Answer:
x²
Step-by-step explanation:
Let "d" represent the divisor (what goes in the blank). Then you have ...
... (x²y)/d = y
Multiplying by d gives ...
... x²y = yd
And dividing by y gives the desired value:
... x² = d
The divisor is x².
Answer:
x=2
Step-by-step explanation:
1. AB=AC (The triangle is isosceles. This means that at least two of its sides are equal in length. Looking at the triangle in the picture, sides AB and AC look the same, so we will assume that they are equal. Note that as you get more advanced, assuming isn't the best strategy. <em>You should always try to look for hints if you are ever unsure. For example, if there are two angles that are the same measure in a triangle, the two sides that are only touching one of these angles are equal in length. This is called the </em><em>base angles theorem converse</em><em>.)</em>
2. 9x-3=6x+3 (Rewrite sides AB and AC as the values given in the picture. This is called substitution.)
3. 9x=6x+6 (Add 3 to each side)
4. 3x=6 (Subtract 6x from each side)
5. x=2 (Divide each side by 3)
let me know if i did anything wrong, hope this helps!!
Answer:
a) The half life of the substance is 22.76 years.
b) 5.34 years for the sample to decay to 85% of its original amount
Step-by-step explanation:
The amount of the radioactive substance after t years is modeled by the following equation:
![P(t) = P(0)(1-r)^{t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29%281-r%29%5E%7Bt%7D)
In which P(0) is the initial amount and r is the decay rate.
A sample of a radioactive substance decayed to 97% of its original amount after a year.
This means that:
![P(1) = 0.97P(0)](https://tex.z-dn.net/?f=P%281%29%20%3D%200.97P%280%29)
Then
![P(t) = P(0)(1-r)^{t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29%281-r%29%5E%7Bt%7D)
![0.97P(0) = P(0)(1-r)^{0}](https://tex.z-dn.net/?f=0.97P%280%29%20%3D%20P%280%29%281-r%29%5E%7B0%7D)
![1 - r = 0.97](https://tex.z-dn.net/?f=1%20-%20r%20%3D%200.97)
So
![P(t) = P(0)(0.97t)^{t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29%280.97t%29%5E%7Bt%7D)
(a) What is the half-life of the substance?
This is t for which P(t) = 0.5P(0). So
![P(t) = P(0)(0.97t)^{t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29%280.97t%29%5E%7Bt%7D)
![0.5P(0) = P(0)(0.97t)^{t}](https://tex.z-dn.net/?f=0.5P%280%29%20%3D%20P%280%29%280.97t%29%5E%7Bt%7D)
![(0.97)^{t} = 0.5](https://tex.z-dn.net/?f=%280.97%29%5E%7Bt%7D%20%3D%200.5)
![\log{(0.97)^{t}} = \log{0.5}](https://tex.z-dn.net/?f=%5Clog%7B%280.97%29%5E%7Bt%7D%7D%20%3D%20%5Clog%7B0.5%7D)
![t\log{0.97} = \log{0.5}](https://tex.z-dn.net/?f=t%5Clog%7B0.97%7D%20%3D%20%5Clog%7B0.5%7D)
![t = \frac{\log{0.5}}{\log{0.97}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%5Clog%7B0.5%7D%7D%7B%5Clog%7B0.97%7D%7D)
![t = 22.76](https://tex.z-dn.net/?f=t%20%3D%2022.76)
The half life of the substance is 22.76 years.
(b) How long would it take the sample to decay to 85% of its original amount?
This is t for which P(t) = 0.85P(0). So
![P(t) = P(0)(0.97t)^{t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29%280.97t%29%5E%7Bt%7D)
![0.85P(0) = P(0)(0.97t)^{t}](https://tex.z-dn.net/?f=0.85P%280%29%20%3D%20P%280%29%280.97t%29%5E%7Bt%7D)
![(0.97)^{t} = 0.85](https://tex.z-dn.net/?f=%280.97%29%5E%7Bt%7D%20%3D%200.85)
![\log{(0.97)^{t}} = \log{0.85}](https://tex.z-dn.net/?f=%5Clog%7B%280.97%29%5E%7Bt%7D%7D%20%3D%20%5Clog%7B0.85%7D)
![t\log{0.97} = \log{0.85}](https://tex.z-dn.net/?f=t%5Clog%7B0.97%7D%20%3D%20%5Clog%7B0.85%7D)
![t = \frac{\log{0.85}}{\log{0.97}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%5Clog%7B0.85%7D%7D%7B%5Clog%7B0.97%7D%7D)
![t = 5.34](https://tex.z-dn.net/?f=t%20%3D%205.34)
5.34 years for the sample to decay to 85% of its original amount
Answer:
Reflection
Step-by-step explanation:
Answer:
A) g(x)= 1/2(x-8)^2-8. The vertex is (8, -8).
Step-by-step explanation:
A. g(x)= 1/2(x-8)^2-8 is the vertex form of the function.
In general it can be written as
f(x) = a(x - h)^2 + k where (h, k) is the vertex.
Here the vertex is (8, -8)