Let's start with triangle RST. This is a 30-60-90 triangle, which means it has the relationship x - x sqrt(3) - 2x.
If RS is 2 sqrt(3), then ST must be 2 and RT must be 4.
Triangle QRT is a 45-45-90 triangle, which means it has the relationship x - x - x sqrt(2).
If RT is 4, then RQ must also be 4.
Answer: x = 4
Hope this helps!
From the right hand side, we will need to find a way to rewriting 3x²y in terms of cube roots.
We know that 27 is 3³, so if we were to rewrite it in terms of cube roots, we will need to multiply everything by itself two more twice. (ie we can rewrite it as ∛(3x²y)³)
Hence, we can say that it's:
![\sqrt[3]{162x^{c}y^{5}} = \sqrt[3]{(3x^{2}y)^{3}} * \sqrt[3]{6y^{d}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B162x%5E%7Bc%7Dy%5E%7B5%7D%7D%20%3D%20%5Csqrt%5B3%5D%7B%283x%5E%7B2%7Dy%29%5E%7B3%7D%7D%20%2A%20%5Csqrt%5B3%5D%7B6y%5E%7Bd%7D%7D)
![= \sqrt[3]{162x^{6}y^{3+d}}](https://tex.z-dn.net/?f=%3D%20%5Csqrt%5B3%5D%7B162x%5E%7B6%7Dy%5E%7B3%2Bd%7D%7D)
Hence, c = 6 and d = 2
In the morning she worked 3 hours and 45 minutes. In the afternoon she worked 5 hours and 15 minutes. That is a total of 9 hours. At $16.50 per hour for 8 hours that comes to $132. Plus the 1 hour over time with breaks down to $18.50 plus $8.25 totaling $24.75. Add that to the $132 and she made a total of $156.75 for Wednesday’s work. I hope this helps with your question.
The answer is D as said above
The answer is A) <span>Increasing: x < 7; decreasing: x > 7</span>