Consider the lines\begin{align*} y&=3x+5 \\ 2y&=4x+5 \\ 3y&=9x-2 \\ 2y&=x-3 \\ 4y&=x-5. \end{align*}Let's say that a pair of lines is $\emph{good}$ if the two lines are either parallel or perpendicular to each other. Among all the pairs of lines shown, how many pairs are good?

x² - 3x - 10 = (x - 5) (x + 2)

x² - 3x - 18 = (x + 3) (x - 6)

Step-by-step explanation:

x² - 3x - 10

x² + 2x - 5x - 10

x(x + 2) - 5(x + 2)

(x - 5) (x + 2)

x² - 3x - 18

x² - 6x + 3x - 18

x(x - 6) + 3(x - 6)

(x + 3) (x - 6)

-TheUnknownScientist

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!

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