parent">
<b>
78
</b>
</a>
</div>
</td>
<td  valgin="top" class="tabsheet1" width="14">
<div align="center">
<a href="../../../algebra_equations_l_1_/base/39/v1.xml" target="_parent">
<b>
80
</b>
</a>
</div>
</td>
</tr>
</table>
</td>
</tr>
</table>
</td>
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<td>
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</td>
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</table>
<br></br>
<table width="100%">
<tr>
<td width="18">
</td>
<td>
<p><b>
<font color="FF9900">
Test - 57
</font>
</b></p>
<b>1. Solve the equation</b>
<table width="100%">
<tr>
<td>
<a href="v0_0.xml" target="_parent">
<img src="../image/detail5.gif"  border="0" align="absmiddle" alt="detail"></img></a>
</td>
<td width="95%">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mrow>
<mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>119 </mi><msup><mi>r</mi><mi>2</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>7 </mi><mi>r</mi></mrow><mrow><mo>+</mo><mi>3 </mi></mrow></mrow>
<mo>=</mo>
<mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>1 </mi></mrow></mrow>
<mo>-</mo>
<mrow><mo maxsize="2">(</mo><mrow>
<mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>2 </mi></mrow></mrow>
</mrow><mo maxsize="2">)</mo></mrow>
<mo>&#x00B7;</mo>
<mrow><mo maxsize="2">(</mo><mrow>
<mrow><mrow><mi>34 </mi><msup><mi>r</mi><mi>2</mi></msup></mrow><mrow><mo>+</mo><mi>2 </mi><mi>r</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>1 </mi></mrow></mrow>
</mrow><mo maxsize="2">)</mo></mrow>
</mrow>
</mrow>
</math>
</td>
</tr>
</table>
<b>2. Solve the equation</b>
<table width="100%">
<tr>
<td>
<a href="v0_1.xml" target="_parent">
<img src="../image/detail5.gif"  border="0" align="absmiddle" alt="detail"></img></a>
</td>
<td width="95%">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mrow>
<mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>66 </mi><msup><mi>v</mi><mi>2</mi></msup></mrow><mrow><mo>+</mo><mi>36 </mi><mi>v</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>2 </mi></mrow></mrow>
<mo>=</mo>
<mrow><mrow><mi>1 </mi></mrow></mrow>
<mo>+</mo>
<mrow><mo maxsize="2">(</mo><mrow>
<mrow><mrow><mi>1 </mi></mrow></mrow>
</mrow><mo maxsize="2">)</mo></mrow>
<mo>&#x00B7;</mo>
<mrow><mo maxsize="2">(</mo><mrow>
<mrow><mo maxsize="2">(</mo><mrow>
<mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>11 </mi><msup><mi>v</mi><mi>2</mi></msup></mrow><mrow><mo>+</mo><mi>6 </mi><mi>v</mi></mrow></mrow>
</mrow><mo maxsize="2">)</mo></mrow>
<mo>-</mo>
<mrow><mrow><mi>5 </mi></mrow></mrow>
</mrow><mo maxsize="2">)</mo></mrow>
</mrow>
</mrow>
</math>
</td>
</tr>
</table>
<b>3. Solve the equation</b>
<table width="100%">
<tr>
<td>
<a href="v0_2.xml" target="_parent">
<img src="../image/detail5.gif"  border="0" align="absmiddle" alt="detail"></img></a>
</td>
<td width="95%">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mrow>
<mrow><mrow><mi>20 </mi><msup><mi>t</mi><mi>2</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>25 </mi><mi>t</mi></mrow><mrow><mo>+</mo><mi>4 </mi></mrow></mrow>
<mo>=</mo>
<mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>16 </mi><msup><mi>t</mi><mi>2</mi></msup></mrow><mrow><mo>+</mo><mi>20 </mi><mi>t</mi></mrow><mrow><mo>+</mo><mi>3 </mi></mrow></mrow>
</mrow>
</mrow>
</math>
</td>
</tr>
</table>
<b>4. Solve the equation</b>
<table width="100%">
<tr>
<td>
<a href="v0_3.xml" target="_parent">
<img src="../image/detail5.gif"  border="0" align="absmiddle" alt="detail"></img></a>
</td>
<td width="95%">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mrow>
<mrow><mrow><mfrac><mi>8</mi><mi>3</mi></mfrac><msup><mi>y</mi><mi>2</mi></msup></mrow><mrow><mo>+</mo><mi>2 </mi><mi>y</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mfrac><mi>2</mi><mi>3</mi></mfrac></mrow></mrow>
<mo>=</mo>
<mrow><mrow><mfrac><mi>4</mi><mi>7</mi></mfrac></mrow></mrow>
</mrow>
</mrow>
</math>
</td>
</tr>
</table>
<b>5. Solve the equation</b>
<table width="100%">
<tr>
<td>
<a href="v0_4.xml" target="_parent">
<img src="../image/detail5.gif"  border="0" align="absmiddle" alt="detail"></img></a>
</td>
<td width="95%">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mrow>
<mrow><mrow><mo>&#x002D;&#x00A0;</mo><mfrac><mi>5</mi><mi>6</mi></mfrac><msup><mi>z</mi><mi>2</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mfrac><mi>10</mi><mi>3</mi></mfrac><mi>z</mi></mrow><mrow><mo>+</mo><mfrac><mi>5</mi><mi>2</mi></mfrac></mrow></mrow>
<mo>=</mo>
<mrow><mrow><mo>&#x002D;&#x00A0;</mo><mfrac><mi>1</mi><mi>3</mi></mfrac><msup><mi>z</mi><mi>2</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mfrac><mi>4</mi><mi>3</mi></mfrac><mi>z</mi></mrow><mrow><mo>+</mo><mfrac><mi>5</mi><mi>6</mi></mfrac></mrow></mrow>
</mrow>
</mrow>
</math>
</td>
</tr>
</table>
</td>
</tr>
</table>
<br></br>
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<td width="18">
</td>
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