Dividing both sides of the equation by 2 gives x = 5. This is a basic linear equation where isolating x is the key step.

The sum of the interior angles in a triangle is always 180°. Subtracting 40° and 60° from 180° results in 80°, which is the measure of the third angle.

3 raised to the power of 2 means 3 multiplied by itself, which equals 9. This is a fundamental concept in exponentiation.

A horizontal line does not rise or fall, so its slope is 0. This basic property of lines is important for understanding linear functions.

The area of a rectangle is calculated by multiplying the length by the width. Here, 5 multiplied by 3 equals 15, which is the correct area.

By adding 5 to both sides, the equation becomes 3x = 15, and dividing by 3 gives x = 5. This step-by-step method isolates x, a key technique in solving linear equations.

The quadratic formula, x = (-b ± √(b² - 4ac))/(2a), is the standard method for solving quadratic equations. It is derived from completing the square and applies to all quadratic equations.

First, distribute 2 to get 2x + 6, and then subtract 4x, resulting in -2x + 6. Rearranging gives the answer as 6 - 2x.

A pentagon has 5 sides and the sum of its interior angles can be calculated using the formula (n - 2) × 180°. For n = 5, the sum is (5 - 2) × 180° = 540°.

Substituting x = 4 into the function gives f(4) = 2(4) + 3 = 8 + 3 = 11. This is an example of evaluating a linear function at a specific input.

Adding the two equations eliminates y, giving 2x = 12, so x = 6. Substituting x back into one of the equations results in y = 4.

The nth term of an arithmetic sequence is given by the formula a + (n - 1)d. This formula is fundamental in understanding patterns in arithmetic sequences.

After 7, the numbers 8, 9, and 10 are composite, making 11 the next prime number. Recognizing prime numbers is an important aspect of number theory.

To calculate 15% of 200, convert 15% to its decimal form 0.15 and multiply by 200. The product, 0.15 × 200, equals 30.

Factor 72 as 36×2 so that √72 can be rewritten as √36 × √2, which simplifies to 6√2. Simplifying radicals in this way is a key algebraic skill.

Differentiating 3x² gives 6x and differentiating 2x gives 2, while the constant -5 reduces to 0. Therefore, the derivative f'(x) is 6x + 2, applying basic rules of calculus.

The equation log₂(x) = 5 means that 2 raised to the power of 5 equals x. Calculating 2❵ gives 32, illustrating the inverse relationship between logarithms and exponents.

First, evaluate g(2) which is 2(2) + 1 = 5, and then substitute into f(x) to get f(5) = 5² = 25. This process demonstrates the concept of function composition.

Cross-multiplying the proportion gives 3 × 12 = 4x, which simplifies to 36 = 4x. Dividing both sides by 4 reveals that x = 9.

Adding 7 to both sides of the inequality gives 2x > 10, and dividing by 2 yields x > 5. This manipulation of inequalities is crucial for finding solution sets.