Answer:
![y=4(3)^x](https://tex.z-dn.net/?f=y%3D4%283%29%5Ex)
Step-by-step explanation:
From the table given in the question,
x y Difference Ratio
1 12 - -
2 36 36-12 = 24 ![\frac{36}{12}=3](https://tex.z-dn.net/?f=%5Cfrac%7B36%7D%7B12%7D%3D3)
3 108 108-36 = 72 ![\frac{108}{36}=3](https://tex.z-dn.net/?f=%5Cfrac%7B108%7D%7B36%7D%3D3)
4 324 324-108 = 216 ![\frac{324}{108}=3](https://tex.z-dn.net/?f=%5Cfrac%7B324%7D%7B108%7D%3D3)
5 972 972-324 = 648 ![\frac{648}{216}=3](https://tex.z-dn.net/?f=%5Cfrac%7B648%7D%7B216%7D%3D3)
There is a common ratio of 3 in each successive term.
Therefore, data given in the table will represent an exponential function.
![y=a(b)^x](https://tex.z-dn.net/?f=y%3Da%28b%29%5Ex)
For a point ![(1, 12),](https://tex.z-dn.net/?f=%281%2C%2012%29%2C)
![12=a(b)^1](https://tex.z-dn.net/?f=12%3Da%28b%29%5E1)
------(1)
For another point of the table
,
![36=a(b)^2](https://tex.z-dn.net/?f=36%3Da%28b%29%5E2)
--------(2)
Equation (2) divided by equation (1)
![\frac{ab^2}{ab}=\frac{36}{12}](https://tex.z-dn.net/?f=%5Cfrac%7Bab%5E2%7D%7Bab%7D%3D%5Cfrac%7B36%7D%7B12%7D)
![b=3](https://tex.z-dn.net/?f=b%3D3)
From equation (1),
![3a=12](https://tex.z-dn.net/?f=3a%3D12)
![a=4](https://tex.z-dn.net/?f=a%3D4)
Therefore, exponential function will be,
![y=4(3)^x](https://tex.z-dn.net/?f=y%3D4%283%29%5Ex)
Answer:
Alternate Interior Angles:
∠3 ≅ ∠5
Corresponding Angles:
∠3 ≅ ∠7
∠4 ≅ ∠8
Supplementary Angles:
∠3 is supplementary to ∠6
Step-by-step explanation:
Answer:
18.16
Step-by-step explanation:
Answer:
![3 \sqrt{11}](https://tex.z-dn.net/?f=3%20%5Csqrt%7B11%7D%20)
Step-by-step explanation:
Since we are given the hypotenuse which is 18 since it slanted, and leans on the house. And we are given one of the legs which is 15 since it is vertical. We can use the pythagorean theorem to solve for this problem.
![{a}^{2} + {b}^{2} = c {}^{2}](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20%2B%20%20%7Bb%7D%5E%7B2%7D%20%20%3D%20c%20%7B%7D%5E%7B2%7D%20)
where a and b are the legs and c is the hypotenuse l.
Let plug it in
![{a}^{2} + 15 {}^{2} = {18}^{2}](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20%2B%2015%20%7B%7D%5E%7B2%7D%20%20%3D%20%20%7B18%7D%5E%7B2%7D%20)
![{a }^{2} + 225 = 324](https://tex.z-dn.net/?f=%20%7Ba%20%7D%5E%7B2%7D%20%20%2B%20225%20%3D%20324)
![{a}^{2} = 99](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20%3D%2099)
![a = \sqrt{99}](https://tex.z-dn.net/?f=a%20%3D%20%20%5Csqrt%7B99%7D%20)
![a = \sqrt{9 \times 11}](https://tex.z-dn.net/?f=a%20%3D%20%20%5Csqrt%7B9%20%5Ctimes%2011%7D%20)
![a = 3 \sqrt{11}](https://tex.z-dn.net/?f=a%20%3D%203%20%5Csqrt%7B11%7D%20)
Option C:
We can find the value of PR using law of cosines.
Solution:
Given data:
∠Q = 18°, r = 9.5, p = 6.0
To find which length could be find in the triangle:
Law of cosines:
![a^{2}=b^{2}+c^{2}-2 b c \cos A](https://tex.z-dn.net/?f=a%5E%7B2%7D%3Db%5E%7B2%7D%2Bc%5E%7B2%7D-2%20b%20c%20%5Ccos%20A)
Substitute a = q, b = r, c = p and A = Q
![q^{2}=r^{2}+p^{2}-2 r p \cos Q](https://tex.z-dn.net/?f=q%5E%7B2%7D%3Dr%5E%7B2%7D%2Bp%5E%7B2%7D-2%20r%20p%20%5Ccos%20Q)
If we substitute the values given, we can find q.
q = PR
![PR^{2}=r^{2}+p^{2}-2 r p \cos Q](https://tex.z-dn.net/?f=PR%5E%7B2%7D%3Dr%5E%7B2%7D%2Bp%5E%7B2%7D-2%20r%20p%20%5Ccos%20Q)
Hence we can find the value of PR using law of cosines.
Option C is the correct answer.