Explanation

Given:

Width = x

Length = 2 × Width = 2x

Perimeter of a rectangle = 2(Length + Width)

= 2(2x + x)

= 2(3x)

= 6x

Explanation

The OS (e.g., Windows, macOS, Linux) manages all hardware/software operations, including:

• Memory allocation.
• File management.
• Running applications (like MS Word).

Example:

Without an OS (Operating System), a computer cannot boot or execute any program

Explanation

The ovary is the female reproductive part of a flower that holds and protects ovules (which develop into seeds after fertilization).

It is part of the pistil (gynoecium) and matures into a fruit after pollination.

Explanation

In cellular respiration, glucose (food) is broken down in cells (via mitochondria) to produce ATP (energy), CO₂, and water.

Chemical equation: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + Energy (ATP)

Explanation

Definition of Equator:

The equator is an imaginary 0° latitude line, encircling Earth’s midpoint.

It divides the planet into the Northern and Southern Hemispheres.

Explanation

Explanation

Subject Identification:

"They" is the subject of the sentence, as it performs the action (knew).

"Both" is an adjective modifying "they," emphasizing the duo.

The subject is who/what the sentence is about.

Here, "they" (the duo) knew each other.

Explanation

The correct sentence should be:

"The old headmaster was walking along the road when he fell down."

Preposition Error:

"Below" means underneath (e.g., "below the surface"), which doesn’t fit the context.

"Along" is correct here, meaning moving in a line next to the road.

Explanation

Let's denote the two numbers as x and y.

Given:

xy = 96 ... (1)

x + y = 35 ... (2)

We can rewrite equation (2) as:

y = 35 - x

Substitute this into equation (1):

x(35 - x) = 96

35x - x² = 96

x² - 35x + 96 = 0

Factoring the quadratic equation:

(x - 3)(x - 32) = 0

x = 3 or x = 32

If x = 3, y = 32

If x = 32, y = 3

The greatest number is 32.

Explanation

Valid Methods for Linear Equations:

Substitution: Solve one equation for a variable and substitute into the other.

Elimination: Add/subtract equations to eliminate a variable.

Cramer’s Rule: Uses determinants for systems with unique solutions.