<span>The correct equation is $50(0.80). The discount is 20% or 0.20, so we multiply the original price by 1-(discount), which is 1-0.2, so we multiply by 0.80.</span>
Answer:
7.50
Step-by-step explanation:
Answer:
<em>Steve should place $6,250 in the 5-year CD and $18,750 in the corporate bond</em>
Step-by-step explanation:
<u>System of Equations</u>
We need to find how Steve will distribute his investments between two possible options: one of them will pay 5% per annum and the other will pay 9% per annum. We know Steve has $25,000 to invest and wants to have an overall annual rate of return of 8%.
Let's call x to the amount Steve will invest in the CD paying 5% per annum and y to the amount he will invest in a corporate bond paying 9% per annum.
The total investment is $25,000 which leads to the first equation
![x+y=25,000](https://tex.z-dn.net/?f=x%2By%3D25%2C000)
If x dollars are invested at 5%, then the interest return is 0.05x. Similarly, y dollars at 9% return 0.09y. The overall return is 8% on the total investment, thus
![0.05x+0.09y=0.08(x+y)](https://tex.z-dn.net/?f=0.05x%2B0.09y%3D0.08%28x%2By%29)
Rearranging:
![0.05x+0.09y=0.08x+0.08y](https://tex.z-dn.net/?f=0.05x%2B0.09y%3D0.08x%2B0.08y)
Simplifying
![0.01y=0.03x](https://tex.z-dn.net/?f=0.01y%3D0.03x)
Multiplying by 100
![y=3x](https://tex.z-dn.net/?f=y%3D3x)
Substituting in the first equation
![x+3x=25,000\\4x=25,000\\x=6,250](https://tex.z-dn.net/?f=x%2B3x%3D25%2C000%5C%5C4x%3D25%2C000%5C%5Cx%3D6%2C250)
And therefore
![y=25,000-6,250=18,750](https://tex.z-dn.net/?f=y%3D25%2C000-6%2C250%3D18%2C750)
Steve should place $6,250 in the 5-year CD and $18,750 in the corporate bond
Answer:
1
Step-by-step explanation:
Factor and cancel common factors from numerator and denominator.
![\displaystyle\frac{2y^3-y^2+2y-1}{y^3-y^2+y-1}\times\frac{2y^2-3y+1}{4y^2-4y+1}\\\\=\frac{(y^2+1)(2y-1)\times (2y-1)(y-1))}{(y^2+1)(y-1)\times (2y-1)^2}=\frac{(y^2+1)(2y-1)^2(y-1)}{(y^2+1)(2y-1)^2(y-1)}\\\\=1](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7B2y%5E3-y%5E2%2B2y-1%7D%7By%5E3-y%5E2%2By-1%7D%5Ctimes%5Cfrac%7B2y%5E2-3y%2B1%7D%7B4y%5E2-4y%2B1%7D%5C%5C%5C%5C%3D%5Cfrac%7B%28y%5E2%2B1%29%282y-1%29%5Ctimes%20%282y-1%29%28y-1%29%29%7D%7B%28y%5E2%2B1%29%28y-1%29%5Ctimes%20%282y-1%29%5E2%7D%3D%5Cfrac%7B%28y%5E2%2B1%29%282y-1%29%5E2%28y-1%29%7D%7B%28y%5E2%2B1%29%282y-1%29%5E2%28y-1%29%7D%5C%5C%5C%5C%3D1)
Side (s) = 6.25 ft
Area = s² = (6.25)² = 39.0625 ft²