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Untitled Quiz

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@HandsomeVariable

Questions and Answers

What does 4q represent?

Four times q

What does 15+r represent?

Fifteen plus r

What does 2a+6 represent?

Two times a plus six

What does 5 times a number mean?

<p>5x</p> Signup and view all the answers

What does 18 decreased by 3 times d represent?

<p>18-3d</p> Signup and view all the answers

What does Three times a number plus 16 represent?

<p>3x+16</p> Signup and view all the answers

What is the result of 35-3×8?

<p>11</p> Signup and view all the answers

What is the result of 29-3(9-4)?

<p>14</p> Signup and view all the answers

What is the result of 18/9+2×6?

<p>14</p> Signup and view all the answers

What is the result of (4+5)6?

<p>54</p> Signup and view all the answers

What is the result of 7(2+1)?

<p>21</p> Signup and view all the answers

What is the result of (9-4)19?

<p>95</p> Signup and view all the answers

What does 2(x+4) represent?

<p>2x+8</p> Signup and view all the answers

What does (4-3m)8 represent?

<p>32-24m</p> Signup and view all the answers

What does -3(2x-6) represent?

<p>-6x+18</p> Signup and view all the answers

What is the commutative property of addition?

<p>A+b=b+a</p> Signup and view all the answers

What is the commutative property of multiplication?

<p>A×b=b×a</p> Signup and view all the answers

What is the associative property of addition?

<p>A+(b+c)=(a+b)+c</p> Signup and view all the answers

What is the associative property of multiplication?

<p>A×(b×c)=(a×b)×c</p> Signup and view all the answers

What is the distributive property?

<p>A×(b+c)=a×b+a×c</p> Signup and view all the answers

What is the additive identity property?

<p>a+0=a</p> Signup and view all the answers

What is the multiplicative identity property?

<p>a×1=a</p> Signup and view all the answers

What is the additive inverse property?

<p>a+(-a)=0</p> Signup and view all the answers

What is the multiplicative inverse property?

<p>a×(1/a)=1</p> Signup and view all the answers

What is the zero property?

<p>a×0=0</p> Signup and view all the answers

What is the reflexive property?

<p>4+7=7+4</p> Signup and view all the answers

What is the symmetric property?

<p>if 8=2+6, then 2+6=8</p> Signup and view all the answers

What is the transitive property?

<p>if 6+9=3+12, and 3+12=15, then 6+9=15</p> Signup and view all the answers

What is the substitution property?

<p>if n=11, then 4n=4-11</p> Signup and view all the answers

What are some meanings of addition?

<p>More than</p> Signup and view all the answers

What are some meanings of subtraction?

<p>Difference</p> Signup and view all the answers

What are some meanings of multiplication?

<p>Product of</p> Signup and view all the answers

What are some meanings of division?

<p>Quotient of</p> Signup and view all the answers

What does PEMDAS stand for?

<p>Parenthesis, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)</p> Signup and view all the answers

What are expressions?

<p>No equal sign; will tell you to simplify</p> Signup and view all the answers

What are equations?

<p>Have an equal sign; will tell you to solve</p> Signup and view all the answers

What is the result of N(3+2)+6=5n+(10-3)?

<p>No solution</p> Signup and view all the answers

What is identity in an equation?

<p>An equation that is true for any number</p> Signup and view all the answers

What is the result of (2 5-8)(3h+6)=[(2h+h)+6]2?

<p>Identity</p> Signup and view all the answers

What is the domain in a relation?

<p>The set of the first numbers of the ordered pairs in a relation (same as input, x, independent variable)</p> Signup and view all the answers

What is a relation in mathematics?

<p>A set of ordered pairs</p> Signup and view all the answers

What is the independent variable?

<p>The variable in a function with a value that is subject to choice</p> Signup and view all the answers

What is the range in a relation?

<p>The set of second numbers of the ordered pairs in a relation (same as output, y, dependent)</p> Signup and view all the answers

What is the dependent variable?

<p>The variable in a relation with a value that depends on the value of the independent variable</p> Signup and view all the answers

Study Notes

Algebraic Expressions

  • Expressions such as 4q, 15+r, and 2a+6 represent combinations of variables and constants, indicating operations like multiplication and addition.
  • 5 times a number can be expressed as 5x, where x represents the number.
  • More complex expressions include 18 decreased by 3 times d which can be written as 18-3d, and Three times a number plus 16, expressed as 3x+16.

Evaluating Numerical Expressions

  • Simple calculations: 35-3×8 evaluates to 11, and 29-3(9-4) resolves to 14.
  • Operations involving fractions and multiplication yield results such as 18/9+2×6 which also equals 14.
  • The expression (4+5)6 simplifies to 54, while 7(2+1) computes to 21.

Properties of Operations

  • Commutative Properties:
    • Addition: (A + b = b + a)
    • Multiplication: (A \times b = b \times a)
  • Associative Properties:
    • Addition: (A + (B + C) = (A + B) + C)
    • Multiplication: (A \times (B \times C) = (A \times B) \times C)
  • Distributive Property: Allows distribution over addition: (A \times (B + C) = A \times B + A \times C).

Identity and Inverse Properties

  • Additive Identity: For any a, (a + 0 = a).
  • Multiplicative Identity: For any a, (a \times 1 = a).
  • Additive Inverse: (a + (-a) = 0), implying for every number, there’s a corresponding negative that sums to zero.
  • Multiplicative Inverse: For non-zero a, (a \times (1/a) = 1).
  • Zero Property: (a \times 0 = 0).

Properties of Equality

  • Reflexive Property: (A = A) shows equality with itself.
  • Symmetric Property: If (A = B), then (B = A).
  • Transitive Property: If (A = B) and (B = C), then (A = C).

Algebra Basics

  • Expressions: Non-equation forms that imply simplification without an equal sign.
  • Equations: Mathematical statements that equate two expressions, directing to solve for the unknowns.

Further Algebra Concepts

  • No Solution and Identities: Equations like (N(3+2)+6=5n+(10-3)) yield no solution, whereas consistent terms define identities.
  • Domain: Refers to the values of the independent variable, the first numbers in ordered pairs of a relation.
  • Range: Represents the dependent variable outputs, being the second numbers in ordered pairs.
  • Independent Variable: The variable chosen freely in a function.
  • Dependent Variable: Its value is contingent upon the independent variable.

Calculating with PEMDAS

  • The acronym PEMDAS stands for:
    • Parentheses
    • Exponents
    • Multiplication and Division (from left to right)
    • Addition and Subtraction (from left to right)

These rules govern the order of operations in simplifying expressions and solving equations.

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