Explanation

The surface area of a cuboid is given by:

2(lb + bh + hl)

Where l = 12cm, b = 8cm, h = 6cm

Surface area = 2(12_8 + 8_6 + 6*12)

= 2(96 + 48 + 72)

= 2(216)

= 432cm²

Explanation

To find the square root:

√2.56 = √(256/100)

= √(16^2 / 10^2)

= 16/10

= 1.6

Explanation

The number of subsets of a set with n elements is 2^n.

Here, A = {a, b, c} has 3 elements, so:

Number of subsets = 2^3

= 8

The subsets are:

{}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}

Explanation

The x-coordinate is negative and the y-coordinate is positive → (-1, √2).

This combination (−, +) always lies in Quadrant II.

Explanation

The square root of any real number is never negative, so √x = -10 has no real solution.

Hence, the solution set is empty, written as { }.

Explanation

Let's factor:

x^2 - y^2 = (x + y)(x - y)

x^2 - xy = x(x - y)

The common factor is (x - y).

Explanation

Given:

P(x) = x^2 - 4x + 3

One root is 1. Let's find the other root.

The sum of roots = -(-4) = 4 (from the coefficient of x)

One root is 1, so the other root would be:

4 - 1 = 3

Explanation

Given:

a + b = 4

ab = 3

The formula for a^3 + b^3 is:

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

However, a simpler approach uses the identity:

a^3 + b^3 = (a + b)^3 - 3ab(a + b)

Plugging in the values:

a^3 + b^3 = (4)^3 - 3(3)(4)

= 64 - 36

= 28

Explanation

Given:

logx(0.001) = -3

This can be rewritten as:

x^(-3) = 0.001

0.001 = 10^(-3)

So:

x^(-3) = 10^(-3)

This implies:

x = 10

Explanation

The calculation confirms that:

3i(2 + 5i) = 6i + 15i^2

= 6i - 15

Comparing this to x + 6i:

x = -15