2. which of the following are terms of the series with nth term t-3n +17? a) 80 b) 170 c)217 d) 312 e) 278 f) 3566

The correct options are a,b,e and f.

Step-by-step explanation:

It is given that the nth terms of the series is defined as

Subtract 17 from both the sides.

Divide both sides by 3.

The term Tₙ is a term of given series if n is a positive integer.

(a) The given term is 80.

Since n is a positive integer, therefore 80 is a term of given series.

(b) The given term is 170.

Since n is a positive integer, therefore 170 is a term of given series.

(c) The given term is 217.

Since n is not a positive integer, therefore 217 is a term of given series.

(d) The given term is 312.

Since n is not a positive integer, therefore 312 is a term of given series.

(e) The given term is 278.

Since n is a positive integer, therefore 278 is a term of given series.

(f) The given term is 3566.

Since n is a positive integer, therefore 3566 is a term of given series.

Thus, the correct options are a, b, e and f.

9x

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)