Good solution, but it's \(5*5, \) not \(5.5\) .

Hey, Manuel! What's up?

Thank you, everyone!

Wow! I wasn't active in such a long time, I'm so sorry. Finally, I saw this post! Happy birthday CPhill, hope you have a blast!

Enjoy my recipe:

Oreo flavor!

That seems better! Thank you, CPhill!

Translating this, we get \(\ln \left(10^{z+2}\right)=\ln \left(27\right).\) Now, we just apply the log rule(\(\log _a\left(x^b\right)=b\cdot \log _a\left(x\right)\)) , and get \(\left(z+2\right)\ln \left(10\right)=\ln \left(27\right).\)

Then, we can simplify this to be \(\left(z+2\right)\ln \left(10\right)=3\ln \left(3\right).\)So, we solve it, and our final answer is \(z=\frac{3\ln \left(3\right)}{\ln \left(10\right)}-2.\)

Continuing on, we have \(\frac{24}{2}, \frac{-20}{2}\). Thus, our answer is \((12,-10)\).

I hope Rom will give you a detailed answer, but there are 10 possible choices out of 90 values, so 10/90=1/9.

For Question 3, I'm getting two different answers. 9, is my first take.

Hint: Difference of Squares! a^2+b^2=c^2, c^2-b^2=a^2, (c+b)(c-b)=36.

You also know the perimeter is 18, so 6+b+c=18, b+c=12.

So, (12)(c-b)=36, c-b=3..

Now, we have two equations, and if we subtract, we will get: c=7.5