The greatest six-digit number is 999999 (all digits are 9).
Any higher number becomes a seven-digit number (starts from 1000000).
Given:
2 : 5 = 6 : x
We can write it as:
2/5 = 6/x
Cross-multiplying:
2x = 6 × 5
2x = 30
x = 30/2
x = 15
Given the proportion:
6 : x :: 9 : 12
6/x = 9/12
6 × 12 = 9 × x
72 = 9x
x = 72/9
x = 8
The given equation (a + b) + c = a + (b + c) is the standard form of the Associative Property of Addition.
It states that the grouping of numbers in an addition operation does not change the sum.
The associative property of the union states that:
A ∪ (B ∪ C) = (A ∪ B) ∪ C
This means that the order in which we perform the union operation does not change the result.
A cyclic quadrilateral is a four-sided figure where all vertices lie on the circumference of a single circle.
Key property: Opposite angles sum to 180°.
The orthocenter is the point where the three altitudes of a triangle intersect.
An altitude is a perpendicular line from a vertex to the opposite side (or its extension).
A matrix is singular when its determinant is 0.
[4, 2; 6, 3]
Det = (4×3) - (2×6) = 12 - 12 = 0 → Singular
If 1 ¥ = 1.81 Pak rupees, then:
1 Pak rupee = 1 / 1.81 ¥
= 0.55 ¥
Inductive reasoning involves observing patterns or examples and forming a generalized conclusion.
It moves from specific cases to a general rule.