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:
The quotient is 2.352
Step-by-step explanation:
The term quotient is simply the result of division
Thus; if we divide 54.096 by 23, we get 2.352
100 seats total.
there are 25 seats per section and 4 sections
they just add in fancy stuff to make it confusing.
Answer:
a. 30 degrees
b. 60 degrees
c. 105 degrees
Step-by-step explanation:
Angle a is 30 degrees becuase it is congruent to the one right above it
Angle b is 60 degrees because the interior angles of a triangle always add up to 180. We know that angle a is 30 degrees and the angle with the mini square is a right angle, and right angles are always 90 degrees. Based on this information, we can subtract 90 from 180 followed by subtracting 30 from 90, which equals 60. Angle b is 60 degrees
Angle c is 105 degrees because a straight angle is 180 degrees. We know that one angle is 75, so we subtract 75 from 180 to get the difference. The difference is 105 degrees, which is also the measurement of angle c.
Hope this helps!
