Answer:
vertex = (- 10, - 10 )
Step-by-step explanation:
The equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square.
Given
h(x) = x² + 20x + 90
add/subtract ( half the coefficient of the x- term )²
h(x) = x² + 2(10)x + 100 - 100 + 90
= (x + 10)² - 10 ← in vertex form
with (h, k ) = (- 10, - 10 )
v-10=-9
Solve for v.
Add 10 to each side of the equation:
v-10+10 =-9+10
v= 1
<h3>
Answer:</h3>
- A
- B
<h3>
Step-by-step explanation:</h3>
1. A decrease of 3.8% is equivalent to a multiplier fraction of -0.038. The only answer choice that has such a multiplier is A.
In an instance such as this, the "rate" is usually some (fractional) change in some period of time. Since the exponent must be unitless, the rate is effectively (some fraction) "per year" so that multiplying by "t" years cancels the units and results in a pure number.
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<em>Comment on the exponential</em>
If the actual change were -3.8% per year, the exponential term would look like (1 - 0.038)^t = 0.962^t. By writing it as e^(-0.038t), the decrease is effectively compounded continuously. As a result, over a year's time, the decrease is actually about 3.73%, not 3.8%.
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2. If ║x/2║ is a magnitude function, answer choices B and D are equivalent. Thus, we must assume it is a "greatest integer" function. Then the number of desserts prepared will be ║x/2║, and the corresponding revenue will be 1.2║x/2║. Since x is in minutes, 2 to 4 hours will be 120–240 minutes. The appropriate choice is B.
