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Linear Equations: Solutions Using Determinants with Three Variables The determinant of a 2 × 2 matrix is defined as follows: The determinant of a 3 × 3 matrix can be defined as shown in the following. Each minor determinant is obtained by crossing out the first column and one row. Example 1 Evaluate the following determinant. First find the minor determinants. The solution is  To use determinants to solve a system of three equations with three variables (Cramer's Rule), say  x ,  y , and  z , four determinants must be formed following this procedure: Write all equations in standard form. Create the denominator determinant,  D , by using the coefficients of  x ,  y , and  z  from the equations and evaluate it. Create the  x ‐numerator determinant,  D  x   , the  y ‐numerator determinant,  D  y   , and the  z ‐numerator determinant,  D  z   , by replacing the respective  x ,  y , and  z  coefficients with the constants from the e

Value added tax (VAT) is charged as a percentage of the price of a product or service. So the first thing we need to know is how to calculate a percentage. The way I like to think of percentages is to break up the word into “per” and “cent”. And since “cent” is short for “century” (think a hundred in years and cricket), percent means “per hundred”. The current VAT rate is 15% – 15 per hundred – meaning you pay R15 of VAT per R100 of cost. For something that costs R100 excluding VAT, we just need to add the R15 VAT to the price, giving us a total of R115 including VAT. To calculate the VAT payable on any amount, it helps to remember that VAT is charged as a percentage “of” the purchase price. And in maths, the word “of” simply means to multiply. To calculate the VAT (15%) of something that costs R25 means we need to multiply R25 by 15%. And since we now know that 15% is just (15/100) we can multiply it by R25. Like this: To get the total cost including VAT, we add the VAT

Optimized -6 min https://www. mathsisfun.com /algebra/completing-square.html View original Completing the Square " Completing the Square " is where we ... ... take a  Quadratic Equation like this: and turn it into this: ax 2  + bx + c = 0 a(x+ d ) 2  +  e  = 0 For those of you in a hurry, I can tell you that: d =  b 2a and: e = c − b 2 4a But if you have time, let me show you how to " Complete the Square " yourself. Completing the Square Say we have a simple expression like  x 2  + bx . Having  x twice in the same expression can make life hard. What can we do? Well, with a little inspiration from Geometry we can convert it, like this: As you can see  x 2  + bx  can be rearranged  nearly  into a square ... ... and we can  complete the square  with  (b/2) 2 In Algebra it looks like this: x 2  + bx + (b/2) 2 = (x+b/2) 2 "Complete the Square" So, by adding  (b