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This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. The symbols, notations, and properties of numbers that form the basis of algebra, as well as exponents and the rules of exponents, are introduced in this chapter. Each property of real numbers and the rules of exponents are expressed both symbolically and literally. Literal explanations are included because symbolic explanations alone may be difficult for a student to interpret.This module contains the proficiency for the chapter "Basic Properties of Real Numbers".

Proficiency exam

For the following problems, simplify each of the expressions.

( [link] ) 8 ( 6 3 ) 5 4 + 3 ( 8 ) ( 2 ) ÷ 4 3

40

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( [link] ) 1 8 + 4 0 + 3 3 ( 1 + 4 ) 2 2 ( 2 + 15 )

137 68

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( [link] ) 2 3 4 10 2 4 3 + 5 ( 2 2 + 3 2 ) 11 6

75

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( [link] ) Write the appropriate relation symbol ( > , < ) in place of the * .
5 ( 2 + 11 ) 2 ( 8 3 ) 2

>

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For the following problems, use algebraic notation.

( [link] ) ( x 1 ) times ( 3 x plus 2 ) .

( x 1 ) ( 3 x + 2 )

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( [link] ) A number divided by twelve is less than or equal to the same number plus four.

x 12 ( x + 4 )

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( [link] ) Locate the approximate position of 1.6 on the number line.

A real number line with arrow on each end, labeled from negative three to three in increments of one.

A number line with arrows on each end, labeled from negative five to five in increments of one. There is a closed circle at a point between negative two and negative one, labeled as negative one point six.

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( [link] ) Is 0 a positive number, a negative number, neither, or both?

Zero is neither positive nor negative.

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( [link] ) Draw a portion of the number line and place points at all even integers strictly between 14 and 20.

A number line with arrows on each end, labeled from fourteen to twenty in increments of one. There are closed circles at sixteen, and eighteen.

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( [link] ) Draw a portion of the number line and place points at all real numbers strictly greater than 1 but less than or equal to 4.

A number line with arrows on each end, labeled from negative four to five in increments of two. There is a closed circle at four, and an open circle at negative one. These circles are connected by a black line.

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( [link] ) What whole numbers can replace x so that the following statement is true? 4 x 5 .

0 , 1 , 2 , 3 , 4 , 5

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( [link] ) Is there a largest real number between and including 6 and 10? If so, what is it?

yes; 10

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( [link] ) Use the commutative property of multiplication to write m ( a + 3 ) in an equivalent form.

( a + 3 ) m

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( [link] ) Use the commutative properties to simplify 3 a 4 b 8 c d .

96 a b c d

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( [link] ) Use the commutative properties to simplify 4 ( x 9 ) 2 y ( x 9 ) 3 y .

24 y 2 ( x 9 ) 2

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( [link] ) Simplify 4 squared times x cubed times y to the fifth.

16 x 3 y 5

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( [link] ) Simplify ( 3 ) ( 3 ) ( 3 ) a a b b b b a b b a ( 3 ) a .

81 a 5 b 6

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For the following problems, use the rules of exponents to simplify each of the expressions.

( [link] , [link] ) ( 3 a b 2 ) 2 ( 2 a 3 b ) 3

72 a 11 b 7

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( [link] , [link] ) x 10 y 12 x 2 y 5

x 8 y 7

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( [link] , [link] ) 52 x 7 y 10 ( y x 4 ) 12 ( y + x ) 5 4 y 6 ( y x 4 ) 10 ( y + x )

13 x 7 y 4 ( y x 4 ) 2 ( y + x ) 4

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( [link] , [link] ) ( x n y 3 m z 2 p ) 4

x 4 n y 12 m z 8 p

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( 5 x + 4 ) 0 ( 3 x 2 1 ) 0

1

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x x y Δ x Δ y

The product of x to the power 'delta plus square minus triangle' and y to the power 'triangle minus delta'.

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( [link] , [link] ) What word is used to describe the letter or symbol that represents an unspecified member of a particular collection of two or more numbers that are clearly defined?

a variable

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Questions & Answers

Discuss the differences between taste and flavor, including how other sensory inputs contribute to our  perception of flavor.
John Reply
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
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omeprazole
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Not really sure
Eli
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include: 1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
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Anatomy is the identification and description of the structures of living things
Kamara
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Oyerinde Reply
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
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Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
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Prince
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it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
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function of digestive
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37 degrees selcius
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Organ Systems Of The Human Body (Continued) Organ Systems Of The Human Body (Continued)
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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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