as you should already know, an absolute value expression, is in effect a piece-wise expression, since it has a ± versions.
![\bf \cfrac{|-2-2r|}{3}=4\implies \begin{cases} \cfrac{+(-2-2r)}{3}=4\\\\ \cfrac{-(-2-2r)}{3}=4 \end{cases}\\\\[-0.35em] ~\dotfill\\\\ \cfrac{-2-2r}{3}=4\implies -2-2r=12\implies -2-12=2r\implies -14=2r \\\\\\ \cfrac{-14}{2}=r\implies \boxed{-7=r}\\\\[-0.35em] ~\dotfill\\\\ \cfrac{-(-2-2r)}{3}=4\implies \cfrac{-2-2r}{3}=-4\implies -2-2r=-12 \\\\\\ -2+12=2r\implies 10=2r\implies \cfrac{10}{2}=r\implies \boxed{5=r}](https://tex.z-dn.net/?f=%20%5Cbf%20%5Ccfrac%7B%7C-2-2r%7C%7D%7B3%7D%3D4%5Cimplies%20%20%5Cbegin%7Bcases%7D%20%5Ccfrac%7B%2B%28-2-2r%29%7D%7B3%7D%3D4%5C%5C%5C%5C%20%5Ccfrac%7B-%28-2-2r%29%7D%7B3%7D%3D4%20%5Cend%7Bcases%7D%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B-2-2r%7D%7B3%7D%3D4%5Cimplies%20-2-2r%3D12%5Cimplies%20-2-12%3D2r%5Cimplies%20-14%3D2r%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B-14%7D%7B2%7D%3Dr%5Cimplies%20%5Cboxed%7B-7%3Dr%7D%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B-%28-2-2r%29%7D%7B3%7D%3D4%5Cimplies%20%5Ccfrac%7B-2-2r%7D%7B3%7D%3D-4%5Cimplies%20-2-2r%3D-12%20%5C%5C%5C%5C%5C%5C%20-2%2B12%3D2r%5Cimplies%2010%3D2r%5Cimplies%20%5Ccfrac%7B10%7D%7B2%7D%3Dr%5Cimplies%20%5Cboxed%7B5%3Dr%7D%20)
Advanced mathematical concepts glencoe answers indeed.
Answer:
number of laps = 5/2 = 2.5 laps
Explanation:
First, we will need to convert the minutes to seconds.
5 minutes = 5 * 60 = 300 seconds
Now, we know that she can run 1/3 of a lap in 40 seconds. To know the number of laps that she can run in 300 seconds, all we have to do is cross multiplication as follows:
40 seconds .................> 1/3 laps
300 seconds ................> ?? laps
number of laps = (300 * 1/3) / 40
number of laps = (100) / 40
number of laps = 5/2 = 2.5 laps
Hope this helps :)
4x3+2 = 14/3 —> 56/12
1x4+3 = 7/4 —> 21/12
56-21 is equal to 35/12
Which is 2 and 11/12
Answer:
$1,100
Step-by-step explanation:
first find the principal first Multiply the rate 0.02 by the time 1 year this gives us 0.02 then divide the interest ($22) by 0.02 then you get $1,100.
Hope that helped!
