Figure efgh on the grid below represents a trapezoidal plate at its starting position on a rotating platform:

the plate is rotated 90° about the origin in the counterclockwise direction. which of the following describes the relationship of the paths traced by f and g as they undergo this rotation?

1. they form concentric circles.
2. they form congruent segments.
3. they form parallel segments.
4. they form perpendicular segments.

They form congruent segments

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.

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)