Explanation

Joining the midpoints of an equilateral triangle forms 1 smaller triangle inside.

That smaller triangle and 3 corner triangles (each between a vertex and midpoints) make a total of 4 triangles.

Explanation

Since ∠A = ∠B, sides AC = BC, and ∠C is the unequal angle.

The angle bisector of ∠C splits the triangle into two congruent triangles by SAS (Side-Angle-Side) rule.

Explanation

(x, y) is equidistant from (0, 1) and (3, 3).

Distance formula gives 6x + 4y = 17.

Check (1.5, 2): 6(1.5) + 4(2) = 9 + 8 = 17.

So, (1.5, 2) is the point.

Explanation

The set of whole numbers includes both odd and even numbers, making it larger and more inclusive.

Therefore, it can act as a universal set containing odd numbers and even numbers as subsets.

Explanation

a:b = 8:9, b:c = 6:5

Make b same:

a:b = 16:18, b:c = 18:15

So, a:b:c = 16:18:15

Explanation

Step 1: Find the prime factors of each number

255 = 3 × 5 × 17

345 = 3 × 5 × 23

495 = 3² × 5 × 11

Step 2: Identify the common factors

The common prime factors are 3 and 5.

Step 3: Calculate the HCF

HCF = 3 × 5 = 15

Explanation

x - 1/x = 4

Square it:

x² - 2 1/x² = 16

Add 2:

x² + 1/x² = 18

Explanation

Discount = Marked Price - Selling Price = 150 - 120 = 30

Discount Percentage = (30 / 150) × 100 = 20%

Explanation

A diverging beam consists of rays spreading out from a point or axis.

It occurs when light passes through a concave lens or reflects from a convex mirror.

Explanation

Casein plastic is made by adding an acid (like vinegar) to milk, which causes the casein protein to form a solid.

This solid can be molded and dried to create a type of early plastic, known as casein plastic.