Answer:
B
Step-by-step explanation:
In this graph we can see a "Parabola", this is the curve for a second degree polynomial function, and based on "Fundamental theorem of algebra" we can know that this polynomial has 2 roots (they can be real or imaginary).
In this graph, the curve doesn't touch the X axis, so we know that this function has not real root. So both roots are complex
2 - 3i is just another of writing (2, -3) in the cartesian plane, the 2-3i however is using the "imaginary axis" for the imaginary plane, is all however the imaginary axis is simply the equivalent of the y-axis. Likewise 9+21i is just (9,21), so let's just use the distance formula.
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{21})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[9-2]^2+[21-(-3)]^2}\implies d=\sqrt{(9-2)^2+(21+3)^2} \\\\\\ d=\sqrt{7^2+24^2}\implies d=\sqrt{49+576}\implies d=\sqrt{625}\implies d=25](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%20%5C%5C%5C%5C%20%28%5Cstackrel%7Bx_1%7D%7B2%7D~%2C~%5Cstackrel%7By_1%7D%7B-3%7D%29%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B9%7D~%2C~%5Cstackrel%7By_2%7D%7B21%7D%29%5Cqquad%20%5Cqquad%20d%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20d%3D%5Csqrt%7B%5B9-2%5D%5E2%2B%5B21-%28-3%29%5D%5E2%7D%5Cimplies%20d%3D%5Csqrt%7B%289-2%29%5E2%2B%2821%2B3%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20d%3D%5Csqrt%7B7%5E2%2B24%5E2%7D%5Cimplies%20d%3D%5Csqrt%7B49%2B576%7D%5Cimplies%20d%3D%5Csqrt%7B625%7D%5Cimplies%20d%3D25)
Answer:
3X/20 (option a) of the pastries submitted by Rashid and Mikhail were brushed with butter
Step-by-step explanation:
Rashid pastries (R)
Mikhail pastries (M)
Rashid and Mikhail submitted a total of x pastries
R+M=x (I)
Rashid made 2/3 as many pastries as Mikhail
(2/3)*R=M (II)
Using II in I
R+(2/3)*R=x
(5/3)*R = x
R=(3/5)*x (III)
Using III in I
(3/5)*x+M=x
M=x-(3/5)*x
M=(2/5)*x (IV)
Mikhail filo dough (MF)
Mikhail shortcrust dough (MS)
Rashid filo dough (RF)
Rashid shortcrust dough (RS)
Mikhail used filo dough for all of his pastries
MF=M
MS=0
Rashid used shortcrust dough for all of his pastries
RS=R
RF=0
Filo dough (FD)
FD=RF+MF=0+MF=MF=M (V)
5/8 of the filo dough pastries were brushed with olive oil
pastries brushed with olive oil (OI)
(5/8)*FD=OI
Using V
(5/8)*M=OI
Using IV
(5/8)*(2/5)*x=OI
(1/4)*x=OI (VI)
pastries brushed with butter (B)
Pastries made out of filo dough are brushed with either olive oil or butter (but not both)
FD=OI+B
B=FD-OI
Using V and VI
B= M - (1/4)*x
Using IV
B = (2/5)*x - (1/4)*x
B= (3/20)*x
3X/20 (option a) of the pastries submitted by Rashid and Mikhail were brushed with butter
