Video: US-SAT04S4-Q25-590132562152

If 𝑒 = π‘₯ + 4 and 𝑒 β‰₯ 0. Which of the following is equivalent to (π‘₯ βˆ’ 3)Β² √π‘₯ + 4. [A] (𝑒 βˆ’ 7)Β² βˆšπ‘’ [B] (𝑒 βˆ’ 4)Β² βˆšπ‘’ [C] (𝑒 βˆ’ 3)Β² βˆšπ‘’ [D] (𝑒 + 1)Β² βˆšπ‘’.

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Video Transcript

If 𝑒 is equal to π‘₯ plus four and 𝑒 is greater than or equal to zero. Which of the following is equivalent to π‘₯ minus three squared multiplied by the square root of π‘₯ plus four. Is it A) 𝑒 minus seven squared multiplied by the square root of 𝑒. B) 𝑒 minus four squared multiplied by the square root of 𝑒. C) 𝑒 minus three squared multiplied by the square root of 𝑒. Or D) 𝑒 plus one squared multiplied by the square root of 𝑒.

Our aim in this question is to find an expression that is equivalent to π‘₯ minus three squared multiplied by the square root of π‘₯ plus four in terms of 𝑒. We’re told that 𝑒 is equal to π‘₯ plus four. This means that we can replace the π‘₯ plus four in the second part of our expression with 𝑒. This gives us the square root of 𝑒. If 𝑒 is equal to π‘₯ plus four, then 𝑒 minus four is equal to π‘₯ as we can subtract four from both sides of the equation. This means that we can replace the π‘₯ in the first part of our expression with 𝑒 minus four. This means that the expression inside the bracket is 𝑒 minus four minus three. Negative four minus three is equal to negative seven. This means that we can simplify the bracket to 𝑒 minus seven.

The expression has now become 𝑒 minus seven squared multiplied by the square root of 𝑒. When 𝑒 is equal to π‘₯ plus four, then the expression π‘₯ minus three squared multiplied by the square root of π‘₯ plus four is equivalent to 𝑒 minus seven squared multiplied by the square root of 𝑒. The correct answer was option A.

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