Algebra I For Dummies, 2nd Edition (For Dummies (Lifestyle))

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Matrices are here to stay. You may be familiar with a method used to solve systems of linear equations using matrices, but this application just scratches the surface of what matrices can do. Divisibility by 11:A number is divisible by 11 if the sums of the alternate digits are different by 0, 11, 22, or 33, or any two-digit multiple of 11. In other words, say you have a six-digit number: Add up the first, third, and fifth digits — the odd ones. Then add the digits in the even places — second, fourth, and sixth. Then subtract the smaller of those totals from the larger total, and if the answer is a multiple of 11, the original number is divisible by 11. For example, let's say we're working with a system that contains the equations y = 3x - 2 and y = -x - 6. If we draw these two lines on a graph, we get one line that goes up at a steep angle, and one that goes down at a mild angle. Since these lines cross at the point (-1,-5), this is a solution to the system. [13] X Research source

You can multiply many exponential expressions together without having to change their form into the big or small numbers they represent. When multiplying exponents, the only requirement is that the bases of the exponential expressions have to be the same. So, you can multiply In this example, you moved the decimal 11 times; also, because you moved the decimal to the left, the exponent is positive. Therefore, a = 11, and so you get Divisibility by 3:A number is divisible by 3 if the sum of the digits in the number is divisible by 3.If you have to take one class in each subject, how many different course loads can you create if you have a choice of four math classes, three history classes, eight English classes, and five science classes? If there’s more than one base in an expression with powers, you can combine the numbers with the same bases, find the values, and then write them all together. For example,

Just be sure that whatever you do to one side of the equation, you also do to the other side. Think of the equation as two expressions pivoting on either side of a balance scale: You need to keep the sides at the same weigh t . Quadratic Equations Multiply 4 x 6 x 2 x 3 = 144. This method doesn’t tell you what all the routes are; it just tells you how many are possible so you know when you’ve listed all of them. (Better get to work on that.) Divisibility by 4:A number is divisible by 4 if the last two digits in the number form a number divisible by 4.How many different ice-cream sundaes can you create if you have a choice of five ice-cream flavors, three sauces, and five sprinkled toppings if you choose one of each type?