To determine which of the ordered pairs is part of the equation \( y = 5x^2 - 2 \), we need to substitute the x-values of each pair into the equation and see if we get the corresponding y-values.
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For the ordered pair \((1, 5)\): \[ y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not match \( y = 5 \).
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For the ordered pair \((-1, 43)\): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not match \( y = 43 \).
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For the ordered pair \((-1, 5)\): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not match \( y = 5 \).
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For the ordered pair \((-1, 3)\): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This matches \( y = 3 \).
The correct ordered pair that is part of the equation \( y = 5x^2 - 2 \) is \((-1, 3)\).