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 a > 0 and b < 0, and a > b then which of the following must be true? a) a + b > 0 b) ab > 0 c) a/b > 0 d) a -b > 0 and ab > 0 a) a + b > 0 Since a > 0 and b < 0, adding them together will always result in a positive number. So, a + b > 0 is always true. b) ab > 0 Since a > 0 and b < 0, the product ab will always be negative. So, ab > 0 is not necessarily true. c) a/b > 0 Since a > 0 and b < 0, the quotient a/b will always be negative. So, a/b > 0 is not necessarily true. d) a + b > 0 and ab > 0 From the analysis above, a + b > 0 is true, but ab > 0 is not necessarily true. Therefore, the only statement that must be true based on the given conditions is: a) a + b > 0 2 / 5 2. If f(x) = 5x² - 3x + 1 and g(x) = 2x² + x - 3, what is f(x) - g(x)? a) 3x² - 4x + 4 b) 3x² + x + 2 c) 3x² + 4x + 4 d) 7x² - 2x + 4 To find the difference f(x) - g(x), we need to subtract the corresponding terms of f(x) and g(x): f(x) - g(x) = (5x² - 3x + 1) - (2x² + x - 3) Subtract g(x) from f(x): 3x² - 4x + 4 Thus, f(x) - g(x) = 3x² - 4x + 4, which corresponds to option A. 3 / 5 3. Solve the following absolute value equation: |3x - 1| = 8. a) x = 3, x = 7/3 b) x = -3, x = -7/3 c) x = 3, x = -7/3 d) x = -3, x = 7/3 To solve the absolute value equation |3x - 1| = 8, we need to split the equation into two separate equations: 3x - 1 = 8 and 3x - 1 = -8 For the first equation, add 1 to both sides: -3x = -9 Divide by 3: x = -3 For the second equation, add 1 to both sides: 3x = -7 Divide by 3: x = -7/3 Thus, the solution to the absolute value equation |3x - 1| = 8 is x = 3 and x = -7/3, which corresponds to option C. 4 / 5 4. Solve the following system of linear inequalities: y >= 2x - 1 and y <= x + 3. a) Above y = 2x - 1 and below y = x + 3 b) Above y = 2x - 1 and above y = x + 3 c) Below y = 2x - 1 and below y = x + 3 d) Below y = 2x - 1 and above y = x + 3 To graph the system of linear inequalities y >= 2x - 1 and y <= x + 3, we first look at the equations y = 2x - 1 (option 1) and y = x + 3 (option 2). Then, test points to see which side of the equations satisfies the inequality. The inequality y >= 2x - 1 is true for points above the line y = 2x - 1 and the inequality y <= x + 3 is true for points below the line y = x + 3. Now, we must find the region where both inequalities are true (overlap). This will be the region below the line y = x + 3 and above the line y = 2x - 1. This corresponds to option A. 5 / 5 5. What are the x-intercepts of the quadratic function y = x² + 4x + 3? a) x = 1, x = 3 b) x = -1, x = 3 c) x = 1, x = -3 d) x = -1, x = -3 To find the x-intercepts, we need to set y = 0 and solve for x: 0 = x² + 4x + 3 Now, we can factor the quadratic expression as follows: 0 = (x + 1)(x + 3) We then set each factor equal to zero to solve for x: x + 1 = 0 => x = -1 x + 3 = 0 => x = -3 Thus, the x-intercepts of the quadratic function y = x² + 4x + 3 are x = -1 and x = -3, which corresponds to option D. Your score is 0% Restart Quiz