To solve x + 3 = 10, subtract 3 from both sides to get x = 7. This basic algebraic manipulation is the key step here.

Parallel lines share the same slope. Since the slope of y = 2x + 5 is 2, any line parallel to it will also have a slope of 2.

Area is calculated using length times width. Multiplying 8 by 5 gives 40, which is the area of the rectangle.

By dividing both the numerator and denominator by 3, the fraction 3/6 simplifies to 1/2. This process is fundamental when reducing fractions.

Using the Pythagorean theorem, the hypotenuse is calculated as √(3² + 4²) = √(9 + 16) = √25 = 5. The classic 3-4-5 triangle is a common example in geometry.

Factor the quadratic to get (x - 2)(x - 3) = 0, which means x can be 2 or 3. Factoring is a typical method to solve quadratic equations.

Substitute x = 5 into the function: f(5) = 3(5) - 4 = 15 - 4 = 11. Evaluating functions correctly is essential in algebra.

First, compute inside the parentheses: 3 + 4 = 7, then multiply by 2 to get 14 and finally subtract 5 to obtain 9. This problem reinforces the order of operations.

The perimeter of a square is found by multiplying the side length by 4. Thus, 4 × 6 = 24, which is the correct answer.

The distributive property states that multiplying a number by a sum is the same as doing each multiplication separately, i.e., a(b + c) = ab + ac. Understanding this property is critical in simplifying expressions.

Ordering the set, the middle value (median) is 9. The median is a key measure of central tendency in statistics.

The slope represents how much y changes for every unit change in x, which is the rate of change. This explanation is crucial when interpreting linear graphs.

By adding 8 to both sides you get 2y = 8, then dividing by 2 yields y = 4. This reinforces simple linear equation solving techniques.

In any parallelogram, the opposite angles are congruent while adjacent angles are supplementary. Recognizing these properties is important in geometric proofs.

Distributing -2 across (x - 3) gives 4x - 2x + 6, which simplifies to 2x + 6. This is a typical problem demonstrating the application of the distributive property.

From the equation x - y = 1, we express y as x - 1. Substituting into 2x + y = 7 gives 3x - 1 = 7, so x = 8/3 and then y = 5/3. This problem examines solving simultaneous equations.

Finding factors of 3 that add up to -4 leads to -1 and -3, so f(x) factors into (x - 1)(x - 3). This refactoring is a common step in solving quadratic equations.

Using the formula C = 2πr, the radius can be calculated as r = C/(2π) = 31.4/(2*3.14) = 5. This exercise applies the relationship between circumference and radius.

The equation log₂(x) = 5 means that 2 raised to the power of 5 equals x. Therefore, x = 2❵ = 32. This reinforces the connection between logarithms and exponents.

Odds in favor are calculated as the ratio of the probability of the event to the probability of it not occurring, which is 0.2/0.8 = 1:4. This problem integrates concepts of probability and ratios.