160 = 2 x 2 x 2 x 2 x 2 x 5 = 2^5 x 5
243 = 3 x 3 x 3 x 3 x 3 = 3^5
So
(160 * 243)^1/5
= 5th root of (160 * 243)
= 5th root of (2^5 * 5 * 3^5)
= 2 * 3 * (5th root of 5)
= 6 * (5th root of 5)
Answer is D. 6 * (5th root of 5)
All that is needed is that it is 270
X = 5 is a solution of the equation 3 – x = 8
Answer: 222cm
Step-by-step explanation:
To find the area of this composite shape you will have to split them into 2 shapes; a rectangle and a triangle.
To work out the area of the rectangle you have to do 15×12= 180
Then, to work out the area of the triangle, you use the formula base times height divided by 2.
7×12=84
84÷2=42
Then to work out the total area of both the rectangle and the triangle, you have to add the area of both.
180+42=222cm
Hope this helps :)
![s=\frac{1}{2}n(n+1) \\ \\ 8s+1=8 \times \frac{1}{2}n(n+1)+1=4n(n+1)+1=4n^2+4n+1=(2n+1)^2](https://tex.z-dn.net/?f=s%3D%5Cfrac%7B1%7D%7B2%7Dn%28n%2B1%29%20%5C%5C%20%5C%5C%0A8s%2B1%3D8%20%5Ctimes%20%5Cfrac%7B1%7D%7B2%7Dn%28n%2B1%29%2B1%3D4n%28n%2B1%29%2B1%3D4n%5E2%2B4n%2B1%3D%282n%2B1%29%5E2)
n is an integer, so 2n+1 is also an integer. 8s+1 is equal to the square of 2n+1, so it's a square number.
2n+1 is an odd integer for any value of n. The square of an odd integer is always an odd integer. Therefore 8s+1=(2n+1)² is odd.
8s+1 is an odd square number.