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. Find the x-intercept of the linear equation 2x - 4y = 12. a) x = -6 b) x = 3 c) x = 6 d) x = 9 To find the x-intercept of the linear equation 2x - 4y = 12, set y = 0 and solve for x: 2x - 4(0) = 12 2x = 12 x = 6 Thus, the x-intercept is x = 6, which corresponds to option C. 2 / 5 2. 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. 3 / 5 3. Solve the following inequality for x: 5 - 3x < 8. a) x < -1 b) x > -1 c) x < 1 d) x > 1 To solve the inequality 5 - 3x < 8, we will isolate the variable x: Step 1: Subtract 5 from both sides of the inequality -3x < 3 Step 2: Divide by -3 (and reverse the inequality direction since we're dividing by a negative number) x > -1 Thus, the inequality 5 - 3x < 8 is true for all values of x greater than -1, which corresponds to option B. 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 is the solution to the absolute value equation |3x - 4| = 8? a) x = -8, x = 4 b) x = 2, x = 4 c) x = 4, x = 8 d) x = 4, x = -4/3 To solve the absolute value equation |3x - 4| = 8, we need to split the equation into two separate equations: 3x - 4 = 8 and 3x - 4 = -8 For the first equation, add 4 to both sides: 3x = 12 Divide by 3: x = 4 For the second equation, add 4 to both sides: 3x = -4 Divide by 3: x = -4/3 Thus, the solution to the absolute value equation |3x - 4| = 8 is x = 4 and x = -4/3, which corresponds to option D. Your score is 0% Restart Quiz