In a survey, 674 adults were asked what television programs they had recently watched. The following information was obtained: 228 adults watched neither the Big Game nor the New Movie, and 285 watched the New Movie. If 183 of those who watched the New Movie did not watch the Big Game, how many of the surveyed adults watched the following?
(a) both programs
(b) at least one program
(c) the Big Game
(d) the Big Game but not the New Movie

(a) both game = 102 adults

(b) At least one game = 446 adults

(c)The big game = 263 adults

(d) The big game but not the new movie= 161 adults

Step-by-step explanation:

Given, 674 adults were polled.

228 adults watched neither the Big Game nor the new movie.

Therefore (674-228)= 446 people either watch one show or both shows.

New movie watched= 285 adults  

New movie watched but did not watch the big game =183 adults..

(285-183) = 102 watched both programs.

Since 183 adults did not watch the big game.

Then(446-183)=263 watched the big game.

102 watched both programs.

Therefore (263-102) = 161 adults watched only big game.

(a) both game = 102 adults

(b) At least one game = 446 adults

(c)The big game = 263 adults

(d) The big game but not the new movie= 161 adults

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)

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb