Explanation

To find the distance between two points (x1, y1) and (x2, y2), use the distance formula:

√((x2 - x1)² + (y2 - y1)²)

Given points (p, q) and (p + 4, q + 5):

Step 1: Apply the distance formula

Distance = √((p + 4 - p)² + (q + 5 - q)²)

= √((4)² + (5)²)

= √(16 + 25)

= √41

Explanation

To convert 45 to binary:

45 ÷ 2 = 22 remainder 1

22 ÷ 2 = 11 remainder 0

11 ÷ 2 = 5 remainder 1

5 ÷ 2 = 2 remainder 1

2 ÷ 2 = 1 remainder 0

1 ÷ 2 = 0 remainder 1

Reading remainders from bottom to top: 101101

Therefore, 45 in binary = 101101.

Explanation

To find the ratio of 1.8 to 2:

Divide 1.8 by 2:

1.8 ÷ 2 = 0.9

Now, multiply by 10 to eliminate the decimal:

0.9 × 10 = 9

The ratio becomes:

9 : 10

Explanation

Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70

Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42

Factors of 28: 1, 2, 4, 7, 14, 28

Common factors: 1, 2, 7, 14 → Highest is 14

So, HCF = 14.

Explanation

2 is the smallest and the only even prime number.

A prime number has exactly two distinct factors: 1 and itself; 1 does not meet this condition.

Explanation

The absolute value | -12 | represents the distance of -12 from zero, which is always positive.

Therefore, | -12 | = 12.

Explanation

Convert the mixed fraction to an improper fraction:

3 4/5 = (3 × 5 + 4) / 5 = 19/5

The reciprocal of 19/5 is 5/19.

Explanation

To evaluate the expression 3x + 6y + 4x, we need to combine like terms:

3x + 6y + 4x = (3x + 4x) + 6y

= 7x + 6y

So, the correct result is 7x + 6y.

Explanation

In a right-angled triangle, one angle is 90°, and the sum of all three angles is 180°.

So, the sum of the two acute angles is:

180° - 90° = 90°

Explanation

f(x) = x², g(x) = 2x, so

fog(x) = f(g(x)) = f(2x) = (2x)² = 4x²