the answer is 1.5 over 24. 1.5/24
i believe the answer is the third option
Given:
f(x) is an exponential function.
![f(-0.5)=27](https://tex.z-dn.net/?f=f%28-0.5%29%3D27)
![f(1.5)=21](https://tex.z-dn.net/?f=f%281.5%29%3D21)
To find:
The value of f(0.5), to the nearest hundredth.
Solution:
The general exponential function is
![f(x)=ab^x](https://tex.z-dn.net/?f=f%28x%29%3Dab%5Ex)
For, x=-0.5,
![f(-0.5)=ab^{-0.5}](https://tex.z-dn.net/?f=f%28-0.5%29%3Dab%5E%7B-0.5%7D)
...(i)
For, x=1.5,
![f(1.5)=ab^{1.5}](https://tex.z-dn.net/?f=f%281.5%29%3Dab%5E%7B1.5%7D)
...(ii)
Divide (ii) by (i).
![\dfrac{21}{27}=\dfrac{ab^{1.5}}{ab^{-0.5}}](https://tex.z-dn.net/?f=%5Cdfrac%7B21%7D%7B27%7D%3D%5Cdfrac%7Bab%5E%7B1.5%7D%7D%7Bab%5E%7B-0.5%7D%7D)
![\dfrac{7}{9}=b^2](https://tex.z-dn.net/?f=%5Cdfrac%7B7%7D%7B9%7D%3Db%5E2)
Taking square root on both sides, we get
![\dfrac{\sqrt{7}}{3}=b](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%7B7%7D%7D%7B3%7D%3Db)
![b\approx 0.882](https://tex.z-dn.net/?f=b%5Capprox%200.882)
Putting b=0.882 in (i), we get
![27=a(0.882)^{-0.5}](https://tex.z-dn.net/?f=27%3Da%280.882%29%5E%7B-0.5%7D)
![27=a(1.0648)](https://tex.z-dn.net/?f=27%3Da%281.0648%29)
![\dfrac{27}{1.0648}=a](https://tex.z-dn.net/?f=%5Cdfrac%7B27%7D%7B1.0648%7D%3Da)
![a\approx 25.357](https://tex.z-dn.net/?f=a%5Capprox%2025.357)
Now, the required function is
![f(x)=25.357(0.882)^x](https://tex.z-dn.net/?f=f%28x%29%3D25.357%280.882%29%5Ex)
Putting x=0.5, we get
![f(0.5)=25.357(0.882)^{0.5}](https://tex.z-dn.net/?f=f%280.5%29%3D25.357%280.882%29%5E%7B0.5%7D)
![f(0.5)=23.81399](https://tex.z-dn.net/?f=f%280.5%29%3D23.81399)
![f(0.5)\approx 23.81](https://tex.z-dn.net/?f=f%280.5%29%5Capprox%2023.81)
Therefore, the value of f(0.5) is 23.81.
Answer: The last option.
Step-by-step explanation:
1. By definiton, the rotation rule 90° about the origin is:
(x,y)⇒(-y,x)
2. You know that the coordinates of triangle X'Y'Z' are the following:
X'(-2,2)
Y'(0,6)
Z'(1,1)
3. Now, when you apply the rule, you obtain that the coordianates of the pre-image are the following:
X(2,2)
Y(6,0)
Z(1,-1)
Therefore, the answer is the last option.
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