Answer:
0.75
Step-by-step explanation:
mark brainliest please
Rational numbers. Rational numbers include fractions, while integers dont :)
We could factor the usual way but let's try Dr. Po Shen Loh's "new" method.
![3m^2x^2 + 2mx - 5 = 0](https://tex.z-dn.net/?f=%203m%5E2x%5E2%20%2B%202mx%20-%205%20%3D%200)
First step is to rewrite as a monic,
![x^2 + \dfrac{2m}{3m^2} x - \dfrac{5}{3m^2} = 0](https://tex.z-dn.net/?f=x%5E2%20%2B%20%5Cdfrac%7B2m%7D%7B3m%5E2%7D%20x%20-%20%5Cdfrac%7B5%7D%7B3m%5E2%7D%20%3D%200)
![x^2 + \dfrac{2}{3m} x - \dfrac{5}{3m^2} = 0](https://tex.z-dn.net/?f=x%5E2%20%2B%20%5Cdfrac%7B2%7D%7B3m%7D%20x%20-%20%5Cdfrac%7B5%7D%7B3m%5E2%7D%20%3D%200)
Now we need two numbers which add to 2/3m and multiply to -5/3m². If they add to 2/3m they average to 1/3m so they're 1/3m-u and 1/3m+u for some u. The product of those two is -5/3m² so we write:
![\left( \dfrac{1}{3m}-u \right)\left( \dfrac{1}{3m} +u \right) = -\dfrac{5}{3m^2}](https://tex.z-dn.net/?f=%5Cleft%28%20%5Cdfrac%7B1%7D%7B3m%7D-u%20%5Cright%29%5Cleft%28%20%5Cdfrac%7B1%7D%7B3m%7D%20%2Bu%20%5Cright%29%20%3D%20-%5Cdfrac%7B5%7D%7B3m%5E2%7D)
![\dfrac{1}{9m^2}-u^2 = -\dfrac{5}{3m^2}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B9m%5E2%7D-u%5E2%20%3D%20-%5Cdfrac%7B5%7D%7B3m%5E2%7D)
![u^2 = \dfrac{1}{9m^2} +\dfrac{5(3)}{(3)3m^2} = \dfrac{16}{9m^2}](https://tex.z-dn.net/?f=u%5E2%20%3D%20%5Cdfrac%7B1%7D%7B9m%5E2%7D%20%2B%5Cdfrac%7B5%283%29%7D%7B%283%293m%5E2%7D%20%3D%20%5Cdfrac%7B16%7D%7B9m%5E2%7D)
![u = \pm \dfrac{4}{3m}](https://tex.z-dn.net/?f=u%20%3D%20%5Cpm%20%5Cdfrac%7B4%7D%7B3m%7D)
So our equation
![0=x^2 + \dfrac{2m}{3m^2} x - \dfrac{5}{3m^2}](https://tex.z-dn.net/?f=0%3Dx%5E2%20%2B%20%5Cdfrac%7B2m%7D%7B3m%5E2%7D%20x%20-%20%5Cdfrac%7B5%7D%7B3m%5E2%7D)
factors as
![0= \left( x +\dfrac{1}{3m}-\dfrac{4}{3m}\right) \left( x + \dfrac{1}{3m} + \dfrac{4}{3m}\right)](https://tex.z-dn.net/?f=0%3D%20%5Cleft%28%20x%20%2B%5Cdfrac%7B1%7D%7B3m%7D-%5Cdfrac%7B4%7D%7B3m%7D%5Cright%29%20%5Cleft%28%20x%20%2B%20%5Cdfrac%7B1%7D%7B3m%7D%20%2B%20%5Cdfrac%7B4%7D%7B3m%7D%5Cright%29)
![0= \left(x - \dfrac{1}{m}\right) \left(x +\dfrac{5}{3m} \right)](https://tex.z-dn.net/?f=0%3D%20%5Cleft%28x%20-%20%5Cdfrac%7B1%7D%7Bm%7D%5Cright%29%20%5Cleft%28x%20%2B%5Cdfrac%7B5%7D%7B3m%7D%20%5Cright%29)
so has roots
![x= \dfrac{1}{m} \textrm{ or } x = -\dfrac{5}{3m}](https://tex.z-dn.net/?f=x%3D%20%5Cdfrac%7B1%7D%7Bm%7D%20%5Ctextrm%7B%20or%20%7D%20x%20%3D%20-%5Cdfrac%7B5%7D%7B3m%7D)
The more standard factorization with the same result is
![0=(mx-1)(3mx+5)](https://tex.z-dn.net/?f=0%3D%28mx-1%29%283mx%2B5%29)
Answer: deductible
Step-by-step explanation:
Answer: Length is 16 ft. Width is 5 feet.
Step-by-step explanation: Take the information given and write an equation. "Length decreased by 3 is 1" becomes L - 3w = 1 .
"Solve" for L. L= 3w +1
Write another equation for the formula of a perimeter. P=2L + 2w.
Substitute the values for L (from the first "solution" you wrote) and P (42 ft, given).
42 = 2(3w +1) + 2w. Solve this.
42= 6w +2 + 2w
42= 8w +2. Subtract 2 from both sides then divide both sides by 8.
W = 5
Substitute that into the first equation you wrote to get the Length.
L - 3(5) = 1
L -15 = 1. L = 1+15
L = 16