birt barcode4j

free birt barcode plugin

birt barcode extension

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C h a p te r 9 : Ve n n D i a g ra m s : V i s u a l i z i n g a n d M a n i p u l a t i n g S e t s

To solve an equation means to find the value of the variable that makes the equation a true statement To solve equations, apply the distributive property and the properties of equality Any properties of equalities that you apply on one side of an equation, you also must apply on the other side Distributive property For any numbers a, b, and c, a(b c) ab ac a(b c) ab ac Example: Use the distributive property to expand the following expression 3(x 2) 3x (3)(2) 3x 6 Addition and subtraction properties of equality If two quantities are equal and the same number is added to (or subtracted from) each, then the resulting quantities also are equal a c b c a c b c Example: Solve x x x 3 3 3 x Example: Solve t t t 2 2 2 t 7 7 10 2 5 5 7 2 5 using the subtraction property 3 3 7 using the addition property

This program initializes the two arrays, $files and $dirs, which will contain the files and directories encountered in $path, and sets the two counters for the numbers of files and directories, $fnum and $dnum, to 0 Then, $path is checked to ensure it s a valid directory If it is, the directory is opened using opendir() and a handle to it is placed in $dh Then, a do loop is entered in which each item in the directory is read in turn into the string $item If the value of $item is FALSE at any time, the end of the directory listing has been encountered However, there s a slight problem because a file or subdirectory could have the name 0 , which would be interpreted as having the value FALSE by PHP To avoid this, instead of comparing using the != operator, !== is used instead This tells PHP not to try to evaluate anything before making the comparison, and only to compare exact values The file names and are also ignored Next the current item is tested to see whether it s a file or a directory If it s a directory, it is placed in the $dirs array and $dnum is incremented If it s a file, it is placed in the $files array and $fnum is incremented The do loop then continues until $item has a value of FALSE, at which point the $dh handle is closed At the end of the code the results are returned in an array of four elements as follows: Element 0: The number of directories found Element 1: The number of files found Element 2: Array containing the directory names Element 3: Array containing the file names If $path was not a valid directory, the return statement will simply return zeros and empty array values.

Multiplication and division properties of equality If two equal quantities each are multiplied by (or divided by) the same number, then the resulting quantities also are equal ac bc a b , for c 0 c c 3 using the multiplication property

1 a 4

( 1 a)(4) 4

6n 6

5:

18 6

Suppose an equation has more than one variable To isolate a variable that is, to solve the equation for a variable write an equivalent equation so that one side contains only that variable with a coefficient of 1 Connecting Math to Physics Isolate the variable P ( pressure) in the ideal gas law equation PV