10

Set 7: Quadratic Equations

Explanation

Answer: A

The path of a basketball is y=−0.1x2+x+6y = -0.1x^2 + x + 6, where x is horizontal distance. How far does it travel horizontally before hitting the ground?

A.

14.4 ft

✓ Correct
B.

10 ft

C.

5 ft

D.

20 ft

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Solve −0.1x2+x+6=0-0.1 x^2 + x + 6 = 0. 1. Multiply by -10: x2−10x−60=0x^2 - 10 x - 60 = 0. 2. Quadratic formula: x=10±100−4(1)(−60)2x = \frac{10 \pm \sqrt{100 - 4(1)(-60)}}{2}. 3. x=10±3402≈10±18.442x = \frac{10 \pm \sqrt{340}}{2} \approx \frac{10 \pm 18.44}{2}. 4. Positive root: x≈28.44/2=14.22x \approx 28.44 / 2 = 14.22. Closest option is 14.4. Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.

Key Steps:

•

The correct answer is 14.4 ft

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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