Answer:
The solution is:
![-7r-4\ge \:\:4r+2\quad \::\quad \:\begin{bmatrix}\mathrm{Solution:}\:&\:r\le \:\:-\frac{6}{11}\:\\ \:\:\mathrm{Decimal:}&\:r\le \:\:-0.54545\dots \:\\ \:\:\mathrm{Interval\:Notation:}&\:(-\infty \:\:,\:-\frac{6}{11}]\end{bmatrix}](https://tex.z-dn.net/?f=-7r-4%5Cge%20%5C%3A%5C%3A4r%2B2%5Cquad%20%5C%3A%3A%5Cquad%20%5C%3A%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3Ar%5Cle%20%5C%3A%5C%3A-%5Cfrac%7B6%7D%7B11%7D%5C%3A%5C%5C%20%5C%3A%5C%3A%5Cmathrm%7BDecimal%3A%7D%26%5C%3Ar%5Cle%20%5C%3A%5C%3A-0.54545%5Cdots%20%5C%3A%5C%5C%20%5C%3A%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%28-%5Cinfty%20%5C%3A%5C%3A%2C%5C%3A-%5Cfrac%7B6%7D%7B11%7D%5D%5Cend%7Bbmatrix%7D)
Please check the attached line graph below.
Step-by-step explanation:
Given the expression
Add 4 to both sides
Simplify
Subtract 4r from both sides
Simplify
Multiply both sides by -1 (reverses the inequality)
Simplify
Divide both sides by 11
Simplify
Therefore, the solution is:
Please check the attached line graph below.
T = (1/0.03) [(8050/7000)-1]
t = 33.33 * 0.15
t= 5 yrs
Answer:
y= -1/4x+3/4
Step-by-step explanation:
You are given (-5,2) and x=4
This means that the slope is 4
When finding perpendicular, the slope is the reverse reciprocal of the original slope. The reverse of 4 is -4. The recirprocal is the opposite of -4/1, so it is -1/4.
Slope= -1/4
The slope-intercept form is y=mx+b where you are trying to find b.
Plug in the y value in (-5,2) for y
Plug in the slope for m
Plug in the x value in (-5,2) for x
y=2
m= -1/4
x= -5
y=mx+b
2= -1/4(-5)+b <u>Plug in everything</u>
2= 5/4+b <u>Multiply -1/4 and -5</u>
3/4=b <u>Subtract 5/4 from 2 and you get b</u>
<u />
Since we have b now we can make an equation using it.
y=mx+b <u>Use the form</u>
y= -1/4x+3/4 <u>Plug in m and b</u>
Since |1-4x|>7 it can also be 1-4x<-7
so you get 1-4x>7 then get the x by its self -4x>7 then you make the x positive. multiply by -1 so you switch the sign 4x<7 divid by 4 and you get x<7/4 now you go on to the other equation 1-4x<-7 you get the x by itself and get -4x<-8 and multiply by -1 to get a positive number so you swith the sign 4x>8 so you didid by 4 and get x>2 so you get an interval notation of (-infinity,7/4) u (2,+infinity)
the |5x-1|<1 interval notation is (-2/5 ,0)
