Write the arithmetic series using summation notation. 7.5+13.5+19.5+25.5+31.5+37.5

Mathematics

1 answer:

Pavlova-9 [17]3 years ago

6 0

Answer:

135

Step-by-step explanation:

its easier to take out the decimal first then add the rest then add the decimals together then add the two numbers to get the final answer

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Find the equation of the line that passes through (1, -1) and is parallel to

daser333 [38]

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

$2x+y-3=0\implies y=\stackrel{\stackrel{m}{\downarrow }}{-2} x+3 \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

so we're really looking for the equation of a line with a slope of -2 and that passes through (1 , -1)

$(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad \qquad \stackrel{slope}{m}\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{-2}(x-\stackrel{x_1}{1}) \\\\\\ y+1=-2x+2\implies y=-2x+1$