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)

Explanation