Explanation

Decomposers like bacteria and fungi break down dead plants and animals.

This process recycles nutrients back into the soil, supporting new plant growth.

Explanation

Explanation

Given points A(3, 1) and B(7, -5), let's calculate the distance using the distance formula:

Distance = √((x2 - x1)² + (y2 - y1)²)

= √((7 - 3)² + (-5 - 1)²)

= √((4)² + (-6)²)

= √(16 + 36)

= √52

= √(4 × 13)

= 2√13

Explanation

Given the area of the rectangle:

x² - 5x + 6

Let's factorize the quadratic expression:

x² - 5x + 6 = x² - 3x - 2x + 6

= x(x - 3) - 2(x - 3)

= (x - 3)(x - 2)

Explanation

Volume of a prism = base area × height.

Substituting values: 260 × 13 = 3380 cm³.

Explanation

Letting the number be x, the equation becomes x + 18 = 2x.

Solving gives x = 18, so the number is 18.

Explanation

A matrix is singular when its determinant is 0.

[4, 2; 6, 3]

Det = (4×3) - (2×6) = 12 - 12 = 0 → Singular

Explanation

The transitive property states that if a < b and b < c, then a < c.

This property shows how inequality (or equality) carries over through a middle term.

Explanation

Given:

(x, 6) = (2, y - 6)

Equating the corresponding components:

x = 2

6 = y - 6

Solving for y:

y = 6 + 6

y = 12

Now, finding x + y:

x + y = 2 + 12

= 14

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)