The sum of the squares of two consecutive integers is 145. What is the larger integer?
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- A car travels 120 miles in 3 hours. If it continues at the same speed, how many miles will it travel in 7 hours?
- Speed = \( \frac{120 \text{ miles}}{3 \text{ hours}} = 40 \text{ mph} \)
- Distance in 7 hours: \( 40 \times 7 = 280 \) miles
- Let the integers be \( x \) and \( x+1 \).
- Equation: \( x^2 + (x+1)^2 = 145 \)
- Expand: \( x^2 + x^2 + 2x + 1 = 145 \) → \( 2x^2 + 2x + 1 = 145 \)
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