Answer:
B
Step-by-step explanation:
We are given the function:
![\displaystyle f(x) = x^2 + 12x + 36](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%20%3D%20x%5E2%20%2B%2012x%20%2B%2036)
And we want to determine the value of:
![\displaystyle f^{-1}(225)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%5E%7B-1%7D%28225%29)
Let this value equal <em>a</em>. In other words:
![\displaystyle f^{-1}(225) = a](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%5E%7B-1%7D%28225%29%20%3D%20a)
Then by the definition of inverse functions:
![\displaystyle \text{If } f^{-1}(225) = a\text{, then } f(a) = 225](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctext%7BIf%20%7D%20f%5E%7B-1%7D%28225%29%20%3D%20a%5Ctext%7B%2C%20then%20%7D%20f%28a%29%20%3D%20225)
Hence:
![\displaystyle f(a) =225 = (a)^2 + 12(a) + 36](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28a%29%20%3D225%20%3D%20%28a%29%5E2%20%2B%2012%28a%29%20%2B%2036)
Solve for <em>a: </em>
![\displaystyle \begin{aligned} 225 &= a^2 + 12a + 36 \\ \\ a^2 + 12a -189 &= 0 \\ \\ (a + 21)(a-9) &= 0\end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7D%20225%20%26%3D%20a%5E2%20%2B%2012a%20%2B%2036%20%5C%5C%20%5C%5C%20a%5E2%20%2B%2012a%20-189%20%26%3D%200%20%5C%5C%20%5C%5C%20%28a%20%2B%2021%29%28a-9%29%20%26%3D%200%5Cend%7Baligned%7D)
By the Zero Product Property:
![\displaystyle a + 21 = 0 \text{ or } a - 9 = 0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20a%20%2B%2021%20%3D%200%20%5Ctext%7B%20or%20%7D%20a%20-%209%20%3D%200)
Hence:
![\displaystyle a = -21 \text{ or } a = 9](https://tex.z-dn.net/?f=%5Cdisplaystyle%20a%20%3D%20-21%20%5Ctext%7B%20or%20%7D%20a%20%3D%209)
Thus, f(9) = 225. Consequently, f⁻¹(225) = 9.
In conclusion, our answer is B.
I'm doing 3
For 3, using a table is very similar to a double number because the numbers are matching up in both ways.
On the bottom of a double number line we have like, for example,-- the bottom of the double number line would have batches. And its 1, 2, 3 ,4 , etc.
And on a table, it would be the same, the numbers on both diagrams have the same methods, have same way of lining things up but they're just drawn differently.
Hope this helped!
C, because the independent variable would be the variable that is changing -- in this case, the temperature. The dependent variable changes according to the independent variable, and is called so because it depends on the temperature of the pool.
Answer:
3
Step-by-step explanation:
15-2x=9
or,-2x=9-15
or, x=-6/-2
x=3
Answer:
In triangle ABC, angle B is obtuse.
Step-by-step explanation:
The type of triangle is obtuse, angle A and C are acute, angle B is obtuse.