Iget confused a lot with the "or" and "and". , i have a test

"and" is where they intersect

"or" is adding both circles (only add the intersection once)

Start at the end of the paragraph and work backwards:

10 people like all 3 flavors so write 10 in the middle (where all 3 intersect).

26 like coffee and pecan so write 16 where those two circles intersect. (26 - 10 = 16, remember that 10 are already included in both circles)

15 like mint and pecan so write 5 where those two circles intersect (15 - 10 = 5, remember that 10 are already included in both circles)

22 like mint and coffee so write 12 where those two circles intersect (22 - 10 = 12, remember that 10 are already included in both circles).

48 like pecan so write 17 in the big circle (48 - 10 - 16 - 5).  The intersections contain 5, 16, and 10, so that leaves a remainder of 17.

52 like coffee so write 14 in the big circle (52 - 10 - 16 - 12).  The intersections contain 12, 16, and 10, so that leaves a remainder of 14.

30 like mint so write 3 in the big circle (30 - 10 - 12 - 5).  The intersections contain 5, 12, and 10, so that leaves a remainder of 3.

Answers:

a) 17 (big pecan circle only)

b) 60 (sum of all numbers in both mint and coffee circles)

c) 23 (the sum of every circle and intersection is 77, subtract that from 100)

d) 32 (pecan circle and intersections but not the pecan/coffee intersection)

e) 16 (intersection of pecan and coffee without the mint)

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)