Answer:
The answer would be y=-8
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.
Answer: 60 degree
Explanation: The sum of the three interior angles of a triangle is always 180°.
180-80-40=60 degree.
Answer:
-384
Step-by-step explanation:
geometric sequence : every new element is generated by multiplying the previous element always with the same number r.
a(n) = a(n-1) * r
a(n) = a(1) * r^(n-1)
so, a(1) = 3, r = -2
a(8) = ?
a(8) = a(1) * r^7 = 3 * (-2)^7
a negative number to an uneven power is again a negative number.
so, (-2)^7 = -128
3 * -128 = -384 = a(8)
Answer:
z=(x-1)/2
Step-by-step explanation:
this is the correct answer
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