Answer:
Th correct option is D. 13
Therefore the value of x is 13.
Step-by-step explanation:
Given:
measure of an intercepted arc = 86°
Center Angle = 86°
measure of the inscribed angle creating the intercepted arc= (3x+4)°
Angle Inscribed in arc = (3x+4)°
To Find:
value of x = ?
Solution:
Inscribed Angle Theorem:
The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.
![\textrm{Angle Inscribed in arc}=\dfrac{1}{2}\textrm{Center Angle}](https://tex.z-dn.net/?f=%5Ctextrm%7BAngle%20Inscribed%20in%20arc%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctextrm%7BCenter%20Angle%7D)
Substituting the values we get
![3x+4=\dfrac{1}{2}86=43\\\\3x=39\\\\x=\dfrac{39}{3}=13\\\\x=13](https://tex.z-dn.net/?f=3x%2B4%3D%5Cdfrac%7B1%7D%7B2%7D86%3D43%5C%5C%5C%5C3x%3D39%5C%5C%5C%5Cx%3D%5Cdfrac%7B39%7D%7B3%7D%3D13%5C%5C%5C%5Cx%3D13)
Therefore the value of x is 13.
Answer:
Where is the question?
Step-by-step explanation:
For this case we have a function of the form:
![y = A * (b) ^ x](https://tex.z-dn.net/?f=%20y%20%3D%20A%20%2A%20%28b%29%20%5E%20x%20%20)
Where,
A: initial population of bacteria
b: growth rate
x: number of hours
Since the diameter is double every hour, then:
![b = 2](https://tex.z-dn.net/?f=%20b%20%3D%202%20%20)
We must now look for the value of A.
To do this, we evaluate an ordered pair of the graph:
For (1, 2):
![2 = A * (2) ^ 1](https://tex.z-dn.net/?f=%202%20%3D%20A%20%2A%20%282%29%20%5E%201%20%20)
Clearing A we have:
![2 = A * 2](https://tex.z-dn.net/?f=%202%20%3D%20A%20%2A%202%20%20)
![A = \frac{2}{2}\\A = 1](https://tex.z-dn.net/?f=%20A%20%3D%20%5Cfrac%7B2%7D%7B2%7D%5C%5CA%20%3D%201%20%20%20)
Then, the function is given by:
![y = 1 * (2) ^ x](https://tex.z-dn.net/?f=%20y%20%3D%201%20%2A%20%282%29%20%5E%20x%20%20)
For after 9 hours we have:
![y = 1 * (2) ^ 9\\y = 512](https://tex.z-dn.net/?f=%20y%20%3D%201%20%2A%20%282%29%20%5E%209%5C%5Cy%20%3D%20512%20%20)
Answer:
the diameter of the bacteria after 9 hours is:
![y = 512](https://tex.z-dn.net/?f=%20y%20%3D%20512%20)
Two answers could be 1 & 5 or 2 & 6