Explanation

Area = 1/2 × (sum of bases) × altitude

48 = 1/2 × (14 + 18) × altitude

48 = 1/2 × 32 × altitude

48 = 16 × altitude

Altitude = 48/16 = 3 cm.

Explanation

Alexander III of Macedon is famously known as "Alexander the Great".

Due to his vast empire stretching from Greece to India.

He is celebrated for his military genius and undefeated record in battles.

Explanation

Given equation: x^2 - 3kx + 4k^2 = 0.

Sum of roots = 3k, Product of roots = 4k^2.

Sum of squares of roots = (sum of roots)^2 - 2(product of roots)

= (3k)^2 - 2(4k^2)

= 9k^2 - 8k^2

= k^2.

Given sum of squares = one of the options.

If sum of squares = 1, then k^2 = 1, so k = ±1

Explanation

A metaphor directly compares two unrelated things without using "like" or "as" — here, life is directly called a box of chocolates.

It implies that life is full of surprises, just like assorted chocolates in a box.

Explanation

To round off 87.321756 to 5 significant figures, we look at the 6th significant figure, which is 6.

Since it's greater than 5, we round up the 5th significant figure.

87.321756 becomes 87.322

Explanation

It is estimated that around 14 muscles are involved when a person smiles.

Major muscles include the zygomaticus major and minor, which lift the corners of the mouth.

Explanation

An electrical impulse causes the cardiac cell's resting potential to convert into an action potential.

This action potential leads to contraction of heart muscle cells, enabling the heart to beat.

Explanation

The sentence “The evil that men do lives after them” is a simple sentence with one independent clause, though it contains a relative clause ("that men do").

A simple sentence can include modifiers or phrases but has only one main clause with a subject and verb.

Explanation

Let's assume the new bonus is 5x and the old bonus is 4x. Given the old bonus is 25000, so 4x = 25000.

x = 25000 / 4 = 6250.

New bonus = 5x = 5 × 6250 = 31250.

Explanation

Silt has fine particles and retains moisture well, making it fertile and ideal for farming.

Sand is used in construction.

Clay is used for pottery.