Explanation

- 9 - x = ?

- 25 - 9 = 16  

- 48 - 25 = 23  

- 81 - 48 = 33  

- 121 - 81 = 40  

Now look at the differences: 16, 23, 33, 40

Now check differences of differences:

- 23 - 16 = 7  

- 33 - 23 = 10  

- 40 - 33 = 7  

There’s a slightly alternating pattern in second differences: 7, 10, 7...

Assuming this pattern continues backward, before 16, we should subtract 10 (alternating) ⇒ 16 - 10 = 6

So:  

9 - x = 6 ⇒ x = 3

Explanation

a² + b² = 3² + 4² = 9 + 16 = 25 → √25 = 5.

Explanation

Explanation

Explanation

A Pythagorean triple satisfies a² + b² = c².

3^2+4^2=9+16=25=5^2 

(5, 12, 13) → $25 + 144 = 169 = 13^2$ 

(6, 8, 10) →36+64=100=10^2 

(7, 9, 6) → largest is 9
$7^2 + 6^2 = 49 + 36 = 85 neq 9^2 (81)$

Explanation

Sum of angles in a triangle = 180°.

Third angle = 180° − (55° + 45°) = 80°.

Explanation

Add the two equations: (x + y) + (x - y) = 10 + 2 ⇒ 2x = 12 ⇒ x = 6

Subtracting gives y = 4, confirming the solution.

Explanation

Step 1: Add 3 to both sides → 4x > 12

Step 2: Divide by 4 → x > 3

Explanation

(a - b)² = (a + b)² - 4ab = 5² - 4 × 5 = 25 - 20 = 5

a − b = √5

Explanation

A square matrix, A , is skew-symmetric if it is equal to the negation of its nonconjugate transpose, A = -A. ' . a i , j = − a j , i . is both skew-symmetric and skew-Hermitian.