Answer:
4th option
Step-by-step explanation:
The given expression is:
![\frac{1}{1+\sqrt{3}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1%2B%5Csqrt%7B3%7D%7D)
In order to simplify this expression we have to multiply and divide it with the conjugate of the denominator i.e multiply and divide the entire expression with
, as shown below:
![\frac{1}{1+\sqrt{3}}\\=\frac{1}{1+\sqrt{3}} \times \frac{1-\sqrt{3}}{1-\sqrt{3}}\\=\frac{1-\sqrt{3}}{(1)^{2}-(\sqrt{3})^{2}}\\\\ =\frac{1-\sqrt{3}}{1-3}\\\\ =\frac{1-\sqrt{3}}{-2}\\\\ =\frac{-1(1-\sqrt{3})}{2}\\\\ =\frac{-1+\sqrt{3}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1%2B%5Csqrt%7B3%7D%7D%5C%5C%3D%5Cfrac%7B1%7D%7B1%2B%5Csqrt%7B3%7D%7D%20%5Ctimes%20%5Cfrac%7B1-%5Csqrt%7B3%7D%7D%7B1-%5Csqrt%7B3%7D%7D%5C%5C%3D%5Cfrac%7B1-%5Csqrt%7B3%7D%7D%7B%281%29%5E%7B2%7D-%28%5Csqrt%7B3%7D%29%5E%7B2%7D%7D%5C%5C%5C%5C%20%3D%5Cfrac%7B1-%5Csqrt%7B3%7D%7D%7B1-3%7D%5C%5C%5C%5C%20%3D%5Cfrac%7B1-%5Csqrt%7B3%7D%7D%7B-2%7D%5C%5C%5C%5C%20%3D%5Cfrac%7B-1%281-%5Csqrt%7B3%7D%29%7D%7B2%7D%5C%5C%5C%5C%20%3D%5Cfrac%7B-1%2B%5Csqrt%7B3%7D%7D%7B2%7D)
Thus, 4th option gives the correct answer.
Answer:
see explanation
Step-by-step explanation:
the sum of the interior angles of a quadrilateral = 360°
sum the 4 angles and equate to 360
4y - 10 + y + 40 + 3y + 20 + 2y + 10 = 360 , that is
10y + 60 = 360 ( subtract 60 from both sides )
10y = 300 ( divide both sides by 10 )
y = 30
then 4 angles are
4y - 10 = 4(30) - 10 = 120 - 10 = 110°
y + 40 = 30 + 40 = 70°
3y + 20 = 3(30) + 20 = 90 + 20 = 110°
2y + 10 = 2(30) + 10 = 60 + 10 = 70°
Since the angles measures are in order around the quadrilateral, then
the opposite angles are congruent, thus quadrilateral is a parallelogram
Answer:
Are you being timed??
Step-by-step explanation:
Answer:
1. E
2. A
3. B
4. AB
5. E
6. D
7. BC
8. CD
9. A
10. C
Step-by-step explanation:
Follow PEMDAS
first simplify the parenthesis
10 + 5 = 15
6 - 5 = 1
9(15)/1
multiply 9 and 15 together
9(15) = 135
135/1 = 135
B. 135 is your answer
hope this helps