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

50-60=10

step-by-step explanation:

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)