Subjects algebra

Distance Time 6B6Fb7

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1. **State the problem:** We have a vehicle traveling 315 miles over 6 hours. The distance traveled as a function of time is $d(t)$, where $t$ is in hours. 2. **Find the function:** Since the vehicle travels 315 miles in 6 hours, the average speed is $$\frac{315}{6} = 52.5$$ miles per hour. The distance function is therefore $$d(t) = 52.5t$$. 3. **Domain and range:** - The domain is the time interval from 0 to 6 hours, so $$0 \leq t \leq 6$$. - The range is the distance traveled from 0 to 315 miles, so $$0 \leq d(t) \leq 315$$. 4. **Check each ordered pair:** - For $(3.6, 240)$: Calculate $d(3.6) = 52.5 \times 3.6 = 189$, which is not 240, so incorrect. - For $(2, 100)$: Calculate $d(2) = 52.5 \times 2 = 105$, which is not 100, so incorrect. - For $(64, 385)$: $t=64$ is outside the domain $[0,6]$, so incorrect. - For $(18, 235)$: $t=18$ is outside the domain $[0,6]$, so incorrect. - For $(0, 315)$: Calculate $d(0) = 52.5 \times 0 = 0$, which is not 315, so incorrect. 5. **Conclusion:** None of the given ordered pairs correctly represent values from the domain and range of the function $d(t) = 52.5t$ over $0 \leq t \leq 6$. **Final answer:** No ordered pairs from the list are correct.