Algebra: Chapter 11, Lesson 7 and Lesson 8, page 509 and 514.
Theorem of Pythagoras and its Uses
`c^2 = a^2 + b^2`,
where `a`, `b` and `c` are the sides of a RIGHT TRIANGLE. `a` and `b` are considered the sides of the triangle where `c` (opposite of the right angle) is called the hypotenuse.
The distance formula is a derivation of the Pythagorean Theorem and you can use it to find the distance from one coordinate point to another. Just remember, like in the slope equation, DON’T MIX UP THE DIRECTION that you define as `x_1` and `y_1`, they both go the same way!
`d = sqrt((x_1 – x_2)^2 + (y_1 – y_2)^2)`
Here is another quick explanation of the Theorem of Pythagoras and the Distance Formula.
Use a calculator with a `sqrt` key, it will make the word problems much easier to do!
Two of tonight’s homework problems solved by MrE are here! Just click it.
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Algebra: Chapter 9, Lesson 4, page 413.
Inequalities and Absolute Value
If the inequality with absolute values looks like: `| A | < b`, then we solve the conjunction `-b < A < b`. Think of a number line, and the solution will be within the bounds of `-b` and `b`. This also works with `≤`.
If the inequality with absolute values look like: `| A | > b`, then we solve the disjunction `A < -b` OR `A > b`. On the number line, these solutions look like arrows on the outside of the values `-b` and `b`. This works for `≥` as well.
Two of tonight’s homework problems solved by MrE are here! Just click it