The lines given by the equations y=2x and y=4x+1 are

Mathematics

1 answer:

BartSMP [9]3 years ago

8 0

the equations are already in slope-intercept form, therefore

$\bf \begin{array}{|c|ll}
\cline{1-1}
slope-intercept~form\\
\cline{1-1}
\\
y=\stackrel{\stackrel{slope}{\downarrow }}{m}x+\stackrel{\stackrel{y-intercept}{\downarrow }}{b}\\\\
y=mx+b
\\\\
\cline{1-1}
\end{array}~\hspace{8em}y=\stackrel{slope}{2}x\qquad y=\stackrel{slope}{4}x+1$

so their slopes are 2 and 4.

parallel lines have exactly the same slope, these ones do not, so they're not parallel.

perpendicular lines, have negative reciprocal slopes, in short, their product gives -1, 2*4 ≠ -1, so they're not perpendicular either.

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Express the terms of the following sequence by giving a recursive formula.

emmasim [6.3K]

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

$a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\$

Step-by-step explanation:

First of all, we have to determine if the given sequence is arithmetic sequence or geometric. For that purpose, we calculate the common difference and common ratio

Given sequence is:

11,4,-3,-10,-17...

Here

$a_1 = 11\\a_2 = 4\\a_3 = -3\\So,\\d = a_2 - a_1 = 4-11 = -7\\d = a_3-a_2 = -3-4 = -7$