Answer:
![\frac{-(-3)+-\sqrt{(-3)^2-4(2)(-5)}}{2(2)}](https://tex.z-dn.net/?f=%5Cfrac%7B-%28-3%29%2B-%5Csqrt%7B%28-3%29%5E2-4%282%29%28-5%29%7D%7D%7B2%282%29%7D)
Step-by-step explanation:
Quadratic formula: ![\frac{-b+-\sqrt{b^2-4ac} }{2a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%2B-%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D)
![2x^2-1=3x+4\\\\2x^2-3x-5=0\\\\\\frac{-(-3)+-\sqrt{(-3)^2-4(2)(-5)}}{2(2)} \\\frac{3+-\sqrt{9+40} }{4}](https://tex.z-dn.net/?f=2x%5E2-1%3D3x%2B4%5C%5C%5C%5C2x%5E2-3x-5%3D0%5C%5C%5C%5C%5C%5Cfrac%7B-%28-3%29%2B-%5Csqrt%7B%28-3%29%5E2-4%282%29%28-5%29%7D%7D%7B2%282%29%7D%20%5C%5C%5Cfrac%7B3%2B-%5Csqrt%7B9%2B40%7D%20%7D%7B4%7D)
![x = \frac{3+-7}{4}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B3%2B-7%7D%7B4%7D)
Hope this helps and God bless!
Answer: (b)
Step-by-step explanation:
Given
The letter "BHUTAN" has to be arranged
For filing the first place of 6 letter word, we have 6 choices
Similarly for filling the second place of the word, we have 5 choices as 1 letter is already filled.
In this way, the remaining places can be filled in 4, 3, 2, and 1 way
On combining the above, 6 places can be filled in
![\Rightarrow 6\times 5\times 4\times 3\times 2\times 1=6!\\\Rightarrow 720\ \text{ways}](https://tex.z-dn.net/?f=%5CRightarrow%206%5Ctimes%205%5Ctimes%204%5Ctimes%203%5Ctimes%202%5Ctimes%201%3D6%21%5C%5C%5CRightarrow%20720%5C%20%5Ctext%7Bways%7D)
Thus, option (b) is correct.
Answer:
Point D
Step-by-step explanation:
Since AB = CD the trapezoid is isosceles, which means that ∡A = ∡D
Therefore also ∡2 = ∡3 (they are half of the congruent angles)
For the properties of parallel lines (BD and AD) crossed by a transversal (BD) we have ∡3 = ∡CBD.
Now consider triangles AOD and BCD:
∡OAD (2) = ∡ADO (3) = ∡CBD (3) = ∡CDB (4)
T<span>he sum of the angles of a triangle must be 180°, t</span>herefore:
∡AOD = 180 - ∡2 - ∡3
∡BCD = 180 - ∡3 - ∡4
∡AOD = ∡BCD because their measure is the difference of congruent angles.
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