1.
the slope of the line y=3x+2 is the coefficient of x, that is 3.
2.
the slope of any line perpendicular to the line y=3x+2, is m, such that:
![3*m=-1](https://tex.z-dn.net/?f=3%2Am%3D-1)
so
![m= \frac{-1}{3}](https://tex.z-dn.net/?f=m%3D%20%5Cfrac%7B-1%7D%7B3%7D%20)
3.
so any line with equation y=-1/3x+k is perpendicular to y=3x+2.
moreover, the line y=-1/3x (so k=0) is the line passing through the origin
(0, 0) and perpendicular to y=3x+2
4. This means that the closest point of y=3x+2 to the origin is the intersection point of lines y=3x+2 and y=-1/3x
5.
to find this point:
3x+2=(-1/3)x
x(3+1/3)=-2
x(9/3+1/3)=-2
x*10/3=-2
![x= \frac{-2*3}{10} = \frac{-6}{10}=-0.6](https://tex.z-dn.net/?f=x%3D%20%5Cfrac%7B-2%2A3%7D%7B10%7D%20%3D%20%5Cfrac%7B-6%7D%7B10%7D%3D-0.6%20)
thus y is : (-1/3)(-6/10)=0.2
Answer: (-0.6, 0.2)
For this case, we must find an expression equivalent to:
![\frac {-9x ^ {- 1} y ^ {- 9}} {- 15x ^ 5y ^ {- 3}}](https://tex.z-dn.net/?f=%5Cfrac%20%7B-9x%20%5E%20%7B-%201%7D%20y%20%5E%20%7B-%209%7D%7D%20%7B-%2015x%20%5E%205y%20%5E%20%7B-%203%7D%7D)
By definition of power properties we have:
![a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}](https://tex.z-dn.net/?f=a%20%5E%20%7B-%201%7D%20%3D%20%5Cfrac%20%7B1%7D%20%7Ba%20%5E%201%7D%20%3D%20%5Cfrac%20%7B1%7D%20%7Ba%7D)
Rewriting the previous expression we have:
The "-" are canceled and we take into account that:
![\frac {9} {15} = \frac {3} {5}](https://tex.z-dn.net/?f=%5Cfrac%20%7B9%7D%20%7B15%7D%20%3D%20%5Cfrac%20%7B3%7D%20%7B5%7D)
So:
![\frac {3} {5x^5 * x ^ 1 *y ^ 9* y ^ {- 3}} =](https://tex.z-dn.net/?f=%5Cfrac%20%7B3%7D%20%7B5x%5E5%20%2A%20x%20%5E%201%20%2Ay%20%5E%209%2A%20y%20%5E%20%7B-%203%7D%7D%20%3D)
According to one of the properties of powers of the same base, we must put the same base and add the exponents:
![\frac {3} {5x ^ {5 + 1} * y ^ {9-3}} =\\\frac {3} {5x ^ 6 * y ^ 6}](https://tex.z-dn.net/?f=%5Cfrac%20%7B3%7D%20%7B5x%20%5E%20%7B5%20%2B%201%7D%20%2A%20y%20%5E%20%7B9-3%7D%7D%20%3D%5C%5C%5Cfrac%20%7B3%7D%20%7B5x%20%5E%206%20%2A%20y%20%5E%206%7D)
Answer:
![\frac {3} {5x ^ 6 * y ^ 6}](https://tex.z-dn.net/?f=%5Cfrac%20%7B3%7D%20%7B5x%20%5E%206%20%2A%20y%20%5E%206%7D)
Option B
Answer:
162
Step-by-step explanation:
324/2 because a square has sides that are all equal, so the area is 2 times the length of a side
I don’t know I need points