Part 1 -
1. f(x) = 5(x-2)^2 + 4
axis of symmetry: x = 2
vertex: (2, 4)
2. f(x) = 12(x + 6)^2 - 5
axis of symmetry: x = -6
vertex: (-6, -5)
3. f(x) = 2x^2 + 8x - 7
axis of symmetry: x = -2
vertex: (-2, -15)
I have to go somewhere right now, but I will get back to you as soon as I can (probably within a couple of hours) to finish answering the rest of your questions.
In normal distribution, 68% of the values are within +_ 1 SD. That leaves 32% outside that range. Thus, 32 people with greater than 13, 100 people greater than 14 (200*0.68/2+32)
Answer:
The lengths of the bases are 9 inches and 15 inches.
Step-by-step explanation:
The area of trapezoid is
![=\frac12(\textrm{ sum of parallel sides})\times height](https://tex.z-dn.net/?f=%3D%5Cfrac12%28%5Ctextrm%7B%20sum%20of%20parallel%20sides%7D%29%5Ctimes%20height)
Given that the height of a trapezoid is 8 in. and its area is 96 in².
Assume the bases of the trapezoid be b₁ and b₂.
Since one base of the trapezoid 6 in. longer than the other.
Let, b₁=b₂+6
The area of the trapezoid is
in²
in²
in²
According to the problem,
![\frac12(2b_2+6)\times8 =96](https://tex.z-dn.net/?f=%5Cfrac12%282b_2%2B6%29%5Ctimes8%20%3D96)
[ Multiplying
]
![\Rightarrow 2b_2+6=24](https://tex.z-dn.net/?f=%5CRightarrow%202b_2%2B6%3D24)
![\Rightarrow 2b_2=24-6](https://tex.z-dn.net/?f=%5CRightarrow%202b_2%3D24-6)
![\Rightarrow 2b_2=18](https://tex.z-dn.net/?f=%5CRightarrow%202b_2%3D18)
![\Rightarrow b_2=\frac{18}{2}](https://tex.z-dn.net/?f=%5CRightarrow%20b_2%3D%5Cfrac%7B18%7D%7B2%7D)
![\Rightarrow b_2=9](https://tex.z-dn.net/?f=%5CRightarrow%20b_2%3D9)
Then, ![b_1=b_2+6](https://tex.z-dn.net/?f=b_1%3Db_2%2B6)
=9+6
=15 in
The lengths of the bases are 9 inches and 15 inches.
D because the measure for every triangle is 180 degrees