Explanation

a*b = (a+b) + ab

3_4 = (3+4) + 3×4 = 7 + 12 = 19

2_3 = (2+3) + 2×3 = 5 + 6 = 11

(3_4) - (2_3) = 19 - 11 = 8

Explanation

5x - 15 = 60

5x = 60 + 15

5x = 75

x = 75/5

x = 15

Explanation

(x+y) + (x-y) = 112

2x = 112

x = 56

Explanation

4x - 15 = 50

4x = 50 + 15

4x = 65

x = 65/4

x = 16.25

Explanation

To isolate X from the equation AX = B, multiply both sides by the inverse of A (A⁻¹):

A⁻¹(AX) = A⁻¹B → (A⁻¹A)X = A⁻¹B → IX = A⁻¹B → X = A⁻¹B.

Explanation

(12 + 2)² / 2

= (14)² / 2  

= 196 / 2  

= 98

Explanation

The constant –1.50 represents a fixed service charge deducted from the total euros received.

This fee is independent of the amount of US dollars exchanged.

Explanation

For collinear points, slope between any two pairs is equal:

Slope(1,2) & (4,m) = Slope(4,m) & (5,6)

(m-2)/(4-1) = (6-m)/(5-4)

(m-2)/3 = 6-m

m-2 = 18-3m

4m = 20

m = 5

Explanation

Let's solve the equation:

4^(2n+3) = 8^(n+5)

Expressing both sides with base 2:

(2^2)^(2n+3) = (2^3)^(n+5)

2^(4n+6) = 2^(3n+15)

Equating exponents:

4n + 6 = 3n + 15

4n - 3n = 15 - 6

n = 9

Explanation

Al'Khwarizmi was an Islamic mathematician who wrote on Hindu-Arabic numerals.

The word algorithm derives from his name.

He wrote the first systematic book on Algebra, Al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala.