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Questions and Answers
Which mathematical operation would correctly solve for $x$ in the equation $2x + 3 = 11$?
What is the greatest common divisor (GCD) of 36 and 60?
In the equation $y = 3x^2 + 2x - 5$, what is the coefficient of $x$?
If $f(x) = 2x + 4$ and $g(x) = x^2$, what is $(f imes g)(2)$?
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Which of these is not a property of equality?
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Study Notes
Solving Equations
- To solve for x in the equation 2x + 3 = 11, you would use subtraction and division.
- First, subtract 3 from both sides to isolate the 2x term.
- Then, divide both sides by 2 to solve for x.
Greatest Common Divisor
- The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder.
- The GCD of 36 and 60 is 12.
Coefficients
- In a polynomial expression, the coefficient is the numerical factor that multiplies a variable.
- In the equation y = 3x² + 2x - 5, the coefficient of x is 2.
Function Composition
- Function composition involves combining two or more functions.
- The notation (f ∘ g)(x) represents the composition of function f with function g.
- To calculate (f ∘ g)(2), first find g(2), which is 2² = 4.
- Then, substitute 4 into the function f(x) to find f(4), which is 2(4) + 4 = 12.
- Therefore, (f ∘ g)(2) is 12.
Properties of Equality
- Properties of equality are rules that allow you to manipulate equations while preserving their truth.
- Some common properties include the reflexive property (a = a), the symmetric property (if a = b, then b = a), and the transitive property (if a = b and b = c, then a = c).
- One property that is NOT a property of equality is the distributive property.
- The distributive property states that a(b + c) = ab + ac, which is a property of multiplication, not equality.
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Description
Test your algebra skills with this quiz covering solving equations, GCD, coefficients, and properties of equality. Answer questions on basic operations and functions to demonstrate your understanding of fundamental algebraic concepts.
