Answer:
#14 
#15 
Step-by-step explanation with pictures.
I hope this helps! :D
The answer is 1 3/4 or 1.75 depends on how u want it
from 1, to 3, to 5 to 7, notice, is simply adding 2 to get the next term.
1+2 =3, 3+2 =5 and so on.
so the common difference is 2, and the first term is of course 1.
![\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=1\\ d=2\\ n=24 \end{cases} \\\\\\ a_{24}=1+(24-1)2\implies a_{24}=1+(23)2\implies a_{24}=1+46\implies a_{24}=47](https://tex.z-dn.net/?f=%5Cbf%20n%5E%7Bth%7D%5Ctextit%7B%20term%20of%20an%20arithmetic%20sequence%7D%0A%5C%5C%5C%5C%0Aa_n%3Da_1%2B%28n-1%29d%5Cqquad%0A%5Cbegin%7Bcases%7D%0An%3Dn%5E%7Bth%7D%5C%20term%5C%5C%0Aa_1%3D%5Ctextit%7Bfirst%20term%27s%20value%7D%5C%5C%0Ad%3D%5Ctextit%7Bcommon%20difference%7D%5C%5C%5B-0.5em%5D%0A%5Chrulefill%5C%5C%0Aa_1%3D1%5C%5C%0Ad%3D2%5C%5C%0An%3D24%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0Aa_%7B24%7D%3D1%2B%2824-1%292%5Cimplies%20a_%7B24%7D%3D1%2B%2823%292%5Cimplies%20a_%7B24%7D%3D1%2B46%5Cimplies%20a_%7B24%7D%3D47)
Answer:
<em>x = 12 and y = 16</em>
Step-by-step explanation:
Given the following lengths;
NO = x + 2y,
MO = 3x,
PQ = 6x + 4, and
OQ = 2y + 4.
The following postulates are true;
MN = PQ
Since MO + ON = MN
MN = 3x + x+2y
MN = 4x + 2y
Recall that PQ = 6x+4
Equating both expressions;
4x + 2y= 6x+4
Collect like terms;
4x-6x + 2y = 4
-2x + 2y = 4
x - y = -4 ...... 1
Also MO = OQ
3x = 2y + 4
3x-2y= 4 ....2
from 1; x = -4 + y
Substitute into 2:
3x-2y= 4
3(-4+y)-2y = 4
-12+3y-2y = 4
-12+y = 4
y = 4 + 12
y = 16
Since x = -4+y
x = -4 + 16
x = 12
<em>Hence x = 12 and y = 16</em>
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