2 equations, 2 unknowns. Call height H and base B.
From the first sentence:
HB = 216
From the second sentence:
H = ⅔ B
Plug the second into the first and solve for B:
(⅔ B)B = 216
B^2 = 324
B = 18
Plug that back into either of the original 2 equations and solve for H:
H(18) = 216
H = 12
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:
17, 2, 0, 2
Step-by-step explanation:
This is a homework problem from Art of Problem Solving Prealgebra 2. If a student copies a solution posted here, AoPS will see, so don't do it. Please a<span>sk for help on the class message board.
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Students do not learn the material if they cheat, so please do not help them cheat.
Answer:
90 pumpkin and 36 green beans
Step-by-step explanation:
Because there is a total of 7 parts (5+2) and I divided 126 by 7 and then put five of the 18ns (the quotient of 126 and 7) for pumpkins (so... multiply 18 by 5) then the other to times 18 is 36. And if you add them together, they equal 126.
