Let's break down each part of your question step by step.
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Equivalent expression for \( \sqrt{600} \)
To simplify \( \sqrt{600} \): \[ \sqrt{600} = \sqrt{100 \times 6} = \sqrt{100} \times \sqrt{6} = 10\sqrt{6} \] So the expression equivalent to \( \sqrt{600} \) is 10 square root of 6.
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Value of \( g(20) \) where \( g(x) = 6(2x + 7) \)
Substitute \( x = 20 \) into the function: \[ g(20) = 6(2(20) + 7) = 6(40 + 7) = 6(47) = 282 \]
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Value of \( f(-2) \) where \( f(x) = -3x^2 + 5 \)
Substitute \( x = -2 \) into the function: \[ f(-2) = -3(-2)^2 + 5 = -3(4) + 5 = -12 + 5 = -7 \]
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Expressions equivalent to \( 12x^2 - 48x + 48 \)
Let's factor \( 12x^2 - 48x + 48 \): \[ 12(x^2 - 4x + 4) = 12(x - 2)^2 \] So one correct answer is 12(x − 2)².
Now let's examine the other options for correctness:
- −12(x² + 4x + 4): This is equivalent to \( -12(x + 2)^2 \), which is not equivalent.
- 12(x − 4)(x − 1): This is not equivalent, as this expands to \( 12(x^2 - 5x + 4) \).
- −12(x + 2)²: This is not equivalent, as it represents a reflection and different dimensions.
- 12(x² − 4x + 4): This expression is the same as what we factored, thus is also equivalent.
So, the two correct responses are:
- 12(x − 2)²
- 12(x² − 4x + 4)
In summary:
- Equivalent to \( \sqrt{600} \): 10 square root of 6
- Value of \( g(20) \): 282
- Value of \( f(-2) \): -7
- Equivalent expressions: 12(x − 2)² and 12(x² − 4x + 4).