To determine which of the given points is a solution to the linear inequality \( y \leq 2x - 445 \), we will substitute each point into the inequality and check whether it holds true.
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For point (−17,−3812): \[ y = -3812 \quad \text{and} \quad x = -17 \] Substitute into the inequality: \[ -3812 \leq 2(-17) - 445 \] Calculate the right side: \[ 2(-17) = -34 \quad \text{so, } -34 - 445 = -479 \] Now compare: \[ -3812 \leq -479 \quad \text{(false)} \]
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For point (1/2,−3): \[ y = -3 \quad \text{and} \quad x = 1/2 \] Substitute into the inequality: \[ -3 \leq 2(1/2) - 445 \] Calculate the right side: \[ 2(1/2) = 1 \quad \text{so, } 1 - 445 = -444 \] Now compare: \[ -3 \leq -444 \quad \text{(false)} \]
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For point (−3,−10): \[ y = -10 \quad \text{and} \quad x = -3 \] Substitute into the inequality: \[ -10 \leq 2(-3) - 445 \] Calculate the right side: \[ 2(-3) = -6 \quad \text{so, } -6 - 445 = -451 \] Now compare: \[ -10 \leq -451 \quad \text{(false)} \]
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For point (1/2,−5): \[ y = -5 \quad \text{and} \quad x = 1/2 \] Substitute into the inequality: \[ -5 \leq 2(1/2) - 445 \] Calculate the right side: \[ 2(1/2) = 1 \quad \text{so, } 1 - 445 = -444 \] Now compare: \[ -5 \leq -444 \quad \text{(true)} \]
Thus, the only point that satisfies the inequality \( y \leq 2x - 445 \) is (1/2,−5).
Therefore, the solution is: d. (1/2,−5).