Explanation

According to Sigmund Freud, the pleasure principle drives human behavior — seeking pleasure and avoiding pain.

This principle is central to his psychoanalytic theory, especially concerning the id, the unconscious part of the mind.

Explanation

Decorated with lights, the house looked beautiful.

This sentence uses the past participle "decorated" to combine the ideas.

It avoids repetition and clearly connects the decoration with the appearance of the house.

Explanation

A solar eclipse occurs when the Moon comes between the Earth and the Sun.

Most commonly, we observe a partial eclipse, where only part of the Sun is obscured by the Moon.

Explanation

Light signals, such as semaphore flags or lantern flashes, were commonly used by sailors to communicate over distances.

These signals conveyed messages visually before the invention of modern communication tools.

Explanation

A transitive verb needs a direct object to complete its meaning.

In this sentence, "brought" is the transitive verb and "a gift" is its direct object.

Explanation

"To catch the bus" starts with "to" + verb, which is an infinitive form.

It functions as a phrase explaining the purpose or reason related to "time."

Explanation

'One-fourth' uses a hyphen (-) to connect two words that together form a fraction.

A hyphen is used to join words or parts of words for clarity and meaning.

Explanation

Carbon has a valency of 4, and Oxygen has a valency of 2.

By crossing the valencies, we get CO₂ (i.e., one carbon and two oxygen atoms), and the ratio simplifies to the empirical and molecular formula: CO₂.

Explanation

Given cos θ = 4/5 and θ lies in the 4th quadrant.

In the 4th quadrant, cosine is positive, and sine is negative.

We know that sin² θ + cos² θ = 1

sin² θ = 1 - cos² θ

= 1 - (4/5)²

= 1 - 16/25

= 9/25

sin θ = ±√(9/25)

= ±3/5

Since θ lies in the 4th quadrant, sin θ is negative:

sin θ = -3/5

Explanation

Given:

a² + b² + c² = 12

a + b + c = 5

We know that:

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

Expanding the equation:

5² = 12 + 2(ab + bc + ca)

25 = 12 + 2(ab + bc + ca)

Subtract 12 from both sides:

13 = 2(ab + bc + ca)

Divide by 2:

ab + bc + ca = 13/2