Perimeter of the triangle ABC is 18.7 units.
Coordinate of the point A is (4, -1), B is (-1, 4) and C is (0, -3).
Length of the side AB = ![\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E%7B2%7D%2B%28y_%7B2%7D-y_%7B1%7D%29%5E%7B2%7D%7D)
AB = ![\sqrt{(-1-4)^{2}+(4+1)^{2}} =\sqrt{50}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-1-4%29%5E%7B2%7D%2B%284%2B1%29%5E%7B2%7D%7D%20%3D%5Csqrt%7B50%7D)
AB = 7.07 units = 7.1 units ( rounded to the nearest 10th)
Length of the side BC = ![\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E%7B2%7D%2B%28y_%7B2%7D-y_%7B1%7D%29%5E%7B2%7D%7D)
BC = ![\sqrt{(0+1)^{2}+(-3-4)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%280%2B1%29%5E%7B2%7D%2B%28-3-4%29%5E%7B2%7D%7D)
BC = ![\sqrt{50}](https://tex.z-dn.net/?f=%5Csqrt%7B50%7D)
BC = 7.07 units = 7.1 units ( rounded to the nearest 10th)
Length of the side CA =![\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E%7B2%7D%2B%28y_%7B2%7D-y_%7B1%7D%29%5E%7B2%7D%7D)
CA = ![\sqrt{(4-0)^{2}+(-1+3)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%284-0%29%5E%7B2%7D%2B%28-1%2B3%29%5E%7B2%7D%7D)
CA = ![\sqrt{20}](https://tex.z-dn.net/?f=%5Csqrt%7B20%7D)
CA = 4.47 units = 4.5 ( rounded to the nearest 10th)
Perimeter of the triangle ABC = sum of all three sides = (7.1 + 7.1 + 4.5) units = 18.7 units
Answer:
102 x 5 = 100 x 5 = 500
00 x 5 = 0
+ 2 x 5 = 10
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510
Given that the equation to find the height of the firework is
h(t) = at² + vt + h₀
with a = -16 ft/s² and v = 128 ft/s. In addition, since the firework starts from the ground, then the initial height, h₀, is equal to 0. Substituting these values, we have
h(t) = -16t² + 128t + 0 = -16t² + 128t
Seeing that h(t) is a quadratic function, then it forms a parabola. To find its maximum height, we can compute for the parabola's vertex.
To find the vertex's x-coordinate, we can use
t = -b/2a = (-128)/(2 · -16) = -128/-32 = 4
Since, it takes 4 seconds for the firework to reach its maximum height, then the maximum height it reaches is equal to h(4). Hence, we have
h(4) = -16(4)² + 128(4) = -16(16) + 512 = 256
Hence, the highest that the firework can reach is equal to 256 ft.
Answer: A. 256 ft
22/6 = 3.66666... = 3.67
It costs $3.67 to rent a bike for one hour.