Answer:
(D)144.8 feet
Step-by-step explanation:
Given the equation which models the path of the baseball
![y = -0.005x^2 +0.7x + 3.5](https://tex.z-dn.net/?f=y%20%3D%20-0.005x%5E2%20%2B0.7x%20%2B%203.5)
where x is the horizontal distance, in feet, the ball travels and y is the height, in feet, of the ball.
To determine how far from the batter the ball will land, we determine the distance x at which the height, y=0.
![y = -0.005x^2 +0.7x + 3.5=0](https://tex.z-dn.net/?f=y%20%3D%20-0.005x%5E2%20%2B0.7x%20%2B%203.5%3D0)
![-0.005x^2 +0.7x + 3.5=0](https://tex.z-dn.net/?f=-0.005x%5E2%20%2B0.7x%20%2B%203.5%3D0)
We use the quadratic formula to solve.
In the quadratic equation above, a=-0.005, b=0.7, c=3.5
![x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a} \\=\dfrac{-0.7\pm\sqrt{0.7^2-4(-0.005*3.5)} }{2*-0.005} \\=\dfrac{-0.7\pm\sqrt{0.49+0.07} }{-0.01}\\=\dfrac{-0.7\pm\sqrt{0.56} }{-0.01}\\x=\dfrac{-0.7+\sqrt{0.56} }{-0.01} \: or\: x=\dfrac{-0.7-\sqrt{0.56} }{-0.01}\\x=-4.83 \: or\: x=144.83](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D%20%5C%5C%3D%5Cdfrac%7B-0.7%5Cpm%5Csqrt%7B0.7%5E2-4%28-0.005%2A3.5%29%7D%20%7D%7B2%2A-0.005%7D%20%5C%5C%3D%5Cdfrac%7B-0.7%5Cpm%5Csqrt%7B0.49%2B0.07%7D%20%7D%7B-0.01%7D%5C%5C%3D%5Cdfrac%7B-0.7%5Cpm%5Csqrt%7B0.56%7D%20%7D%7B-0.01%7D%5C%5Cx%3D%5Cdfrac%7B-0.7%2B%5Csqrt%7B0.56%7D%20%7D%7B-0.01%7D%20%5C%3A%20or%5C%3A%20x%3D%5Cdfrac%7B-0.7-%5Csqrt%7B0.56%7D%20%7D%7B-0.01%7D%5C%5Cx%3D-4.83%20%5C%3A%20or%5C%3A%20x%3D144.83)
Since x cannot be negative, x=144.8 feet to the nearest tenth of a foot.
<u>The correct option is D.</u>