Explanation

A material that absorbs all wavelengths (colors) of visible light reflects none, so no light reaches your eyes.

This absence of reflected light makes the object appear black.

Explanation

Let's denote the cost of a geometry box as x. Since the cost of a bag is three times the cost of a geometry box, the cost of a bag is 3x.

Given that the cost of 2 bags and 3 geometry boxes is Rs.3,960, we can set up the equation:

2(3x) + 3(x) = 3960

6x + 3x = 3960

9x = 3960

Divide both sides by 9:

x = 3960 / 9

x = 440

Explanation

Step 1: Perform polynomial long division or synthetic division

To find the quotient when (2x³ - 5x²y + 5xy² - 3y³) is divided by (2x - 3y), let's try factoring or direct division.

Step 2: Factor the numerator if possible

Notice that (2x³ - 5x²y + 5xy² - 3y³) can be factored as:

(2x³ - 3x²y) + (-2x²y + 3xy²) + (2xy² - 3y³)

= x²(2x - 3y) - xy(2x - 3y) + y²(2x - 3y)

= (2x - 3y)(x² - xy + y²)

Step 3: Identify the quotient

Given the factorization (2x - 3y)(x² - xy + y²), the quotient when (2x³ - 5x²y + 5xy² - 3y³) is divided by (2x - 3y) is x² - xy + y².

Explanation

Given:

μ + v = 8

μv = 15

The formula for (μ - v)² is:

(μ - v)² = (μ + v)² - 4μv

= 8² - 4 × 15

= 64 - 60

= 4

μ - v = ±√4

μ - v = ±2

Explanation

Let the smaller number be x.

The larger number is x + 2.

Given:

x² + (x + 2)² = 100

x² + x² + 4x + 4 = 100

2x² + 4x - 96 = 0

x² + 2x - 48 = 0

(x + 8)(x - 6) = 0

x = -8 or x = 6

If x = -8, larger number = -8 + 2 = -6

If x = 6, larger number = 6 + 2 = 8

Explanation

Given:

α + β = 5 (sum of roots)

αβ = k (product of roots)

3α + 2β = 16

From α + β = 5, we get:

α = 5 - β

Substitute α in 3α + 2β = 16:

3(5 - β) + 2β = 16

15 - 3β + 2β = 16

-β = 1

β = -1

Now, α = 5 - β

α = 5 - (-1)

α = 6

k = αβ

k = 6 × (-1)

k = -6

Explanation

Given:

a - b = 7

ab = 6

The formula for a³ - b³ is:

a³ - b³ = (a - b)(a² + ab + b²)

= (a - b)((a - b)² + 3ab)

Substitute the values:

a³ - b³ = 7((7)² + 3(6))

= 7(49 + 18)

= 7 × 67

= 469

Explanation

Given:

Selling Price (SP) = Rs. 49755

Profit Percentage = 7%

Let Cost Price (CP) be x.

SP = CP + Profit

49755 = x + 7% of x

49755 = x + 0.07x

49755 = 1.07x

x = 49755/1.07

x = 46500

Explanation

The multiplicative inverse of a number is its reciprocal.

For -1/9, the reciprocal is -9/1 or simply -9.

Explanation

Discount = 450 - 369 = 81

Discount % = (81 / 450) × 100 = 18%