Answer:
4
Step-by-step explanation:
<span>5x-20=2(3x-10)=6x-20, eqivalent to 5x-20=6x-20, it s a contradicion; a 2. 4x - 16 - 2x = 2(x - 8), for this 4x - 16 - 2x =4x-2x-16=2x-16, and 2(x-8)=2x-16, so 4x - 16 - 2x = 2(x - 8) is a identity
3. For the case of 6x - 15 = 3(2x - 6)=6x-16, we have 6x - 15 = 6x-16 it is contradiction
4. 5x - 3(x - 4) = 2(x - 6), we know that 5x - 3(x - 4) =5x -3x+12=2x+12, and 2(x-6)=2x-12, so we have 2x+12=2x-12. That is also a cotradiction, finally we have
1.B, 2.A, 3.B, 4.B</span>
Answer:
30 in the class as total. 24/3= 8 30/3 =10
Step-by-step explanation:
![\bf \begin{array}{clclll} -6&+&6\sqrt{3}\ i\\ \uparrow &&\uparrow \\ a&&b \end{array}\qquad \begin{cases} r=\sqrt{a^2+b^2}\\ \theta =tan^{-1}\left( \frac{b}{a} \right) \end{cases}\qquad r[cos(\theta )+i\ sin(\theta )]\\\\ -------------------------------\\\\](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bclclll%7D%0A-6%26%2B%266%5Csqrt%7B3%7D%5C%20i%5C%5C%0A%5Cuparrow%20%26%26%5Cuparrow%20%5C%5C%0Aa%26%26b%0A%5Cend%7Barray%7D%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0Ar%3D%5Csqrt%7Ba%5E2%2Bb%5E2%7D%5C%5C%0A%5Ctheta%20%3Dtan%5E%7B-1%7D%5Cleft%28%20%5Cfrac%7Bb%7D%7Ba%7D%20%5Cright%29%0A%5Cend%7Bcases%7D%5Cqquad%20r%5Bcos%28%5Ctheta%20%29%2Bi%5C%20sin%28%5Ctheta%20%29%5D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C)
now, notice, there are two valid angles for such a tangent, however, if we look at the complex pair, the "a" is negative and the "b" is positive, that means, "x" is negative and "y" is positive, and that only occurs in the 2nd quadrant, so the angle is in the second quadrant, not on the fourth quadrant.
thus
![\bf 12\left[cos\left( \frac{2\pi }{3} \right) +i\ sin\left( \frac{2\pi }{3} \right) \right]](https://tex.z-dn.net/?f=%5Cbf%2012%5Cleft%5Bcos%5Cleft%28%20%5Cfrac%7B2%5Cpi%20%7D%7B3%7D%20%5Cright%29%20%2Bi%5C%20sin%5Cleft%28%20%5Cfrac%7B2%5Cpi%20%7D%7B3%7D%20%5Cright%29%20%5Cright%5D)
Step-by-step explanation:
4 the greatest common factor is four
