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The simplified value of
$open parentheses 1 minus fraction numerator 2 xy over denominator straight x squared plus straight y squared end fraction close parentheses space divided by space space open parentheses fraction numerator straight x cubed minus straight y cubed over denominator straight x minus straight y end fraction minus 3 xy close parentheses$ is

$fraction numerator 1 over denominator straight x squared minus straight y squared end fraction$
$fraction numerator 1 over denominator straight x squared plus straight y squared end fraction$
$fraction numerator 1 over denominator straight x minus straight y end fraction$
$fraction numerator 1 over denominator straight x minus straight y end fraction$

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32.
If (2³)² = 4^x, then 3^x is equal to

3

6

9

9

(2³)² = 4x
⟹ (2)⁶ = 2^2x
⟹ 6 = 2x
⟹ x = 3
∴ 3^x = 3³ = 27

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33.

If $square root of 3 space equals space 1.732 comma space$ then the value of $fraction numerator 9 plus 2 square root of 3 over denominator square root of 3 end fraction$ is:

7.169
7.196
5.198
7.296

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34.

The value of $fraction numerator left parenthesis 2.3 right parenthesis cubed space plus space 0.027 over denominator left parenthesis 2.3 right parenthesis squared space minus 0.69 space plus space 0.09 end fraction$ is

2
2.27
2.33
2.6

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35.

$fraction numerator 0.125 plus 0.027 over denominator 0.25 space minus space 0.15 space plus space 0.09 end fraction$ is equal to

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36.

$fraction numerator 256 space cross times space 256 space minus space 144 space cross times space 144 over denominator 112 end fraction$ is equal to

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37.

0.001 is equal to

$1 over 1000$
$1 over 999$
$1 over 99$
$1 over 9$

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38.

$fraction numerator 4.41 space cross times space 0.16 over denominator 2.1 space cross times space 1.6 space cross times space 0.21 end fraction$ is simplified to

1
0.1
0.01
10

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39.

$open parentheses 1 1 half space plus space 11 1 half space plus space 111 1 half space plus space 1111 1 half close parentheses$ is equal to

1236
$1234 1 half$
618
617

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40.

The value of $fraction numerator 2 begin display style 1 third end style minus 1 begin display style 2 over 11 end style over denominator 3 plus begin display style fraction numerator 1 over denominator 3 plus begin display style fraction numerator 1 over denominator 3 plus begin display style 1 third end style end fraction end style end fraction end style end fraction$ is