Answer:
Step-by-step explanation:
Since G(0) = g(0) = 20, the parabolic graphs of these functions share a y-intercept: (0, 20).
Completing the square puts these equations into vertex form, which simplifies comparisons of the graphs:
G(x) = 2x^2 - 12x + 20 becomes
2(x^2 - 6x + 9 - 9) + 20, or
2(x - 3)^2 - 18 + 20, or 2(x - 3)^2 + 2. Comparing this result to
a(x - h)^2 + k, we see that the vertex is located at (3, 2).
Going through the same process for g(x) 2x^2+12x+20, we get:
g(x) = 2(x + 3)^2 + 2, whose vertex is at (-3, 2).
Next time, please include ALL info pertaining to your question, including the set of possible answer choices. Thank you.
Answer:
Three times
Step-by-step explanation:
Given
Figures: Rectangular Prism and Rectangular Pyramid
Let the dimension of the prism be:
Amount of sand used is the volume (V1) and it is calculated using;
Since the pyramid has the same base area and height as the prism, the its dimension would be:
Amount of sand used is the volume (V2) and it is calculated using;
So, we have:
Substitute lwh for V1 in the second equation
Multiply both sides by 3
Reorder
<em>Hence, the amount of sand used in building the prism is three times the amount of sand used in building the pyramid</em>
This is an exponential decay problem.
Using the equation Y = a *(1-rate)^time
where Y is the future value given as 12,000 and a is the starting value given as 13,000.
The rate is also given as 5%.
The equation becomes:
12,000 = 13,000(1-0.05)^x
12,000 = 13,000(0.95)^x
Divide each side by 13000:
12000/13000 = 0.95^x/13000
12/13 = 0.95^x
Use the natural log function:
x = ln(12/13) / ln(0.95)
x = 1.56 years. ( this will equal 12,000
Round to 2 years it will be less than 12000.
Answer:
Option C is correct. Option f is the same as option C
Step-by-step explanation:
From the question, There are three high schools in the district, each with grades between nine to twelve. The school board decided to pool all of the students together and randomly samples 250 students in the whole district that has schools between the grade of nine to twelve.
In order to test for high school students in the district for Attention Deficit disorder(ADD), they could have chosen any 250 students from any school with grades betweem nine to twelve throughout the district.
