Explanation

Total production for Jan-March = 1500 tons × 3 months = 4500 tons

Total production for Jan-April = 4500 tons + 1200 tons = 5700 tons

New average = Total production / Number of months = 5700 tons / 4 months = 1425 tons

Explanation

The given ratio is:

5:10 :: 5:x

This is a proportion, so we can set up an equation:

5/10 = 5/x

Cross-multiply:

5x = 5 × 10

5x = 50

Divide by 5:

x = 50/5

x = 10

Explanation

To find the product of x^a and x^b:

x^a × x^b

Using the rule of exponents that states when multiplying two powers with the same base, add the exponents:

x^(a + b)

Explanation

To find the distance from the tip of the pole to the tip of the shadow, use the Pythagorean theorem:

Distance² = Pole height² + Shadow length²

Given:

Pole height = 5 m

Shadow length = 3 m

Distance² = 5² + 3²

Distance² = 25 + 9

Distance² = 34

Distance = √34 ≈ 5.83 m

Explanation

The sum of the internal angles of a polygon can be found using the formula:

(n-2) × 180°

where n is the number of sides.

For a regular octagon (8 sides):

(8-2) × 180° = 6 × 180° = 1080°

Since it's a regular octagon, all internal angles are equal. To find the measure of each internal angle, divide the total sum by the number of angles:

1080° ÷ 8 = 135°

Explanation

To find the percentage discount:

Marked price = Rs. 80

Sale price = Rs. 72

Discount = Marked price - Sale price

Discount = 80 - 72

Discount = 8

Percentage discount = (Discount / Marked price) × 100

Percentage discount = (8 / 80) × 100

Percentage discount = 10%

Explanation

To find the sum of the four numbers, multiply the average by the total count of numbers:

Average = 24

Total count = 4

Sum = Average × Total count

Sum = 24 × 4

Sum = 96

Explanation

A rhombus has four equal sides, but its internal angles are not 90°.

The angles are typically oblique (less than or greater than 90°).

A square has four equal sides and 90° angles.

While a parallelogram has opposite sides equal but not necessarily all sides equal or internal angles 90°.

Explanation

If two circles touch externally, the distance between their centers is equal to the sum of their radii.

This is because the circles are externally tangent, meaning the distance from one center to the other is the total length of both radii combined.

Explanation

5^(x + 3) = 25(3x - 4)

Rewrite 25 as 5²:

5^(x + 3) = 5²(3x - 4)

Equate the exponents:

x + 3 = 2(3x - 4)

Simplify:

x + 3 = 6x - 8

Subtract x from both sides:

3 = 5x - 8

Add 8 to both sides:

11 = 5x

Divide by 5:

x = 11/5