How do the themes of Anthem reveal Objectivism's philosophical concepts? Check all that apply.
Equality 7-2521's inner thoughts show Objectivism's belief in the subjective nature of the world.
Equality 7-2521's break from collectivism highlights Objectivism's belief in individualism and self-
interest as essential.
Equality 7-2521's criticism of a collectivist society highlights Objectivism's belief that an individual's
unique contributions to society wetermine his value as a man.
Equality 7-2521's discovery that mankind lost its greatest technological advancements as
collectivism increased highlights Objectivism's belief that individualism is the key to progress.
Equality 7-2521's determination to use his mind as a "searchlight that can find the truth" highlights
Objectivism's belief that reason must be used to discover knowledge.

step-by-step explanation: it is d

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)

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation: