Question

this is a multi-part item. use the equation $y = \sqrt3{27x - 54} + 5$. which is an equivalent equation of the form $y = a\sqrt3{x - h} + k$? $y = 27\sqrt3{x - 2} + 5$ $y = 3\sqrt3{x - 2} + 5$ $y = -3\sqrt3{x + 2} + 5$ $y = -27\sqrt3{x + 2} + 5$

Explanation:

Step1: Factor out 27

Factor 27 from the radicand: \( y = \sqrt[3]{27(x - 2)} + 5 \)

Step2: Simplify the cube root

Simplify \( \sqrt[3]{27} \) to 3: \( y = 3\sqrt[3]{x - 2} + 5 \)

Answer:

\( y = 3\sqrt[3]{x - 2} + 5 \) (the middle option)