Parallel Lines | MathHelp.com - By MathHelp.com
| 00:0-1 | in this problem we are given a diagram and we're | |
| 00:03 | asked to find the value of X . Y . | |
| 00:06 | And Z notice that lines are and S . Are | |
| 00:11 | parallel . And using the trans versatile Q . We | |
| 00:16 | can see that the angle marked as nine Y and | |
| 00:20 | the angle marked as 45 are corresponding angles . Since | |
| 00:26 | we know that if two parallel lines are cut by | |
| 00:29 | a trans versatile , then corresponding angles are congruent . | |
| 00:34 | We can set up the equation nine y equals 45 | |
| 00:42 | And dividing both sides by nine . We find that | |
| 00:46 | y equals five next . Using the transfer cell , | |
| 00:55 | P . And the parallel lines are and S . | |
| 00:59 | We can see that the angles marked as 100 and | |
| 01:02 | 20 and 10 . Z are same side interior angles | |
| 01:08 | . And since we know that if two parallel lines | |
| 01:11 | are cut by a trans versatile , then same side | |
| 01:15 | . Interior angles are supplementary . We can set up | |
| 01:19 | the equation 120 plus 10 z equals 180 . Subtracting | |
| 01:31 | 100 and 20 from both sides gives us tensy equals | |
| 01:41 | 60 And dividing both sides by 10 , we find | |
| 01:48 | that Z equals six . Finally , to find the | |
| 01:56 | value of X notice that the angles marked as tensy | |
| 02:02 | X and nine y form a straight angle So we | |
| 02:07 | know that these angles must add to 180 . And | |
| 02:12 | since we know that Z equals six then tensy must | |
| 02:16 | equal 60 . And since we know that why equals | |
| 02:20 | five , The nine Y Must Equal 45 . So | |
| 02:25 | we have 60 plus x plus 45 equals 180 . | |
| 02:36 | Simplifying on the left , gives us 105 plus x | |
| 02:42 | equals 180 . And subtracting 105 from both sides . | |
| 02:49 | Yes , yes . We find that x equals 75 | |
| 03:01 | , So x equals 75 , y equals five And | |
| 03:06 | z equals six . |
DESCRIPTION:
This lesson covers imaginary numbers. Students learn that the imaginary number "i" is equal to the square root of -1, which means that i^2 is equal to (the square root of -1) squared, which equals -1. Students also learn to simplify imaginary numbers. For example, to simplify the square root of -81, think of it as the square root of -1 times the square root of 81, which simplifies to i times 9, or 9i. To simplify 11/8i, the first step is to get rid of the "i" in the denominator by multiplying both the numerator and the denominator of the fraction by i, to get 11i/8i^2, and remember that i^2 = -1, so we have 11i/8(-1), or 11i/-8, or -11i/8.
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