well, if m = 1, let's see, then f(x) = √(mx) = √(1x) = √x
and then g(x) = m√x = 1√x = √x
well, if both equations are equal, then their ranges are also equal.
now, if m = "any positive real number"
f(x) = √(mx) = √m √x will yield some value over the y-axis
g(x) = m√x will yield some range over the y-axis, however, "m" is a larger value than "√m".
what that means is that so long "m" is a positive real number, the ranges of f(x) and g(x) will be the same over an infinite range on the y-axis, even though g(x) is moving faster than f(x), f(x) is moving slower because √m makes a stretch transformation which is smaller than one "m" does.
2 is the greatest common factor. Neither 4 nor 8 divides into 8-22 without a remainder.
Thus, 8 - 22 = 2(4 -11) (answer)
Answer: y<2
Step-by-step explanation:
Since we can say a functions could be added to the system without changing the solution set if after including it to the system the feasible region of entire system is not affected.
Here, the solution to the system of inequalities is,
y≤ 0.5x+2
y>3x-3
Since after ploting these two enequslties in the graph we get our feasible region.
When we include y > 2 in the system there is no solution of the system.
Therefore it affects the system.
Now when we include y < 2 in the system the solution or feasible region remain same.
Therefore it does not affect the system.
When we include y > 3 in the system there is no solution of the system.
Therefore it affects the system.
When we include line y=3 in the system then the system has no solution.
Therefore, it affects the system.
Thus, second Option is correct.
Answer:
4/15
Step-by-step explanation:
2/3 play sports
2/5 play football
Of the 2/3 that play sports, 2/5 of them play football
2/3(2/5) = 4/15
Answer:
<em>The correct option is C.</em>
Step-by-step explanation:
<u>Root Of Complex Numbers</u>
If a complex number is expressed in polar form as

Then the cubic roots of Z are
![\displaystyle Z_1=\left(\sqrt[3]{r},\frac{\theta}{3}\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Z_1%3D%5Cleft%28%5Csqrt%5B3%5D%7Br%7D%2C%5Cfrac%7B%5Ctheta%7D%7B3%7D%5Cright%29)
![\displaystyle Z_2=\left(\sqrt[3]{r},\frac{\theta}{3}+120^o\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Z_2%3D%5Cleft%28%5Csqrt%5B3%5D%7Br%7D%2C%5Cfrac%7B%5Ctheta%7D%7B3%7D%2B120%5Eo%5Cright%29)
![\displaystyle Z_3=\left(\sqrt[3]{r},\frac{\theta}{3}+240^o\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Z_3%3D%5Cleft%28%5Csqrt%5B3%5D%7Br%7D%2C%5Cfrac%7B%5Ctheta%7D%7B3%7D%2B240%5Eo%5Cright%29)
We are given the complex number in rectangular components

Converting to polar form


It's located in the second quadrant, so

The number if polar form is

Its cubic roots are
![\displaystyle Z_1=\left(\sqrt[3]{2},\frac{120^o}{3}\right)=\left(\sqrt[3]{2},40^o\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Z_1%3D%5Cleft%28%5Csqrt%5B3%5D%7B2%7D%2C%5Cfrac%7B120%5Eo%7D%7B3%7D%5Cright%29%3D%5Cleft%28%5Csqrt%5B3%5D%7B2%7D%2C40%5Eo%5Cright%29)
![\displaystyle Z_2=\left(\sqrt[3]{2},40^o+120^o\right)=\left(\sqrt[3]{2},160^o\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Z_2%3D%5Cleft%28%5Csqrt%5B3%5D%7B2%7D%2C40%5Eo%2B120%5Eo%5Cright%29%3D%5Cleft%28%5Csqrt%5B3%5D%7B2%7D%2C160%5Eo%5Cright%29)
![\displaystyle Z_3=\left(\sqrt[3]{2},40^o+240^o\right)=\left(\sqrt[3]{2},280^o\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Z_3%3D%5Cleft%28%5Csqrt%5B3%5D%7B2%7D%2C40%5Eo%2B240%5Eo%5Cright%29%3D%5Cleft%28%5Csqrt%5B3%5D%7B2%7D%2C280%5Eo%5Cright%29)
Converting the first solution to rectangular coordinates
![z_1=\sqrt[3]{2}(\ cos40^o+i\ sin40^o)](https://tex.z-dn.net/?f=z_1%3D%5Csqrt%5B3%5D%7B2%7D%28%5C%20cos40%5Eo%2Bi%5C%20sin40%5Eo%29)
The correct option is C.