Answer:
log4(1024)=5
Step-by-step explanation:
the 4 is a subscript
7+3 = 10 total marbles
1st pick = 7/10 for a red one
2nd pick = 6/9 reduces to 2/3 for a red one
3rd pick = 3/8 for a white one
7/10 x 2/3 =14/30 reduces to 7/15
7/15 x 3/8 = 21/120 reduces to 7/40
probability = 7/40
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!
Answer:
See below.
Step-by-step explanation:
So we have the two functions:
1)
First, find the values of each function:
Therefore:
2)
Plug in the number into the function:
3)
Like the last one:
The answer is the second option, increase (1,infinity) and decrease (negative infinity,1)
Look at the x axis, not y
