Explanation

The equation |-x| = 0 simplifies to x = 0 since the absolute value of any number is zero only when the number itself is zero.

Therefore, the solution set contains only {0}.

Explanation

To find the value of x^2, we need to square the value of x:

x^2 = (2)^2

= 2 × 2

= 4

So, the correct answer is: 4

Explanation

Explanation

Explanation

Given:

Zˣ = 32

Since 32 is a power of 2:

32 = 2⁵

So, Zˣ = 2⁵

Now, equate the exponents:

X = 5

Now, find X²:

X² = 5² = 25

Explanation

Let the total number of rabbits = x

Let the total number of pigeons = y

total number of head = 20 

                x + y = 20        eq (1)

total number of feet = 48 

             4x  +2y  = 48

              2x + y   = 24    eq (2)

Subtracting equation (2) from eq (1)

   2x + y -x - y = 24 -20

        x = 4

Explanation

Given log₁₂(12³) = x:

Using logarithm properties, logₐ(aⁿ) = n:

x = 3

Explanation

To find the cube root of 0.000126:

0.000126 = 126/1,000,000

Cube root of (126/1,000,000) = (6/100) = 0.06

So, the cube root of 0.000126 is 0.06.

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

Let the cost of 1 chair be Rs. x and the cost of 1 table be Rs. y.

From the first set of values, we get: 3x + 2y = 700 ... (i)

From the second set of values, we get: 5x + 3y = 1100 ... (ii)

Multiply equation (i) by 5: 15x + 10y = 3500 ... (iii)

Multiply equation (ii) by 3: 15x + 9y = 3300 ... (iv)

Subtract equation (iv) from equation (iii): y = 200

Substitute y = 200 in equation (i): 3x + 2(200) = 700 => 3x = 300 => x = 100

Finally, find the cost of 2 chairs and 2 tables: 2x + 2y = 2(100 + 200) = Rs. 600