Explanation

Explanation

Let's denote the two parts as x and 12 - x.

The sum of their squares is x² + (12 - x)².

Twice their product is 2x(12 - x).

According to the problem:

x² + (12 - x)² - 2x(12 - x) = 4

x² + 144 - 24x + x² - 24x + 2x² = 4

4x² - 48x + 140 = 0

x² - 12x + 35 = 0

(x - 7)(x - 5) = 0

x = 7 or x = 5

The two parts are 5 and 7.

Let's check:

5² + 7² = 25 + 49 = 74

2 × 5 × 7 = 70

74 - 70 = 4

This satisfies the condition.

The answer is 5 and 7.

Explanation

In direct proportion, both quantities increase or decrease together at the same rate.

In inverse proportion, when one quantity increases, the other decreases in the same ratio.

Explanation

The intersection of two sets X and Y (X ∩ Y) is the set of elements that are common to both X and Y.

Given:

X = {2, 4, 6, 8}

Y = {1, 2, 3, 6}

The common elements are 2 and 6.

So, X ∩ Y = {2, 6}.

Explanation

Let's solve for x:

x/2 + x/3 + x/6 = 10

To add these fractions, find a common denominator (6):

3x/6 + 2x/6 + x/6 = 10

6x/6 = 10

x = 10

Explanation

A right bisector of a line segment is a line that cuts it into two equal parts at 90°.

It always passes through the midpoint of the segment.

Explanation

42 ÷ 7 = Rs. 6 per folder

50 ÷ 6 ≈ Rs. 8.33 per folder

56 ÷ 8 = Rs. 7 per folder

72 ÷ 9 = Rs. 8 per folder

Explanation

6 people dig a 200m well in 15 days.

To find the total work done in terms of "man-days":

6 people × 15 days = 90 man-days

Now, let's find the number of people required to dig the same well in 18 days:

Let x be the number of people required.

x people × 18 days = 90 man-days

x = 90 / 18

x = 5

Explanation

The greatest 5-digit number is 99999.

Adding 2 gives 99999 + 2 = 100001, which is 1 more than the smallest 6-digit number (100000).

Explanation

Let's identify the prime numbers from the list:

Given numbers:

7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18

A prime number has only two divisors: 1 and itself.

Prime numbers are:

7

11

13

17

Total prime numbers = 4