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Questions and Answers
How many subsets does set A have if the set A has 3 elements?
How many subsets does set A have if the set A has 3 elements?
8
If A = {1, 3, 5} and B = {1, 2, 3, 4, 5, 6} then A ∪ B equals?
If A = {1, 3, 5} and B = {1, 2, 3, 4, 5, 6} then A ∪ B equals?
{1, 2, 3, 4, 5, 6}
Given A = {1, 3, 5}, B = {2, 4, 6}, and C = {1, 2, 3, 4, 5, 6}, then A ∪ (B ∩ C) equals?
Given A = {1, 3, 5}, B = {2, 4, 6}, and C = {1, 2, 3, 4, 5, 6}, then A ∪ (B ∩ C) equals?
{1, 2, 3, 4, 5, 6}
Select all that justify the statement: 3 + (y + 5) = y + 8.
Select all that justify the statement: 3 + (y + 5) = y + 8.
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Select all that justify the statement: 2 * 1/2 = 1.
Select all that justify the statement: 2 * 1/2 = 1.
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Select all that justify the statement: 8 * 1/8 + (-1) + 5 = 5.
Select all that justify the statement: 8 * 1/8 + (-1) + 5 = 5.
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Select all that justify the statement: 10 + x * 12 = 12x + 10.
Select all that justify the statement: 10 + x * 12 = 12x + 10.
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If ƒ = {(5, 1),(6, 2),(7, 3),(8, 1),(9, 7)}, then the range of ƒ is?
If ƒ = {(5, 1),(6, 2),(7, 3),(8, 1),(9, 7)}, then the range of ƒ is?
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The inverse of a function is a function.
The inverse of a function is a function.
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Given that ƒ(x) = x² + 5x, evaluate ƒ(-2).
Given that ƒ(x) = x² + 5x, evaluate ƒ(-2).
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Evaluate g(3) if g(x) = 2x + 1.
Evaluate g(3) if g(x) = 2x + 1.
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If F(x) = x² + 5x and G(x) = 2x + 1, find F(5) + G(6).
If F(x) = x² + 5x and G(x) = 2x + 1, find F(5) + G(6).
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If g(x) = 2x + 1, find g(a + h) - g(a).
If g(x) = 2x + 1, find g(a + h) - g(a).
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Simplify the expression in exponential notation: a * a * a.
Simplify the expression in exponential notation: a * a * a.
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Simplify the expression in exponential notation: 2 * a * b * a * b.
Simplify the expression in exponential notation: 2 * a * b * a * b.
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The expression 3x² represents?
The expression 3x² represents?
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(3a)^3 = This expression without exponents is?
(3a)^3 = This expression without exponents is?
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(abc)^2 = This expression without exponents is?
(abc)^2 = This expression without exponents is?
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Express in simplified exponential notation: x^3 * x^5 = ?
Express in simplified exponential notation: x^3 * x^5 = ?
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In simplified exponential notation, the expression a^2 * a^-3 * a = ?
In simplified exponential notation, the expression a^2 * a^-3 * a = ?
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Express in simplified exponential notation: 18a^3b^2 / 2ab = ?
Express in simplified exponential notation: 18a^3b^2 / 2ab = ?
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Evaluate each expression: 3^-2 = ?
Evaluate each expression: 3^-2 = ?
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Simplify: 5(x - 2) + 3x.
Simplify: 5(x - 2) + 3x.
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Simplify: 7 - 2(5 - 2x).
Simplify: 7 - 2(5 - 2x).
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Simplify: 3(x + 2) + 4(x - 5).
Simplify: 3(x + 2) + 4(x - 5).
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Study Notes
Subsets and Union
- A set with 3 elements has a total of 8 subsets.
- The union of sets A = {1, 3, 5} and B = {1, 2, 3, 4, 5, 6} results in the set {1, 2, 3, 4, 5, 6}.
- For sets A = {1, 3, 5}, B = {2, 4, 6}, and C = {1, 2, 3, 4, 5, 6}, A ∪ (B ∩ C) equals {1, 2, 3, 4, 5, 6}.
Algebraic Justifications
- The equation 3 + (y + 5) = y + 8 is justified by the commutative and associative properties of addition.
- For the equation 2 × 1/2 = 1, the justification lies in the inverse property of multiplication.
- The equation 8 × 1/8 + (-1) + 5 = 5 is supported by the inverse properties of addition and multiplication.
- 10 + x × 12 = 12x + 10 relies on the commutative properties of addition and multiplication.
Functions and Evaluations
- The range of the function f = {(5, 1), (6, 2), (7, 3), (8, 1), (9, 7)} is {1, 2, 3, 7}.
- The inverse of a function can sometimes be a function.
- For f(x) = x² + 5x, evaluating f(-2) yields -6.
- If g(x) = 2x + 1, then g(3) = 7.
- F(5) + G(6) results in 63, where F(x) = x² + 5x and G(x) = 2x + 1.
- Finding g(a + h) - g(a) for g(x) results in 2h.
Exponential Notation
- The expression a × a × a simplifies to a³.
- The expression 2 × a × b × a × b simplifies to 2a²b².
- 3x² represents the product of (3)(x)(x).
- The expression (3a)³ expands to 3aaa.
- (abc)² expands to abcabc or aabbcc.
- The expression x³ × x⁵ simplifies to x⁸.
- The expression a² × a⁻³ × a simplifies to 1.
- The algebraic expression (18a³b²) / (2ab) simplifies to 9a²b.
- Evaluating 3⁻² gives 1/9.
Simplification of Algebraic Expressions
- The expression 5(x - 2) + 3x simplifies to 8x - 10.
- 7 - 2(5 - 2x) simplifies to 4x - 3.
- 3(x + 2) + 4(x - 5) simplifies to 7x - 14.
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Description
Test your understanding of sets, structures, and functions with this algebra quiz. The questions cover topics such as subsets, unions, and equations. Ideal for students looking to reinforce their knowledge in algebraic concepts.
