Explanation

36/9 = 4

9/9 = 1

Explanation

To find the greatest length of a tape that can measure both 52 m and 36 m exactly, we need the HCF (Highest Common Factor) of 52 and 36.

Step-by-step:

Factors of 52: 1, 2, 4, 13, 26, 52

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Common factors: 1, 2, 4

Greatest common factor = 4

Explanation

Let's simplify 9/√12:

9/√12 = 9/√(4 × 3)

= 9/(2√3)

= (9 × √3) / (2 × 3)

= 3√3 / 2

The additive inverse is the negative of this:

-(3√3 / 2)

Explanation

Given:

√x is an integer

This means that x is a perfect square, since the square root of x is an integer.

Examples: x = 1, 4, 9, 16, 25, ...

Explanation

The expression x² + 7x + 3 has three terms.

A polynomial with three terms is called a trinomial.

Explanation

4³ = 4 × 4 × 4 = 64

Now, divide by 4:

64 ÷ 4 = 16

Explanation

De Morgan's laws describe relationships between unions and intersections of sets.

They are also fundamental in logic and Boolean algebra.

Explanation

Square of -6 means (-6) × (-6) = 36.

Negative × Negative = Positive.

Explanation

A rational number is a number that can be written as a fraction (p/q) where p and q are integers and q ≠ 0.

3/0 is a rational number.

Explanation

Partial fractions refer to expressing a complex rational expression as the sum of simpler fractions.

Each resulting fraction has a single factor in the denominator, making calculations and integration easier.