Answer:
Step-by-step explanation:
![1-2\sin^2x=\sin x\\\\\text{substitute}\ t=\sin x,\ t\in[-1,\ 1]\\\\1-2t^2=t\qquad\text{subtract t from both sides}\\\\-2t^2-t+1=0\qquad\text{change the signs}\\\\2t^2+t-1=0\\\\2t^2+2t-t-1=0\\\\2t(t+1)-1(t+1)=0\\\\(t+1)(2t-1)=0\iff t+1=0\ \vee\ 2t-1=0\\\\t+1=0\qquad\text{subtract 1 from both sides}\\\boxed{t=-1}\\\\2t-1=0\qquad\text{add 1 to both sides}\\2t=1\qquad\text{divide both sides by 2}\\\boxed{t=\dfrac{1}{2}}](https://tex.z-dn.net/?f=1-2%5Csin%5E2x%3D%5Csin%20x%5C%5C%5C%5C%5Ctext%7Bsubstitute%7D%5C%20t%3D%5Csin%20x%2C%5C%20t%5Cin%5B-1%2C%5C%201%5D%5C%5C%5C%5C1-2t%5E2%3Dt%5Cqquad%5Ctext%7Bsubtract%20t%20from%20both%20sides%7D%5C%5C%5C%5C-2t%5E2-t%2B1%3D0%5Cqquad%5Ctext%7Bchange%20the%20signs%7D%5C%5C%5C%5C2t%5E2%2Bt-1%3D0%5C%5C%5C%5C2t%5E2%2B2t-t-1%3D0%5C%5C%5C%5C2t%28t%2B1%29-1%28t%2B1%29%3D0%5C%5C%5C%5C%28t%2B1%29%282t-1%29%3D0%5Ciff%20t%2B1%3D0%5C%20%5Cvee%5C%202t-1%3D0%5C%5C%5C%5Ct%2B1%3D0%5Cqquad%5Ctext%7Bsubtract%201%20from%20both%20sides%7D%5C%5C%5Cboxed%7Bt%3D-1%7D%5C%5C%5C%5C2t-1%3D0%5Cqquad%5Ctext%7Badd%201%20to%20both%20sides%7D%5C%5C2t%3D1%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%202%7D%5C%5C%5Cboxed%7Bt%3D%5Cdfrac%7B1%7D%7B2%7D%7D)
<span>This is a 30 - 45 - 105 angled triangle, so the answer would be A.
"</span><span>Largest angle = 105, Middle angle = 45, Smallest angle = 30"</span>
16. 5x^3 y^-5 • 4xy^3
20x^4y^-2
20x^4 • 1/y^2
=20x^4/y^2
17. -2b^3c • 4b^2c^2
= -8b^5c^3
18. a^3n^7 / an^4 (a^3 minus a = a^2 same as n^7 minus n^4 = n^3)
=a^2n^3
19. -yz^5 / y^2z^3
= -z^2/y
20. -7x^5y^5z^4 / 21x^7y^5z^2 (divide -7 to 21 and minus xyz)
= -z / 3x^2
21. 9a^7b^5x^5 / 18a^5b^9c^3
=a^2c^2 / 2b^4
22. (n^5)^4
n ^5 x 4
=n^20
23. (z^3)^6
z ^3 x 6
=z^18
Slope of line t is -1/5
If two lines are perpendicular, the product of their slopes is -1
I believe the answer is A! If not I’m so sorry but I hope you pass!
