![r = \left(\dfrac{33}{13}\right)](https://tex.z-dn.net/?f=r%20%3D%20%5Cleft%28%5Cdfrac%7B33%7D%7B13%7D%5Cright%29)
![s = \left(\dfrac{10}{13}\right)](https://tex.z-dn.net/?f=s%20%3D%20%5Cleft%28%5Cdfrac%7B10%7D%7B13%7D%5Cright%29)
Step-by-step explanation:
Let's multiply and divide the given fraction by the conjugate of the denominator:
![\dfrac{6+\sqrt{27}}{4-\sqrt{3}}×\dfrac{4+\sqrt{3}}{4+\sqrt{3}}](https://tex.z-dn.net/?f=%5Cdfrac%7B6%2B%5Csqrt%7B27%7D%7D%7B4-%5Csqrt%7B3%7D%7D%C3%97%5Cdfrac%7B4%2B%5Csqrt%7B3%7D%7D%7B4%2B%5Csqrt%7B3%7D%7D)
![\;\;\;\;= \dfrac{24 + 6\sqrt{3} + 4\sqrt{3} + \sqrt{27}\sqrt{3}}{13}](https://tex.z-dn.net/?f=%5C%3B%5C%3B%5C%3B%5C%3B%3D%20%5Cdfrac%7B24%20%2B%206%5Csqrt%7B3%7D%20%2B%204%5Csqrt%7B3%7D%20%2B%20%5Csqrt%7B27%7D%5Csqrt%7B3%7D%7D%7B13%7D)
![\;\;\;\;=\frac{1}{13}(24 + 10\sqrt{3} + \sqrt{81})](https://tex.z-dn.net/?f=%5C%3B%5C%3B%5C%3B%5C%3B%3D%5Cfrac%7B1%7D%7B13%7D%2824%20%2B%2010%5Csqrt%7B3%7D%20%2B%20%5Csqrt%7B81%7D%29)
![\;\;\;\;=\frac{1}{13}(33 + 10\sqrt{3})](https://tex.z-dn.net/?f=%5C%3B%5C%3B%5C%3B%5C%3B%3D%5Cfrac%7B1%7D%7B13%7D%2833%20%2B%2010%5Csqrt%7B3%7D%29)
![\;\;\;\;=\left(\dfrac{33}{13}\right) + \left(\dfrac{10}{13}\right)\dfrac{\sqrt{3}}{13}](https://tex.z-dn.net/?f=%5C%3B%5C%3B%5C%3B%5C%3B%3D%5Cleft%28%5Cdfrac%7B33%7D%7B13%7D%5Cright%29%20%2B%20%5Cleft%28%5Cdfrac%7B10%7D%7B13%7D%5Cright%29%5Cdfrac%7B%5Csqrt%7B3%7D%7D%7B13%7D)
We can see here that
![r = \left(\dfrac{33}{13}\right)](https://tex.z-dn.net/?f=r%20%3D%20%5Cleft%28%5Cdfrac%7B33%7D%7B13%7D%5Cright%29)
![s = \left(\dfrac{10}{13}\right)](https://tex.z-dn.net/?f=s%20%3D%20%5Cleft%28%5Cdfrac%7B10%7D%7B13%7D%5Cright%29)
$140.2375, $140.24(rounded to hundredth)
If either a or b or both are 0, we have |ab|= 0 and |a|*|b|=0
For any real number a and b non equal to 0, one of the 3 following cases are true:
i) both a and b are positive:
then |ab|=ab, |a|=a, |b|=b
ab=a*b
|ab|=|a|*|b|
ii) both a and b are negative:
then |a|=-a, |b|=-b
|ab|=ab, for example if a=-3, b=-7: |(-3)(-7)|=|21|=21=(-3)(-7)=a*b
so
ab=(-a)*(-b)
|ab|=|a|*|b|
iii) one of them is positive and the other negative.
In our case let a be positive, b negative:
|a|=a, |b|=-b,
and |ab|=-ab, for example if a=3, b=-4; |3*(-4)|=|-12|=12=3*(4)=a*(-b)
thus:
-ab= a*(-b)
|ab|= |a||b|.
In each possible case of the signs of a and b we get: |ab|= |a||b|.
Answer:
<h2><u><em>
94°</em></u></h2>
Step-by-step explanation:
Find x
(180 - 36) : 2 =
72°
so angle 2x is 144°
sum of all interior angles = 720°
Find y
720 - 144 - 111 - 105 - 165 - 101 =
94°
Answer: Equations (b) and (e) do not have solutions
Step-by-step explanation: b) The x cancels out (-10x + 35) = -10x + 318; 35 = 318???? NO. e) 3(x + 2) + 1 = x + 2(4 + x); 3x + 7 = 3x + 8. The x cancels out again.
The other s can be solved for x.