Explanation

Using the identity:

(1 - ω + ω²)ⁿ = (-1)ⁿ ω²ⁿ

Substituting n = 7:

(1 - ω + ω²)⁷ = (-1)⁷ ω²⁷

= -1 × ω²⁷ (since (-1)⁷ = -1)

= -128ω² (since ω²⁷ = (ω²)⁷ × ω⁰ = (ω²)⁷ = 2⁷ω² = 128ω², and multiplying by -1)

The correct answer is:

-128ω²

Explanation

Given Data:

m∠B = 120°

Ratio of m∠A : m∠C = 5 : 7

Step-by-Step Solution:

Triangle Angle Sum Property:

m∠A + m∠B + m∠C = 180°

m∠A + 120° + m∠C = 180°

m∠A + m∠C = 60°

Solving Using Ratio:

Let m∠A = 5x and m∠C = 7x

5x + 7x = 60

12x = 60

x = 5

Finding m∠A:

m∠A = 5 × 5 = 25°

Explanation

Factor the numerator:

(a² - b²) = (a + b)(a - b)

Now, divide by (a + b):

[(a + b)(a - b)] ÷ (a + b)

= (a - b)

Explanation

Like terms are terms that have the same variable(s) with the same exponent(s).

x² and - √3x² are like terms because they both have the same variable (x) with the same exponent (²).

Explanation

Let's calculate the value of 3x – 4y – z using x = 2, y = -3, z = -5:

3(2) – 4(-3) – (-5)

= 6 + 12 + 5

= 23