For the first question, we need to determine which of the given ordered pairs satisfies the equation \(y = 2.5x - 2\).
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For the ordered pair \((-2, 0)\): \[ y = 2.5(-2) - 2 = -5 - 2 = -7 \quad (\text{not } 0) \]
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For the ordered pair \((2, 5)\): \[ y = 2.5(2) - 2 = 5 - 2 = 3 \quad (\text{not } 5) \]
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For the ordered pair \((2, 3)\): \[ y = 2.5(2) - 2 = 5 - 2 = 3 \quad (\text{is } 3) \]
Thus, the pair \((2, 3)\) satisfies the equation, so the answer is:
(2, 3)
For the second question, we need to determine which allocation is reasonable given that there are 12 new cheerleaders in total.
- \(8\) varsity cheerleaders and \(4\) junior varsity cheerleaders: This sums to \(8 + 4 = 12\) (reasonable).
- \(0\) varsity cheerleaders and \(12\) junior varsity cheerleaders: This sums to \(0 + 12 = 12\) (reasonable).
- \(15\) varsity cheerleaders and \(-3\) junior varsity cheerleaders: This sums to \(15 - 3 = 12\), but you cannot have negative cheerleaders (not reasonable).
- \(8\) varsity cheerleaders and \(8\) junior varsity cheerleaders: This sums to \(8 + 8 = 16\) (not reasonable).
Thus, the reasonable allocations are:
8 varsity cheerleaders and 4 junior varsity cheerleaders or 0 varsity cheerleaders and 12 junior varsity cheerleaders.
1 answer