Explanation

The triangle with vertices A(1,2), B(0,4), and C(3,5) has two sides of equal length.

This makes it an isosceles triangle, where at least two sides are equal.

Explanation

Temperature is continuous data because it can take any value within a range (e.g., 30.5°C, 30.55°C).

Continuous data can be measured on a scale, not just counted.

Explanation

Let the price of the pen be x.

The price of the paintbrush is 1/3x

Set up the equation.

x + 1/3 x = 156x + 1/3x = 156

Solve for x.

4/3x = 156

x = 156 × 3/4

x = 117

Explanation

Factorize the quadratic expression.

3x^2 - 9x + 6 = 3(x^2 - 3x + 2)

= 3(x^2 - 2x - x + 2)

= 3(x(x - 2) - 1(x - 2))

= 3(x - 1)(x - 2)

Explanation

Given:

Hyder’s investment = Rs. 90,000

Ahsan’s investment = Rs. 60,000

Total profit = Rs. 45,000

Step 1: Find the ratio of their investments

Hyder : Ahsan = 90,000 : 60,000 = 3 : 2

Step 2: Divide the profit in the ratio 3:2

Total parts = 3 + 2 = 5

Ahsan’s share = (2/5) × 45,000 = Rs. 18,000

Explanation

Find the least common multiple (LCM) of 10, 11, and 17.

The LCM of 10, 11, and 17 is the smallest number that is a multiple of all three numbers.

Calculate the LCM.

The prime factorization of the numbers is:

10 = 2 × 5

11 = 11

17 = 17

The LCM is the product of the highest powers of all prime factors: LCM = 2 × 5 × 11 × 17 = 1870.

Explanation

When rotating a point (x, y) 270° clockwise, the new coordinates are (y, -x).

For P(2, -9), the new coordinates P' will be (-9, -2).

Explanation

Hazrat Ruqayyah was the Second daughter and third child of Hazrat Muhammad ﷺ and Hazrat Khadijah

She married (1st time) Utbah ibn Abi Lahab, but the marriage was never consummated.

She married (2nd time) to the third caliph Uthman

She had only one son (Abd Allah) but died at the age of six

Ruqayyah (RA died on the victory day of the Battle of Badr.

Additional Information:

Hazrat Usman (RA) could not participate in the Battle of Badr because his wife Ruqayyah (RA) was on his deathbed.

Prophet Muhammad ﷺ had three sons and four daughters.

Explanation

دعوتِ ذوالعشیرہ کے موقع پر نبی کریم ﷺ نے اپنے قریبی رشتہ داروں کو اسلام کی دعوت دی۔

آپ ﷺ نے انہیں اللہ کی توحید اور اپنی نبوت پر ایمان لانے کی طرف بلایا، جو ابتدائی دعوتِ اسلام کا مرکزی پیغام تھا۔

Explanation

Physiological needs (like food, water, air, and shelter) are the most basic and essential for survival.

According to Maslow's hierarchy, if these are unmet for long, other needs like safety or esteem become secondary.