Explanation

The points form a scalene triangle:

Calculate the distances AB, BC, and AC. If all sides are unequal, it's a scalene triangle.

AB = √((1 - (-4))² + (4 - (-2))²) = √(5² + 6²) = √61

BC = √((6 - 1)² + (11 - 4)²) = √(5² + 7²) = √74

AC = √((6 - (-4))² + (11 - (-2))²) = √(10² + 13²) = √269

All sides are unequal (√61 ≠ √74 ≠ √269), so the points form a scalene triangle.

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

1/2 (sum of parallel sides × altitude) formula is derived from the fact that a trapezium can be divided into a rectangle and a triangle. 

The area of the trapezium is the sum of the areas of these two shapes, which simplifies to 1/2 × (a + b) × h, where a and b are the lengths of the parallel sides, and h is the altitude.

Explanation

To find the LCM, break down the numbers into their prime factors:

12 = 2² * 3

15 = 3 * 5

20 = 2² * 5

30 = 2 * 3 * 5

Step 1: Identify the highest powers of prime factors

The highest power of 2 is 2² (from 12 and 20).

The highest power of 3 is 3 (from 12, 15, and 30).

The highest power of 5 is 5 (from 15, 20, and 30).

Step 2: Calculate the LCM

LCM = 2² * 3 * 5

= 4 * 3 * 5

= 60

Explanation

Smallest 5-digit number: 10000

Greatest 4-digit number: 9999

Result = 10000 - 9999= 1

Explanation

In large numbers, commas are placed after every three digits starting from the right.

For example, 1,000 and 10,000,000 have commas after every three digits.

Explanation

If a² + b² < c², then angle C is greater than 90°, making it an obtuse triangle.

This follows from the converse of the Pythagorean Theorem.

Explanation

To find the length of the chord:

Let's denote the chord's length as 2x (since x would be half the chord's length due to symmetry).

The distance from the center to the chord is 10cm, forming a right triangle with hypotenuse 30cm (radius) and one leg 10cm (distance to chord).

The other leg (x) can be found using the Pythagorean theorem:

x² + 10² = 30²

x² + 100 = 900

x² = 800

x = √800 = √(400*2) = 20√2

The full chord's length is 2x = 2 * 20√2 = 40√2

Explanation

Total rabbits = 3/8 of 480 = (3 × 480) ÷ 8 = 180

White rabbits = 1/3 of 180 = 180 ÷ 3 = 60

Explanation