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
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.
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
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.
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.
The absolute value | -12 | represents the distance of -12 from zero, which is always positive.
Therefore, | -12 | = 12.
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.
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.
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°
f(x) = x², g(x) = 2x, so
fog(x) = f(g(x)) = f(2x) = (2x)² = 4x²