Answer: ![x=-\frac{3}{5}](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7B3%7D%7B5%7D)
Step-by-step explanation:
By the negative exponent rule, you have that:
![(\frac{1}{a})^n=a^{-n}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7Ba%7D%29%5En%3Da%5E%7B-n%7D)
By the exponents properties, you know that:
![(m^n)^l=m^{(nl)}](https://tex.z-dn.net/?f=%28m%5En%29%5El%3Dm%5E%7B%28nl%29%7D)
You can rewrite 16 and 9 as following:
16=4²
9=3²
Therefore, you can rewrite the left side of the equation has following:
![(\frac{4^2}{3^2})^{(2x+5)}=(\frac{3}{4})^{(x-7)}\\\\(\frac{3^2}{4^2})^{-(2x+5)}=(\frac{3}{4})^{(x-7)}\\\\(\frac{3}{4})^{-2(2x+5)}=(\frac{3}{4})^{(x-7)}](https://tex.z-dn.net/?f=%28%5Cfrac%7B4%5E2%7D%7B3%5E2%7D%29%5E%7B%282x%2B5%29%7D%3D%28%5Cfrac%7B3%7D%7B4%7D%29%5E%7B%28x-7%29%7D%5C%5C%5C%5C%28%5Cfrac%7B3%5E2%7D%7B4%5E2%7D%29%5E%7B-%282x%2B5%29%7D%3D%28%5Cfrac%7B3%7D%7B4%7D%29%5E%7B%28x-7%29%7D%5C%5C%5C%5C%28%5Cfrac%7B3%7D%7B4%7D%29%5E%7B-2%282x%2B5%29%7D%3D%28%5Cfrac%7B3%7D%7B4%7D%29%5E%7B%28x-7%29%7D)
As the base are equal, then:
![-2(2x+5)=x-7](https://tex.z-dn.net/?f=-2%282x%2B5%29%3Dx-7)
Solve for x:
![-2(2x+5)=x-7\\-4x-10=x-7\\-4x-x=-7+10\\-5x=3\\x=-\frac{3}{5}](https://tex.z-dn.net/?f=-2%282x%2B5%29%3Dx-7%5C%5C-4x-10%3Dx-7%5C%5C-4x-x%3D-7%2B10%5C%5C-5x%3D3%5C%5Cx%3D-%5Cfrac%7B3%7D%7B5%7D)
Answer:
9
Step-by-step explanation:
two negatives make a positve
2 mph is the speed that he is walking
Answer:
160 ft²
Step-by-step explanation:
The width is 40% of the length, so is ...
0.40 × 20 ft = 8 ft
The area is the product of length and width:
A = LW
A = (20 ft)(8 ft) = 160 ft²