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one hop this time slide to the left - inBeat

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 5Question: An elementary school student learns that the average time it takes for sunlight to reach Mars is about 12.5 minutes, while it takes 8 minutes to reach Earth. If a beam of light is sent simultaneously from the Sun to both Mars and Earth, what is the average travel time, in minutes, for the light to reach the two planets?

📌 Solution: To find the average travel time, we compute the arithmetic mean of the two times: 12.5 minutes and 8 minutes. The formula for the average is:

📌 \text{Average} = \frac{12.5 + 8}{2} = \frac{20.5}{2} = 10.25

📌 Thus, the average time is 10.25 minutes.

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Now evaluate $ T(3) $:
T(3) = (3)^2 - 6(3) + 13 = 9 - 18 + 13 = 4
Thus, the minimum time predicted by the model is $ \boxed{4} $.
Question: Factor the expression $ 16x^2 - 40x + 25 $ completely.
Check if the trinomial is a perfect square trinomial:
16x^2 = (4x)^2, \quad 25 = (5)^2, \quad -40x = 2(4x)(-5)
This confirms the expression is of the form $ a^2 - 2ab + b^2 = (a - b...
16x^2 - 40x + 25 = (4x - 5)^2
Thus, the factored form is $ \boxed{(4x - 5)^2} $.
Question: If $ x + \frac{1}{x} = 4 $, what is the value of $ x^2 + \fr...

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