Math 2 Final Exam Practice Quiz

Subtracting 3 from both sides gives 2x = 4, then dividing by 2 results in x = 2. This straightforward linear equation tests basic algebra skills.

Every triangle, regardless of its shape, has interior angles that add up to 180 degrees. This is a foundational concept in geometry.

A horizontal line has no vertical change, so its slope is 0. This demonstrates the basic definition of slope as 'rise over run.'

x² - 9 is a difference of squares and factors into (x + 3)(x - 3). Recognizing this pattern is key in factoring expressions.

Following the order of operations, multiplication is done before addition: 4 � - 2 equals 8, and then adding 3 results in 11. This question reinforces correct operation sequencing.

The quadratic factors as (x - 2)(x - 3) = 0, which gives the solutions x = 2 and x = 3. Factoring is an essential method for solving quadratic equations.

In the slope-intercept form y = mx + b, the constant b represents the y-intercept. Here, b is 5, so the line crosses the y-axis at 5.

Adding the two equations yields 2x = 6, so x = 3, and substituting back gives y = 2. This elimination method is a standard approach for solving systems of equations.

Substituting x = 3 into the function gives f(3) = 2(3) - 4 = 6 - 4 = 2. This simple evaluation reinforces the concept of functions.

Cross-multiplying gives 4x = 60, leading to x = 15. This problem tests the ability to solve proportions.

Using the power rule (x^a)^b = x^(a*b), we find (x³)² = x^(3� - 2) = x❶. This rule is a crucial part of exponent manipulation.

In the standard circle equation, the radius is the square root of the right-hand side. Since √16 = 4, the radius is 4.

The absolute value equation splits into two cases: x - 3 = 5 and x - 3 = -5, yielding x = 8 and x = -2. This method is standard for solving absolute value equations.

Converting to a common denominator, 2/3 becomes 8/12 and 1/4 becomes 3/12, so the sum is 11/12. This reinforces fraction addition skills.

The mean is calculated by summing the values (3 + 7 + 7 + 10 + 13 = 40) and dividing by the number of values (5), resulting in 8. This question reinforces the concept of averages in statistics.

Using the quadratic formula, x = [3 ± √(9 + 40)] / 4 simplifies to x = [3 ± 7] / 4, giving the solutions x = 2.5 and x = -1. This application of the quadratic formula is vital when factoring is not straightforward.

The discriminant is calculated as b² - 4ac, which here is 12² - 4(4)(9) = 144 - 144 = 0. A discriminant of 0 indicates a single repeated real root.

Isolating one square root and then squaring both sides allows you to eliminate the radicals and solve for x, resulting in x = 19. It is important to check the solution in the original equation to avoid extraneous results.

Let the sides be expressed as a-d, a, and a+d. With a perimeter of 30, a equals 10, and the triangle inequality forces d to be less than 5. Thus, the maximum integer value for d is 4.

Rewriting the inequality as (3 - x)/(x - 1) > 0 and analyzing the sign changes, we determine that the inequality holds true when x is between 1 and 3. It is crucial to consider that x cannot equal 1 because of the denominator.