Find a single translation that has the same effect as the following composition of translations. (x, y) (x-5,y+7) followed by (x, y) (x+3,y)

( x - 2 , y + 7 )

Step-by-step explanation:

( x , y ) > ( x - 5 , y + 7 ) > ( x - 5 + 3 , y + 7 ) = ( x - 2 , y + 7 )

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)