Explanation

Since a 20% discount reduced the price to Rs. 100:

x - (20% of x) = 100

To find 20% of x, multiply x by 0.20:

x - 0.20x = 100

Combine like terms:

0.80x = 100

Divide by 0.80:

x = 125

Explanation

Given that x = 3 is a solution to the equation:

x² + rx - 20 = 4

Substitute x = 3 into the equation:

(3)² + r(3) - 20 = 4

Simplify:

9 + 3r - 20 = 4

Combine like terms:

3r - 11 = 4

Add 11 to both sides:

3r = 15

Divide by 3:

r = 5

Explanation

Explanation

When a coin is flipped, there are two possible outcomes: heads (H) or tails (T).

The probability of getting a head is the number of favorable outcomes (getting a head) divided by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes

= 1 (head) / 2 (head or tail)

= 1/2

Explanation

To compare fractions, convert them to decimal values:

7/9 = 0.777

5/6 = 0.833

8/9 = 0.888

8/7 = 1.142

The smallest value among them is 7/9.

Explanation

We know that 1/7 of x is 4:

(1/7)x = 4

To find x, multiply both sides by 7:

x = 4 × 7

x = 28

Now, find 1/4 of x:

(1/4)x = (1/4) × 28

= 7

Explanation

The exterior angle theorem states that an exterior angle is equal to the sum of the two opposite interior angles.

Here, the exterior angle at A (x) is equal to 40° + 100° (sum of interior angles opposite to x).

x = 140° as per the exterior angle theorem.

Explanation

A regular polygon has all sides and angles equal.

Among triangles, only an equilateral triangle has all three sides and angles equal, making it a regular polygon.

Explanation

The lateral surface area of a right circular cone is given by the formula: πrℓ, where r is the radius and ℓ is the slant height.

This excludes the base area; the total surface area would be πr(r + ℓ).

Explanation

When two lines intersect, they form four angles around the intersection point.

The sum of these four angles is always 360°, as they complete a full circle.