Explanation

Explanation

The radius is the distance from the center of the circle to any point on its boundary.

It is half the length of the diameter.

Explanation

A scalar matrix is a diagonal matrix where all diagonal elements are equal (here, 2), and non-diagonal elements are zero.

Explanation

Commutative property means the order doesn’t matter: 𝐴 ∗ 𝐵 = 𝐵 ∗ 𝐴.

Union ∪ is commutative, so 𝐴 ∪ 𝐵 = 𝐵 ∪ 𝐴.

Explanation

B - A represents the set of elements that are in B but not in A.

The correct notation is: {x | x ∈ B and x ∉ A}

Explanation

A function f: A → B is into if it doesn't cover the entire codomain B, meaning there are elements in B that aren't mapped to by any element in A. 

This happens when the range of f (the set of elements in B that are actually mapped to) is a proper subset of B.

Therefore, f is into if Range f ≠ B.

Explanation

A tangent is a line that touches a circle at exactly one point.

It does not cross the circle and is perpendicular to the radius at the point of contact.

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

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

Area of square = 225 m², side = √225 = 15 m.

Perimeter = 4 × side = 4 × 15 = 60 m.

Cost = Perimeter × Rate = 60 × 235 = 14100.