Math Quiz -Algebra Report a question What's wrong with this question? You cannot submit an empty report. Please add some details. Math Quiz -Algebra Covering: linear equations, inequalities, systems of equations, absolute value expressions, and quadratic equations. 1 / 5 1. If f(x) = 2x² - 6x + 5, find the value of f(3). a) 5 b) 3 c) -2 To find the value of f(3), substitute x = 3 into the function f(x): f(3) = 2(3)² - 6(3) + 5 f(3) = 2(9) - 18 + 5 f(3) = 18 - 18 + 5 f(3) = 0 + 5 f(3) = 5 Thus, the value of f(3) is 5, which corresponds to option A. 2 / 5 2. Solve the following exponential equation: 5^(2x - 3) = 25 a) x = 1 b) x = 2 c) x = 5/2 d) x = 3 To solve the exponential equation 5^(2x - 3) = 25, we can rewrite 25 as a power of 5 (since 25 = 5²): 5^(2x - 3) = 5^2 Now we can equate the exponents: 2x - 3 = 2 Add 3 to both sides: 2x = 5 Divide by 2: x = 5/2 Thus, the solution to the exponential equation 5^(2x - 3) = 25 is x = 5/2, which corresponds to option C. 3 / 5 3. Using the quadratic formula, determine if the quadratic equation 2x² + 2x - 1 = 0 has real, imaginary, or no solutions. a) Two real solutions b) Two imaginary solutions c) One real solution d) No solutions The discriminant (∆) in the quadratic formula helps us determine the nature of the solutions for a quadratic equation ax² + bx + c = 0: ∆ = b² - 4ac If ∆ > 0, there are two real solutions. If ∆ = 0, there is exactly one real solution. If ∆ < 0, there are two imaginary (complex) solutions. For the given quadratic equation, we have: a = 2, b = 2, and c = -1 Now calculate the discriminant: ∆ = (2)² - 4(2)(-1) ∆ = 4 + 8 ∆ = 12 Since ∆ > 0, the quadratic equation has two real solutions, which corresponds to option A. 4 / 5 4. What is the domain of the function f(x) = sqrt(4 - x²)? a) -2 ≤ x ≤ 2 b) -4 ≤ x ≤ 4 c) 2 ≤ x ≤ 4 d) 0 ≤ x ≤ 4 To find the domain of the function f(x) = sqrt(4 - x²), we must find all possible values of x for which the function is defined. In other words, we need to ensure the argument of the square root (4 - x²) is greater than or equal to 0: 4 - x² >= 0 x² <= 4 Taking the square root of both sides: |x| <= 2 Thus, the domain of the function f(x) = sqrt(4 - x²) consists of all values of x between -2 and 2, inclusive, which corresponds to option A. 5 / 5 5. What is the solution to the rational equation (x - 2)/(x + 3) = (3 - x)/(4 - x)? a) x = 2/3 b) x = 6/17 c) x = 17/6 d) x = 3/2 To solve the rational equation (x - 2)/(x + 3) = (3 - x)/(4 - x), we can cross-multiply to eliminate the fractions: (x - 2)(4 - x) = (x + 3)(3 - x) Expand both sides: 4x - x² - 8 + 2x = 3x - x² + 9 - 3x Combine like terms: 6x - x² - 8 = -x² + 9 Add x² to both sides: 6x - 8 = 9 Add 8 and subtract 9 from both sides: 6x = 17 Divide by 6: x = 17/6 Thus, the solution to the rational equation is x = 17/6, which corresponds to option C. Your score is 0% Restart Quiz