Step-by-step explanation:
I assume that "ground" is at 0 ft height. which is in an actual scenario not airways the case.
y = -16x² + 64x + 89
shows us that the tower is 89 ft tall (the result for x = 0, at the start).
anyway, if the original assumption is correct, then we need to solve
0 = -16x² + 64x + 89
the general solution for such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/)2a)
in our case
a = -16
b = 64
c = 89
x = (-64 ± sqrt(64² - 4×-16×89))/(2×-16) =
= (-64 ± sqrt(4096 + 5696))/-32 =
= (-64 ± sqrt(9792))/-32
x1 = (-64 + 98.95453501...)/-32 = -1.092329219... s
x2 = (-64 - 98.95453501...)/-32 = 5.092329219... s
the negative solution for time is but useful here (it would be the time calculated back to ground at the start).
so, x2 is our solution.
the rocket hits the ground after about 5.09 seconds.
Answer:
Δ BEC ≅ Δ AED
Step-by-step explanation:
Consider triangles BCA and ADB. Each of them share a common side, AB. Respectively each we should be able to tell that AD is congruent to BC, and DB is congruent to CA, so by SSS the triangles should be congruent.
_________
So another possibility is triangles BEC, and AED. As you can see, by the Vertical Angles Theorem m∠BEC = m∠ADE, resulting in the congruency of an angle, rather a side. As mentioned before AD is congruent to BC, and perhaps another side is congruent to another in the same triangle. It should be then, by SSA that the triangles are congruent - but that is not an option. SSA does is one of the exceptions, a rule that is not permitted to make the triangles congruent. Therefore, it is highly unlikely that triangles BEC and AED are congruent, but that is what our solution, comparative to the rest.
Δ BEC ≅ Δ AED .... this is our solution
here's the solution,
let the length of shorter peice = x
then the lenght of longer peice = 6x + 8
now, we know that the sum of length of peices measures 99 feet,
So,
=》x + 6x + 8 = 99
=》7x = 91
=》x = 13
shorter piece length = 13 feet
longer peice length = 13 × 6 + 8 = 78 + 8 = 86 feet
In your question where as the amount of gasoline that 80 drivers bought to fill their cars gas tanks is shown in your diagram and the problem as to find how many drivers bought more than 12 gallons and the best answer would be 36. I hope you are satistfied with my answer and if you need some clarification, please feel free to ask for more
Answer:9.75
Step-by-step explanation:12x12 =144 and 7x7= 49 subtract 144-49 and get 95 the square root of 95 is approximately 9.747 rounded to the nearest hundredths place is 9.75
