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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.
Select all that justify the statement: 2 * 1/2 = 1.
Select all that justify the statement: 2 * 1/2 = 1.
Select all that justify the statement: 8 * 1/8 + (-1) + 5 = 5.
Select all that justify the statement: 8 * 1/8 + (-1) + 5 = 5.
Select all that justify the statement: 10 + x * 12 = 12x + 10.
Select all that justify the statement: 10 + x * 12 = 12x + 10.
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?
The inverse of a function is a function.
The inverse of a function is a function.
Given that ƒ(x) = x² + 5x, evaluate ƒ(-2).
Given that ƒ(x) = x² + 5x, evaluate ƒ(-2).
Evaluate g(3) if g(x) = 2x + 1.
Evaluate g(3) if g(x) = 2x + 1.
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).
If g(x) = 2x + 1, find g(a + h) - g(a).
If g(x) = 2x + 1, find g(a + h) - g(a).
Simplify the expression in exponential notation: a * a * a.
Simplify the expression in exponential notation: a * a * a.
Simplify the expression in exponential notation: 2 * a * b * a * b.
Simplify the expression in exponential notation: 2 * a * b * a * b.
The expression 3x² represents?
The expression 3x² represents?
(3a)^3 = This expression without exponents is?
(3a)^3 = This expression without exponents is?
(abc)^2 = This expression without exponents is?
(abc)^2 = This expression without exponents is?
Express in simplified exponential notation: x^3 * x^5 = ?
Express in simplified exponential notation: x^3 * x^5 = ?
In simplified exponential notation, the expression a^2 * a^-3 * a = ?
In simplified exponential notation, the expression a^2 * a^-3 * a = ?
Express in simplified exponential notation: 18a^3b^2 / 2ab = ?
Express in simplified exponential notation: 18a^3b^2 / 2ab = ?
Evaluate each expression: 3^-2 = ?
Evaluate each expression: 3^-2 = ?
Simplify: 5(x - 2) + 3x.
Simplify: 5(x - 2) + 3x.
Simplify: 7 - 2(5 - 2x).
Simplify: 7 - 2(5 - 2x).
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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