This is an example of an arithmetic series: 6 + 8 + 10 + 12 + . . . + (4 + 2n) + . . .
1 answer:
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Answer:
(x) =
Step-by-step explanation:
let y = - 8x + 4
rearrange making x the subject
add 8x to both sides
8x + y = 4 ( subtract y from both sides )
8x = 4 - y ( divide both sides by 8 )
x =
change y back into terms of x, then
(x) =
Check the picture below.
so we know S is the midpoint of PQ, and T is the midpoint of QR, thus
so, what's the distance from S to T?
![\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &S&(~ -6 &,& 7~) % (c,d) &T&(~ -3 &,& 4~) \end{array}\\\\\\ % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ ST=\sqrt{[-3-(-6)]^2+[4-7]^2}\implies ST=\sqrt{(-3+6)^2+(4-7)^2} \\\\\\ ST=\sqrt{3^2+(-3)^2}\implies ST=\sqrt{18}\implies ST=\sqrt{9\cdot 2} \\\\\\ ST=\sqrt{3^2\cdot 2}\implies ST=3\sqrt{2}](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%5C%5C%0A%5Cbegin%7Barray%7D%7Bccccccccc%7D%0A%26%26x_1%26%26y_1%26%26x_2%26%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0A%26S%26%28~%20-6%20%26%2C%26%207~%29%20%0A%25%20%20%28c%2Cd%29%0A%26T%26%28~%20-3%20%26%2C%26%204~%29%0A%5Cend%7Barray%7D%5C%5C%5C%5C%5C%5C%20%0A%25%20%20distance%20value%0Ad%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AST%3D%5Csqrt%7B%5B-3-%28-6%29%5D%5E2%2B%5B4-7%5D%5E2%7D%5Cimplies%20ST%3D%5Csqrt%7B%28-3%2B6%29%5E2%2B%284-7%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AST%3D%5Csqrt%7B3%5E2%2B%28-3%29%5E2%7D%5Cimplies%20ST%3D%5Csqrt%7B18%7D%5Cimplies%20ST%3D%5Csqrt%7B9%5Ccdot%202%7D%0A%5C%5C%5C%5C%5C%5C%0AST%3D%5Csqrt%7B3%5E2%5Ccdot%202%7D%5Cimplies%20ST%3D3%5Csqrt%7B2%7D)
so we know S is the midpoint of PQ, and T is the midpoint of QR, thus
so, what's the distance from S to T?