Answer:
√65 ft = 8.1 ft
Step-by-step explanation:
We solve using Pythagoras Theorem
c² = a² + b²
c = √a² + b²
Where c = Length of the Hypotenuse
a = 4ft , b = 7ft
Hence
c = √4² + 7²
c = √16 + 49
c = √(65)
c = 8.0622577483 ft
Approximately = 8.1 ft
Therefore, the length of the hypotenuse is √65 ft = 8.1 ft
Yes, the table represents a function.
None of the independent (x) values are repeated and each one has a corresponding (y) value.
If you had a repeated (x) value in the table, it would not represent a function.
Answer:

The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.
Thus, domain of f(x): x∈R = range of f¯¹(x)
and range of f(x): x∈R =domain of f¯¹(x)
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
The sum of the angles equals 540
There are 3 angles that measure (x - 30) and 2 angles that measure (x)
3(x - 30) + 2(x) = 540
3x - 90 + 2x = 540
5x - 90 = 540
5x = 630
x = 126
x - 30 = 126 - 30 = 96
Answer: x = 126, x-30 = 96