Answer:
A(2, -3) and B(3, -2), o(0, 0) Let C(x, y)
Here c divide AB line in the ratio of 1:2
From the line intersection law, we get x=(m1×x2+m2×x1)/(m1+m2)
and y=(m1×y2+m2×y1)/(m1+m2)
where m1=1, m2=2, x1=2, x2=3, y1=-3, y2=-2;
so x=(3+4)/3
or, x=7/3;
y=(-2-6)/3
or, y=-8/3;
so, oc=√((0-7/3)²+(0-(-8/3))²)
oc=3.54
Answer:
Option (b) is correct.
![(2^\frac{1}{4} )^4=2^\frac{1}{4} \times 2^\frac{1}{4}\times 2^\frac{1}{4}\times 2^\frac{1}{4}=2^{(\frac{1}{4}+ \frac{1}{4}+ \frac{1}{4}+ \frac{1}{4} )}=2^{1}=2](https://tex.z-dn.net/?f=%282%5E%5Cfrac%7B1%7D%7B4%7D%20%29%5E4%3D2%5E%5Cfrac%7B1%7D%7B4%7D%20%5Ctimes%202%5E%5Cfrac%7B1%7D%7B4%7D%5Ctimes%202%5E%5Cfrac%7B1%7D%7B4%7D%5Ctimes%202%5E%5Cfrac%7B1%7D%7B4%7D%3D2%5E%7B%28%5Cfrac%7B1%7D%7B4%7D%2B%20%5Cfrac%7B1%7D%7B4%7D%2B%20%5Cfrac%7B1%7D%7B4%7D%2B%20%5Cfrac%7B1%7D%7B4%7D%20%29%7D%3D2%5E%7B1%7D%3D2)
Step-by-step explanation:
Given: ![(2^\frac{1}{4} )^4](https://tex.z-dn.net/?f=%282%5E%5Cfrac%7B1%7D%7B4%7D%20%29%5E4)
We have too choose the correct simplification for the given statement.
Consider ![(2^\frac{1}{4} )^4](https://tex.z-dn.net/?f=%282%5E%5Cfrac%7B1%7D%7B4%7D%20%29%5E4)
Using property of exponents,
We have,
![(2^\frac{1}{4} )^4=2^\frac{1}{4} \times 2^\frac{1}{4}\times 2^\frac{1}{4}\times 2^\frac{1}{4}](https://tex.z-dn.net/?f=%282%5E%5Cfrac%7B1%7D%7B4%7D%20%29%5E4%3D2%5E%5Cfrac%7B1%7D%7B4%7D%20%5Ctimes%202%5E%5Cfrac%7B1%7D%7B4%7D%5Ctimes%202%5E%5Cfrac%7B1%7D%7B4%7D%5Ctimes%202%5E%5Cfrac%7B1%7D%7B4%7D)
Again applying property of exponents ![a^m\times a^m=a^{n+m}](https://tex.z-dn.net/?f=a%5Em%5Ctimes%20a%5Em%3Da%5E%7Bn%2Bm%7D)
We have,
![(2^\frac{1}{4} )^4=2^{(\frac{1}{4}+ \frac{1}{4}+ \frac{1}{4}+ \frac{1}{4} )}](https://tex.z-dn.net/?f=%282%5E%5Cfrac%7B1%7D%7B4%7D%20%29%5E4%3D2%5E%7B%28%5Cfrac%7B1%7D%7B4%7D%2B%20%5Cfrac%7B1%7D%7B4%7D%2B%20%5Cfrac%7B1%7D%7B4%7D%2B%20%5Cfrac%7B1%7D%7B4%7D%20%29%7D)
Simplify, we have,
![(2^\frac{1}{4} )^4=2^{\frac{4}{4}}](https://tex.z-dn.net/?f=%282%5E%5Cfrac%7B1%7D%7B4%7D%20%29%5E4%3D2%5E%7B%5Cfrac%7B4%7D%7B4%7D%7D)
we get,
![(2^\frac{1}{4} )^4=2^{1}=2](https://tex.z-dn.net/?f=%282%5E%5Cfrac%7B1%7D%7B4%7D%20%29%5E4%3D2%5E%7B1%7D%3D2)
Thus, ![(2^\frac{1}{4} )^4=2](https://tex.z-dn.net/?f=%282%5E%5Cfrac%7B1%7D%7B4%7D%20%29%5E4%3D2)
Option (b) is correct.
X−7<1
Add 7 to both sides.
x−7+7<1+7
x<8
To plot this on a number line, put a circle around 8 and a line going to the left with an arrow at the end.