If we are to connect the root of the tree to a person to the top of the tree, we form two right triangles. If we let x and and 200 - x be the distance of Harris and Annabelle from the tree, respectively and h be the height, we form the trigonometric functions,
tan 30° = h/x
tan 35° = h/(200 - x)
The values of h and x in the equations are 63.28 ft and 109.62 ft, respectively. Thus, the answer to this item is approximately 63.28 ft.
<span>55 = 11 * 5 and 132 = 11 * 12. The numerator and the denominator of the fraction are both divisible by 11. Therefore we will divide both by 11: 55/132 : 11/11 = 5/12 ( or 5 to 12 ). Answer: B ) 5 to 12.Hope this helps. Let me know if you need additional help!I hope that I could help :) sometines those questions are tricky. Let me know if you need additional help</span>
Answer:
A
Step-by-step explanation:
For a quadratic equation in standard form:
![ax^2+bx+c=0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0)
The discriminant, symoblized as Δ, is given by:
![\Delta=b^2-4ac](https://tex.z-dn.net/?f=%5CDelta%3Db%5E2-4ac)
If:
- Δ>0 (positive), then our quadratic has two real roots.
- Δ<0 (negative), then our quadratic has no real roots. It does, however, have two imaginary (complex) roots.
- And if Δ=0 (zero), then our quadratic has exactly one real root.
We have the equation:
![-2x^2+x-28=0](https://tex.z-dn.net/?f=-2x%5E2%2Bx-28%3D0)
Thus:
![a=-2, b=1, c=-28](https://tex.z-dn.net/?f=a%3D-2%2C%20b%3D1%2C%20c%3D-28)
Substituting them for our discriminant:
![\Delta=(1)^2-(4)(-2)(-28)](https://tex.z-dn.net/?f=%5CDelta%3D%281%29%5E2-%284%29%28-2%29%28-28%29)
Evaluate:
![\Delta=1-224=-223](https://tex.z-dn.net/?f=%5CDelta%3D1-224%3D-223%3C0)
Since our discriminant is negative, there is no real solutions.
Hence, our answer is A.