Answer:
![\frac{1}{(28)^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%2828%29%5E%7B2%7D%20%7D)
Step-by-step explanation:
Step 1;
Write expression
![4^{-2} . 7^{-2\\\frac{\frac{1}{4^{-2} } }{y\frac{1}{7^{-2} } } }](https://tex.z-dn.net/?f=4%5E%7B-2%7D%20.%207%5E%7B-2%5C%5C%5Cfrac%7B%5Cfrac%7B1%7D%7B4%5E%7B-2%7D%20%7D%20%7D%7By%5Cfrac%7B1%7D%7B7%5E%7B-2%7D%20%7D%20%7D%20%7D)
![\frac{1}{4^{2} .7^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%5E%7B2%7D%20.7%5E%7B2%7D%20%7D)
![\frac{1}{(4x7)^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%284x7%29%5E%7B2%7D%20%7D)
![\frac{1}{(28)^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%2828%29%5E%7B2%7D%20%7D)
3 years
15 = 250(0.06)
45/15 = 3
Answer:
![\displaystyle y=-\frac{1}{5}x+\frac{17}{5}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D-%5Cfrac%7B1%7D%7B5%7Dx%2B%5Cfrac%7B17%7D%7B5%7D)
Step-by-step explanation:
<u>Equation of a line</u>
A line can be represented by an equation of the form
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
Where x is the independent variable, m is the slope of the line, b is the y-intercept and y is the dependent variable.
We need to find the equation of the line passing through the point (7,2) and is perpendicular to the line y=5x-2.
Two lines with slopes m1 and m2 are perpendicular if:
![m_1.m_2=-1](https://tex.z-dn.net/?f=m_1.m_2%3D-1)
The given line has a slope m1=5, thus the slope of our required line is:
![\displaystyle m_2=-\frac{1}{m_1}=-\frac{1}{5}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m_2%3D-%5Cfrac%7B1%7D%7Bm_1%7D%3D-%5Cfrac%7B1%7D%7B5%7D)
The equation of the line now can be expressed as:
![\displaystyle y=-\frac{1}{5}x+b](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D-%5Cfrac%7B1%7D%7B5%7Dx%2Bb)
We need to find the value of b, which can be done by using the point (7,2):
![\displaystyle 2=-\frac{1}{5}*7+b](https://tex.z-dn.net/?f=%5Cdisplaystyle%202%3D-%5Cfrac%7B1%7D%7B5%7D%2A7%2Bb)
Operating:
![\displaystyle 2=-\frac{7}{5}+b](https://tex.z-dn.net/?f=%5Cdisplaystyle%202%3D-%5Cfrac%7B7%7D%7B5%7D%2Bb)
Multiplying by 5:
![10=-7+5b](https://tex.z-dn.net/?f=10%3D-7%2B5b)
Operating:
![10+7=5b](https://tex.z-dn.net/?f=10%2B7%3D5b)
Solving for b:
![\displaystyle b=\frac{17}{5}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20b%3D%5Cfrac%7B17%7D%7B5%7D)
The equation of the line is:
![\boxed{\displaystyle y=-\frac{1}{5}x+\frac{17}{5}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cdisplaystyle%20y%3D-%5Cfrac%7B1%7D%7B5%7Dx%2B%5Cfrac%7B17%7D%7B5%7D%7D)
Answer:
Step-by-step explanation:
So the two lines before and after the expression means absolute value, or modulus of, knowing this, it means that the answer must always yield positive. So if x-6 is positive, it will stay positive, if x-6 is negative, it will turn positive, therefore it can never yield a negative value.
Now im assuming the second question is meant to be absolute value of x-5 is less than 0, because it makes no sense otherwise.
So now knowing that x-5 is always positive, or 0, but this inequality only wants less than 0, this means there are no solutions for the inequality.