Explanation

Convert all fractions to decimals:

2/3 = 0.666...,

4/9 ≈ 0.444,

5/8 = 0.625,

7/16 = 0.4375

2/3 (≈ 0.666) is the greatest among them.

Explanation

To find the distance between two points, use the distance formula:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

Given points:

(x₁, y₁) = (2, 3)

(x₂, y₂) = (7, 3)

Substitute the values:

Distance = √((7 - 2)² + (3 - 3)²)

= √((5)² + 0²)

= √(25)

= 5

Explanation

Given the proportion:

a³ - b³ : a² - b² :: a² + ab + b² : x

We know a³ - b³ = (a - b)(a² + ab + b²) and a² - b² = (a - b)(a + b)

So, the proportion becomes:

(a - b)(a² + ab + b²) : (a - b)(a + b) :: a² + ab + b² : x

Canceling (a - b):

(a² + ab + b²) : (a + b) :: a² + ab + b² : x

This implies x = a + b.

Explanation

Given the quadratic equation mx² - 5x + n = 0:

Sum of roots = -(-5/m) = 5/m

Product of roots = n/m

Given both sum and product of roots are equal to 10:

5/m = 10 => m = 1/2

n/m = 10 => n = 10m

n = 10 * (1/2)

n = 5

Explanation

Given w⁻¹³ = w², let's assume a cyclic pattern:

If w¹⁵ = 1, then w⁻¹³ = w² fits the pattern w⁻¹³ = w^(15-13) = w².

Explanation

Given the trigonometric identity:

cosec²x = 1 + cot²x

Rearranging:

cosec²x - 1 = cot²x

Explanation

Given A = [1  2] and B = [3; 2], let's calculate the product AB:

AB = [1_3 + 2_2]

= [3 + 4]

= [7]

Explanation

Explanation

The degree of the polynomial 9x⁴ - 11x + 17 is 4 (highest power of x).

The divisor is x ÷ 5, which simplifies to x/5 or just x (since dividing by a constant doesn't change the variable's degree).

When a polynomial is divided by a term of degree 1 (x), the degree of the quotient becomes:

4 (numerator degree) - 1 (denominator degree) = 3

Explanation

A power set contains all possible subsets of a given set, including the empty set and the set itself.

Example: If set = {a, b}, then power set = {∅, {a}, {b}, {a, b}}.