Practice Quiz for Exam Success

Adding 7 and 5 gives 12. Basic addition confirms the result is 12.

Multiplying 8 by 3 gives 24 because 8 added 3 times equals 24. This is standard multiplication.

By subtracting 3 from both sides, x equals 5. This is a simple linear equation.

Dividing 100 by 25 results in 4 because 25 goes into 100 exactly 4 times.

2 is even because it is divisible by 2. The other options are odd numbers.

Add 4 to both sides to get 2x = 14, and then divide by 2 to obtain x = 7. This simple algebraic manipulation confirms the answer.

Distribute 3 over (x + 4) to get 3x + 12, and then subtract 2x to simplify to x + 12. This uses the distributive property effectively.

In the slope-intercept form y = mx + b, the coefficient m represents the slope. Here, m = 2, making the slope 2.

The sum of the interior angles of any triangle is always 180 degrees. This is a fundamental property of triangles.

Multiply both sides by 4 to obtain 3x = 36, then divide by 3, yielding x = 12. This demonstrates the technique for solving equations with fractions.

The quadratic formula provides the solution for quadratic equations and is given by x = (-b ± √(b² - 4ac))/(2a). This formula is derived from completing the square.

First evaluate the inner expression (2 - 3) which equals -1, then subtracting a negative is equivalent to addition, so 5 + 1 = 6. This demonstrates the handling of negative numbers in subtraction.

Plug 4 into the function: f(4) = 3(4) + 2 = 12 + 2 = 14. This is a direct application of function evaluation.

The expression x² - 9 is a difference of squares and factors into (x - 3)(x + 3). This is a standard factoring technique used in algebra.

The square root of 49 is 7 because 7 � - 7 equals 49. This is a basic knowledge of perfect squares.

Combining the fractions leads to the equation 2x/(x² - 1) = 1, which simplifies to x² - 2x - 1 = 0. Solving this quadratic gives x = 1 ± √2, thus the solution set is {1 + √2, 1 - √2}.

Let the width be w, then the length is 3w and the perimeter is 2(w + 3w) = 8w = 64. Solving yields w = 8 and length = 24, so the area is 8 � - 24 = 192.

To find the inverse, swap x and y in the equation y = (x - 2)/(x + 3) and solve for y. The solution yields f❻¹(x) = (-3x - 2)/(x - 1), which is the correct inverse function.

There are 2³ = 8 possible outcomes when flipping a coin three times. Exactly two heads occur in 3 of these outcomes, so the probability is 3/8.

By finding a common denominator for the fractions in the numerator and the denominator, the expression simplifies to (x + y)/(y - x). This is a typical approach to simplify complex fractions.