The correct congruence statement for the triangles shown is∆ BLG~=∆PFX.
I think it's 12 and 18.
They both have 6 factors.
Answer:
from least to greatest
1.25, -(-2). 3, 4
Step-by-step explanation:
it's just from least to greatest and to negatives cancel out leading 2 to become a positive number. The difference between 1.25 and 2 is 0.75 so you would have them 0.75 distance a part and the rest with 1 distance apart.
Question: Which equation is equivalent to ![16^{2 p}=32^{p+3}?](https://tex.z-dn.net/?f=16%5E%7B2%20p%7D%3D32%5E%7Bp%2B3%7D%3F)
Option A: ![8^{4 p}=8^{4 p+3}](https://tex.z-dn.net/?f=8%5E%7B4%20p%7D%3D8%5E%7B4%20p%2B3%7D)
Option B: ![8^{4 p}=8^{4 p+12}](https://tex.z-dn.net/?f=8%5E%7B4%20p%7D%3D8%5E%7B4%20p%2B12%7D)
Option C: ![2^{8 p}=2^{5 p+15}](https://tex.z-dn.net/?f=2%5E%7B8%20p%7D%3D2%5E%7B5%20p%2B15%7D)
Option D: ![2^{8 p}=2^{5 p+3}](https://tex.z-dn.net/?f=2%5E%7B8%20p%7D%3D2%5E%7B5%20p%2B3%7D)
Answer:
Option C: ![2^{8 p}=2^{5 p+15}](https://tex.z-dn.net/?f=2%5E%7B8%20p%7D%3D2%5E%7B5%20p%2B15%7D)
Solution:
Given expression: ![16^{2 p}=32^{p+3}](https://tex.z-dn.net/?f=16%5E%7B2%20p%7D%3D32%5E%7Bp%2B3%7D)
Convert 16 to the base 2 and 32 to the base 2.
![(2^4)^{2 p}=(2^5)^{p+3}](https://tex.z-dn.net/?f=%282%5E4%29%5E%7B2%20p%7D%3D%282%5E5%29%5E%7Bp%2B3%7D)
Using exponential rule: ![\left(a^{b}\right)^{c}=a^{b c}](https://tex.z-dn.net/?f=%5Cleft%28a%5E%7Bb%7D%5Cright%29%5E%7Bc%7D%3Da%5E%7Bb%20c%7D)
![2^{8p}=2^{5p+15}](https://tex.z-dn.net/?f=2%5E%7B8p%7D%3D2%5E%7B5p%2B15%7D)
Using the rule, ![\text { If } d^{f(x)}=d^{g(x)}, \text { then } f(x)=g(x)](https://tex.z-dn.net/?f=%5Ctext%20%7B%20If%20%7D%20d%5E%7Bf%28x%29%7D%3Dd%5E%7Bg%28x%29%7D%2C%20%5Ctext%20%7B%20then%20%7D%20f%28x%29%3Dg%28x%29)
8p = 5p + 15
3p = 15
p = 5
Substitute p = 5 in given expression, we get
![16^{10}=32^{8}\ \ \ \ \ \ \ \ \ \Rightarrow 1099511627776=1099511627776](https://tex.z-dn.net/?f=16%5E%7B10%7D%3D32%5E%7B8%7D%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%20%5CRightarrow%201099511627776%3D1099511627776)
<u>To find the equivalent expression to the given expression:</u>
Option A: ![8^{4 p}=8^{4 p+3}](https://tex.z-dn.net/?f=8%5E%7B4%20p%7D%3D8%5E%7B4%20p%2B3%7D)
Using the rule, ![\text { If } d^{f(x)}=d^{g(x)}, \text { then } f(x)=g(x)](https://tex.z-dn.net/?f=%5Ctext%20%7B%20If%20%7D%20d%5E%7Bf%28x%29%7D%3Dd%5E%7Bg%28x%29%7D%2C%20%5Ctext%20%7B%20then%20%7D%20f%28x%29%3Dg%28x%29)
⇒ 4p = 4p + 3
⇒ 0p = 3
No solution for p, so it is not equivalent to the given expression.
Option B: ![8^{4 p}=8^{4 p+12}](https://tex.z-dn.net/?f=8%5E%7B4%20p%7D%3D8%5E%7B4%20p%2B12%7D)
Using the rule, ![\text { If } d^{f(x)}=d^{g(x)}, \text { then } f(x)=g(x)](https://tex.z-dn.net/?f=%5Ctext%20%7B%20If%20%7D%20d%5E%7Bf%28x%29%7D%3Dd%5E%7Bg%28x%29%7D%2C%20%5Ctext%20%7B%20then%20%7D%20f%28x%29%3Dg%28x%29)
⇒ 4p = 4p + 12
⇒ 0p = 12
No solution for p, so it is not equivalent to the given expression.
Option C: ![2^{8 p}=2^{5 p+15}](https://tex.z-dn.net/?f=2%5E%7B8%20p%7D%3D2%5E%7B5%20p%2B15%7D)
Using the rule, ![\text { If } d^{f(x)}=d^{g(x)}, \text { then } f(x)=g(x)](https://tex.z-dn.net/?f=%5Ctext%20%7B%20If%20%7D%20d%5E%7Bf%28x%29%7D%3Dd%5E%7Bg%28x%29%7D%2C%20%5Ctext%20%7B%20then%20%7D%20f%28x%29%3Dg%28x%29)
⇒ 8p = 5p + 15
⇒ 3p = 15
⇒ p = 5
Substitute p = 5 in
, we get
![2^{40}=2^{40}\ \ \ \ \ \ \ \ \ \Rightarrow 1099511627776=1099511627776](https://tex.z-dn.net/?f=2%5E%7B40%7D%3D2%5E%7B40%7D%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%20%5CRightarrow%201099511627776%3D1099511627776)
It is equivalent to the given expression.
Option D: ![2^{8 p}=2^{5 p+3}](https://tex.z-dn.net/?f=2%5E%7B8%20p%7D%3D2%5E%7B5%20p%2B3%7D)
Using the rule, ![\text { If } d^{f(x)}=d^{g(x)}, \text { then } f(x)=g(x)](https://tex.z-dn.net/?f=%5Ctext%20%7B%20If%20%7D%20d%5E%7Bf%28x%29%7D%3Dd%5E%7Bg%28x%29%7D%2C%20%5Ctext%20%7B%20then%20%7D%20f%28x%29%3Dg%28x%29)
⇒ 8p = 5p + 3
⇒ 3p = 3
⇒ p = 1
Substitute p = 1 in
, we get
![2^{8}=2^{8}\ \ \ \ \ \ \ \ \ \Rightarrow 256=256](https://tex.z-dn.net/?f=2%5E%7B8%7D%3D2%5E%7B8%7D%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%20%5CRightarrow%20256%3D256)
It is not equivalent to the given expression.
Hence Option C is the correct answer.