Explanation

Use law of exponents: a^m · a^n = a^(m+n)

a^(x-1) · a^(x+1) = a^[(x-1) + (x+1)] = a^(2x)

Given a^(2x) = a^10

Bases are same, so exponents must be equal: 2x = 10

x = 10/2 = 5

Last verified on 08-06-2026

Explanation

Slope m = (y₂ - y₁)/(x₂ - x₁)

For a vertical line, x stays the same for all points → x₂ - x₁ = 0

So m = something / 0 → division by zero = undefined/infinite

Last verified on 08-06-2026

Explanation

For vectors a and b, dot product a · b = |a||b|cosθ

If vectors are perpendicular → angle θ = 90°  

cos(90°) = 0

So a · b = |a||b| × 0 = 0

Last verified on 08-06-2026

Explanation

det(A) ≠ 0 → Non-singular / Invertible matrix. Has an inverse A⁻¹

det(A) = 0 → Singular / Non-invertible matrix. No inverse exists

Diagonal and Identity matrices can have det = 0 only if they have a zero on diagonal. But "det = 0" by itself defines "Singular".

So rows/columns are linearly dependent - the matrix "collapses" space.

Last verified on 08-06-2026

Explanation

tan 45° = 1

cot 45° = 1

tan² 45° + cot² 45°

= 1² + 1²

= 1 + 1

= 2

Last verified on 19-03-2026