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Which of the following ordered pairs is part of the solution set for the equation y=5x2−2 ?%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A(−1,43)%0D%0Aleft parenthesis negative 1 comma 43 right parenthesis%0D%0A%0D%0A(−1,5)%0D%0Aleft parenthesis negative 1 comma 5 right parenthesis%0D%0A%0D%0A(−1,3)%0D%0Aleft parenthesis negative 1 comma 3 right parenthesis%0D%0A%0D%0A(1,5)

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To determine which ordered pair is part of the solution set for the equation \( y = 5x^2 - 2 \), we will substitute the x-value from each ordered pair into the equation and see if the resulting y-value matches.

  1. For the ordered pair \( (-1, 43) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not match 43.

  2. For the ordered pair \( (-1, 5) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not match 5.

  3. For the ordered pair \( (-1, 3) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This matches 3.

  4. For the ordered pair \( (1, 5) \): \[ y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not match 5.

The only ordered pair that is part of the solution set for the equation \( y = 5x^2 - 2 \) is \( (-1, 3) \).