Explanation

The philosophy of education helps define the purpose, goals, and values of the educational system.

It provides a foundation for curriculum design, teaching methods, and learner outcomes.

Explanation

"Taller" is the correct comparative form of the regular adjective "tall".

Regular adjectives typically form the comparative by adding “-er” (e.g., tall → taller).

Explanation

Brainstorming is a group creativity technique used to generate new ideas by encouraging open and free thinking.

It aims to lower social inhibitions so participants feel comfortable sharing even unusual or bold ideas.

Explanation

The phrase "to vote" is an infinitive acting as the subject complement or noun in the sentence.

It answers "what" is valuable — the right to vote, making it a noun phrase.

Explanation

The Case Study Method presents real-life or hypothetical scenarios to explore critical issues or dilemmas.

It encourages role-playing, critical thinking, and problem-solving through discussion and analysis.

Explanation

This sentence uses the second conditional ("If I had time..."), which refers to an unreal present or future.

The correct structure is: If + past simple, would + base verb → If I had time, I would learn to play the guitar.

Explanation

Shortwave radio operates in the high frequency (HF) band, typically between 3 MHz and 30 MHz.

The range 5.9 MHz to 26.1 MHz is commonly used for long-distance communication like international broadcasting.

Explanation

Fiber optics uses light to transmit data at high speeds through thin glass or plastic fibers.

It is mainly used in communication networks like internet, telephone, and cable TV.

Explanation

Let the smaller number be x.

The larger number is x + 2.

Given:

x² + (x + 2)² = 100

x² + x² + 4x + 4 = 100

2x² + 4x - 96 = 0

x² + 2x - 48 = 0

(x + 8)(x - 6) = 0

x = -8 or x = 6

If x = -8, larger number = -8 + 2 = -6

If x = 6, larger number = 6 + 2 = 8

Explanation

Given:

a - b = 7

ab = 6

The formula for a³ - b³ is:

a³ - b³ = (a - b)(a² + ab + b²)

= (a - b)((a - b)² + 3ab)

Substitute the values:

a³ - b³ = 7((7)² + 3(6))

= 7(49 + 18)

= 7 × 67

= 469