2x^2 because you do (-4x^2)-x=(-6x^2) and solve for x to get 2x^2.
Answer:
![22\ m < x < 74\ m](https://tex.z-dn.net/?f=22%5C%20m%20%3C%20x%20%3C%2074%5C%20m)
Step-by-step explanation:
Let
x ----> the length for the third side
we know that
The <u><em>Triangle Inequality Theorem</em></u> states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Applying the triangle inequality theorem
1) ![26+48> x](https://tex.z-dn.net/?f=26%2B48%3E%20x)
solve for x
![74> x](https://tex.z-dn.net/?f=74%3E%20x)
Rewrite
![x < 74\ m](https://tex.z-dn.net/?f=x%20%3C%2074%5C%20m)
2) ![26+x>48](https://tex.z-dn.net/?f=26%2Bx%3E48)
solve for x
subtract 26 both sides
![x> 22\ m](https://tex.z-dn.net/?f=x%3E%2022%5C%20m)
therefore
The range of possible lengths, in meters, for the third side is equal to
![22\ m < x < 74\ m](https://tex.z-dn.net/?f=22%5C%20m%20%3C%20x%20%3C%2074%5C%20m)
Answer:
The rate of interest for the investment is 4.7%
Step-by-step explanation:
Given as :
The interest amount for investment = I = $250
The investment amount = p = $3500
The time period for investment = 18 months = 1.5 years
Let The rate of interest applied = r%
<u>Now, From Compound Interest </u>
Amount = Principal × ![(1+\dfrac{\textrm rate}{100})^{\textrm time}](https://tex.z-dn.net/?f=%281%2B%5Cdfrac%7B%5Ctextrm%20rate%7D%7B100%7D%29%5E%7B%5Ctextrm%20time%7D)
∵ Interest = Amount - Principal
So, I = A - p
Or, A = I + p
Or, A = $250 + $3500
i.e A = $3750
∴ A = p × ![(1+\dfrac{\textrm r}{100})^{\textrm t}](https://tex.z-dn.net/?f=%281%2B%5Cdfrac%7B%5Ctextrm%20r%7D%7B100%7D%29%5E%7B%5Ctextrm%20t%7D)
Or, $3750 = $3500 × ![(1+\dfrac{\textrm r}{100})^{\textrm 1.5}](https://tex.z-dn.net/?f=%281%2B%5Cdfrac%7B%5Ctextrm%20r%7D%7B100%7D%29%5E%7B%5Ctextrm%201.5%7D)
Or,
= ![(1+\dfrac{\textrm r}{100})^{\textrm 1.5}](https://tex.z-dn.net/?f=%281%2B%5Cdfrac%7B%5Ctextrm%20r%7D%7B100%7D%29%5E%7B%5Ctextrm%201.5%7D)
Or, 1.071428 =
= ![(1 + \dfrac{r}{100})](https://tex.z-dn.net/?f=%281%20%2B%20%5Cdfrac%7Br%7D%7B100%7D%29)
Or, 1.047069 = ![(1 + \dfrac{r}{100})](https://tex.z-dn.net/?f=%281%20%2B%20%5Cdfrac%7Br%7D%7B100%7D%29)
Or, 1.047069 - 1 = ![\dfrac{r}{100}](https://tex.z-dn.net/?f=%5Cdfrac%7Br%7D%7B100%7D)
Or, 0.047069 = ![\dfrac{r}{100}](https://tex.z-dn.net/?f=%5Cdfrac%7Br%7D%7B100%7D)
∴ r = 0.047069 × 100
i.e r = 4.7069
So, The rate of interest = r = 4.7%
Hence, The rate of interest for the investment is 4.7% Answer
wouldn't this just be 2+2+2+2+10+10+10+10? or is it times I'm not sure but I hope this helps anyone to answer this fully :)