Answer:
x=4
Step-by-step explanation:
You can split this shape into two shapes; a rectangle on top and a horizontal rectangle underneath. The top rectangle would be 4 x 2 = 8 square units, and the bottom rectangle would be 7 x 1 (3 - 2) = 7 square units. Now you just add these to get 15 square units. I hope this helps!
53 3/4=53.75
To find out how many 4ft ropes you can make divide 53.75 by 4
53.75/4=13.4375
You can make 13 4ft ropes out of a 53.75ft rope
f(1) = -8, simply is a way of saying, the 1st value in the arithmetic sequence is -8.
f(n) = f(n-1) - 3, is another way of saying, following values are just, the previous minus -3.
so in short, -3 is the common difference, since that is what we're "adding" to get the new value in the sequence.
![\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ d = -3\\ a_1 = -8 \end{cases} \\\\\\ a_n=-8+(n-1)(-3)\implies a_n=-8-3n+3\implies \stackrel{f(n)}{a_n}=\stackrel{\stackrel{explicit}{\downarrow }}{-3n-5}](https://tex.z-dn.net/?f=%5Cbf%20n%5E%7Bth%7D%5Ctextit%7B%20term%20of%20an%20arithmetic%20sequence%7D%20%5C%5C%5C%5C%20a_n%3Da_1%2B%28n-1%29d%5Cqquad%20%5Cbegin%7Bcases%7D%20a_n%3Dn%5E%7Bth%7D%5C%20term%5C%5C%20n%3D%5Ctextit%7Bterm%20position%7D%5C%5C%20a_1%3D%5Ctextit%7Bfirst%20term%7D%5C%5C%20d%3D%5Ctextit%7Bcommon%20difference%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20d%20%3D%20-3%5C%5C%20a_1%20%3D%20-8%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20a_n%3D-8%2B%28n-1%29%28-3%29%5Cimplies%20a_n%3D-8-3n%2B3%5Cimplies%20%5Cstackrel%7Bf%28n%29%7D%7Ba_n%7D%3D%5Cstackrel%7B%5Cstackrel%7Bexplicit%7D%7B%5Cdownarrow%20%7D%7D%7B-3n-5%7D)