Answer:
None of the expression are equivalent to ![49^{(2t - 0.5)}](https://tex.z-dn.net/?f=49%5E%7B%282t%20-%200.5%29%7D)
Step-by-step explanation:
Given
![49^{(2t - 0.5)}](https://tex.z-dn.net/?f=49%5E%7B%282t%20-%200.5%29%7D)
Required
Find its equivalents
We start by expanding the given expression
![49^{(2t - 0.5)}](https://tex.z-dn.net/?f=49%5E%7B%282t%20-%200.5%29%7D)
Expand 49
![(7^2)^{(2t - 0.5)}](https://tex.z-dn.net/?f=%287%5E2%29%5E%7B%282t%20-%200.5%29%7D)
![7^2^{(2t - 0.5)}](https://tex.z-dn.net/?f=7%5E2%5E%7B%282t%20-%200.5%29%7D)
Using laws of indices: ![(a^m)^n = a^{mn}](https://tex.z-dn.net/?f=%28a%5Em%29%5En%20%3D%20a%5E%7Bmn%7D)
![7^{(2*2t - 2*0.5)}](https://tex.z-dn.net/?f=7%5E%7B%282%2A2t%20-%202%2A0.5%29%7D)
![7^{(4t - 1)}](https://tex.z-dn.net/?f=7%5E%7B%284t%20-%201%29%7D)
This implies that; each of the following options A,B and C must be equivalent to
or alternatively, ![7^{(4t - 1)}](https://tex.z-dn.net/?f=7%5E%7B%284t%20-%201%29%7D)
A. ![\frac{7^{2t}}{49^{0.5}}](https://tex.z-dn.net/?f=%5Cfrac%7B7%5E%7B2t%7D%7D%7B49%5E%7B0.5%7D%7D)
Using law of indices which states;
![a^{mn} = (a^m)^n](https://tex.z-dn.net/?f=a%5E%7Bmn%7D%20%3D%20%28a%5Em%29%5En)
Applying this law to the numerator; we have
![\frac{(7^{2})^{t}}{49^{0.5}}](https://tex.z-dn.net/?f=%5Cfrac%7B%287%5E%7B2%7D%29%5E%7Bt%7D%7D%7B49%5E%7B0.5%7D%7D)
Expand expression in bracket
![\frac{(7 * 7)^{t}}{49^{0.5}}](https://tex.z-dn.net/?f=%5Cfrac%7B%287%20%2A%207%29%5E%7Bt%7D%7D%7B49%5E%7B0.5%7D%7D)
![\frac{49^{t}}{49^{0.5}}](https://tex.z-dn.net/?f=%5Cfrac%7B49%5E%7Bt%7D%7D%7B49%5E%7B0.5%7D%7D)
Also; Using law of indices which states;
![\frac{a^{m}}{a^n} = a^{m-n}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5E%7Bm%7D%7D%7Ba%5En%7D%20%3D%20a%5E%7Bm-n%7D)
becomes
![49^{t-0.5}}](https://tex.z-dn.net/?f=49%5E%7Bt-0.5%7D%7D)
This is not equivalent to ![49^{(2t - 0.5)}](https://tex.z-dn.net/?f=49%5E%7B%282t%20-%200.5%29%7D)
B. ![\frac{49^{2t}}{7^{0.5}}](https://tex.z-dn.net/?f=%5Cfrac%7B49%5E%7B2t%7D%7D%7B7%5E%7B0.5%7D%7D)
Expand numerator
![\frac{(7*7)^{2t}}{7^{0.5}}](https://tex.z-dn.net/?f=%5Cfrac%7B%287%2A7%29%5E%7B2t%7D%7D%7B7%5E%7B0.5%7D%7D)
![\frac{(7^2)^{2t}}{7^{0.5}}](https://tex.z-dn.net/?f=%5Cfrac%7B%287%5E2%29%5E%7B2t%7D%7D%7B7%5E%7B0.5%7D%7D)
Using law of indices which states;
![(a^m)^n = a^{mn}](https://tex.z-dn.net/?f=%28a%5Em%29%5En%20%3D%20a%5E%7Bmn%7D)
Applying this law to the numerator; we have
![\frac{7^{2*2t}}{7^{0.5}}](https://tex.z-dn.net/?f=%5Cfrac%7B7%5E%7B2%2A2t%7D%7D%7B7%5E%7B0.5%7D%7D)
![\frac{7^{4t}}{7^{0.5}}](https://tex.z-dn.net/?f=%5Cfrac%7B7%5E%7B4t%7D%7D%7B7%5E%7B0.5%7D%7D)
Also; Using law of indices which states;
![\frac{a^{m}}{a^n} = a^{m-n}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5E%7Bm%7D%7D%7Ba%5En%7D%20%3D%20a%5E%7Bm-n%7D)
= ![7^{4t - 0.5}](https://tex.z-dn.net/?f=7%5E%7B4t%20-%200.5%7D)
This is also not equivalent to ![49^{(2t - 0.5)}](https://tex.z-dn.net/?f=49%5E%7B%282t%20-%200.5%29%7D)
C. ![7^{2t}\ *\ 49^{0.5}](https://tex.z-dn.net/?f=7%5E%7B2t%7D%5C%20%2A%5C%2049%5E%7B0.5%7D)
![7^{2t}\ *\ (7^2)^{0.5}](https://tex.z-dn.net/?f=7%5E%7B2t%7D%5C%20%2A%5C%20%287%5E2%29%5E%7B0.5%7D)
![7^{2t}\ *\ 7^{2*0.5}](https://tex.z-dn.net/?f=7%5E%7B2t%7D%5C%20%2A%5C%207%5E%7B2%2A0.5%7D)
![7^{2t}\ *\ 7^{1}](https://tex.z-dn.net/?f=7%5E%7B2t%7D%5C%20%2A%5C%207%5E%7B1%7D)
Using law of indices which states;
![a^m*a^n = a^{m+n}](https://tex.z-dn.net/?f=a%5Em%2Aa%5En%20%3D%20a%5E%7Bm%2Bn%7D)
![7^{2t+ 1}](https://tex.z-dn.net/?f=7%5E%7B2t%2B%201%7D)
This is also not equivalent to ![49^{(2t - 0.5)}](https://tex.z-dn.net/?f=49%5E%7B%282t%20-%200.5%29%7D)
Answer:
27 hours
Step-by-step explanation:
Just do the reverse. 65-11 = 54. 54 / 2 = 27.
Answer:
-1.5
Step-by-step explanation:
y=-1.5x-5