Δefi is dilated by a scale factor of one third with the center of dilation at point f. then, it is reflected over line a to create δhfg. based on these transformations, which statement is true?

line segments eg and hi intersect at point f, forming triangles efi and hfg. line a intersects with both triangles at point f.

segment fe = segment fh over 3, segment fi = segment fg over 3, and segment ei = segment hg over 3; δefi ~ δhfg
segment fe = segment fg over 3, segment fi = segment fh over 3, and segment ei = segment hg over 3; δefi ~ δgfh
segment fe over 3 = segment fg, segment fi over 3 = segment fh, and segment ei over 3 = segment hg; δefi ~ δgfh

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)

step-by-step explanation:

in geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. by extension, a line and a plane, or two planes, in three-dimensional euclidean space that do not share a point are said to be parallel.