If
is true, then
is false, which in turn means
is true.
If
is false, then
is true, and so
is false.
So, because
in both cases, the statement is a tautology (always true).
If you were to put this in a table, you would have one column each for
. In the first column (
) you can think of
as an independent variable that can only take two values, true and false. In the next column (
), you would negate the value in the previous column. And so on.
It should roughly look like this:
p ... ~p ... ~(~p)
T ... F ... T
F ... T ... F
Answer:
The answer is 3.
Step-by-step explanation:
This is because f(-3) = -(-3) = 3.
Answer:
1a) f(x) = -1/3(x + 12)² + 9
1b) f(x) = -1/3x² - 8x - 39
General Formulas and Concepts:
<u>Algebra I</u>
Equality Properties
Expand by FOIL (First Outside Inside Last)
Standard Form: ax² + bx + c = 0
Transformations Graph: f(x) = a(bx - c)² + d
- a = vertical shrink/stretch
- b = horizontal shrink/stretch
- c = horizontal movement left/right
- d = vertical movement up/down
Step-by-step explanation:
<u>Step 1: Define</u>
Reflected down and vertically stretched by 1/3: a = -1/3
Shifted vertically by 9 units: d = 9
Shifted horizontally by -12 units: c = -12
<u>Step 2: Write Vertex Form</u>
- Define: f(x) = a(bx - c)² + d
- Substitute: f(x) = -1/3(x + 12)² + 9
<u>Step 3: Write Standard Form</u>
- Define: f(x) = -1/3(x + 12)² + 9
- Expand: f(x) = -1/3(x² + 24x + 144) + 9
- Distribute -1/3: f(x) = -1/3x² - 8x - 48 + 9
- Combine like terms: f(x) = -1/3x² - 8x - 39
And we have our final answers!
