The key is to find the first term a(1) and the difference d.
in an arithmetic sequence, the nth term is the first term +(n-1)d
the firs three terms: a(1), a(1)+d, a(1)+2d
the next three terms: a(1)+3d, a(1)+4d, a(1)+5d,
a(1) + a(1)+d +a(1)+2d=108
a(1)+3d + a(1)+4d + a(1)+5d=183
subtract the first equation from the second equation: 9d=75, d=75/9=25/3
Plug d=25/3 in the first equation to find a(1): a(1)=83/3
the 11th term is: a(1)+(25/3)(11-1)=83/3 +250/3=111
Please double check my calculation. <span />
we have the following:

solving for b:

therefore, the answer is 16
Answer:
-3x⁴ + 8x³ - 9x² - 7x - 9
General Formulas and Concepts:
Step-by-step explanation:
<u>Step 1: Define expression</u>
(5x³ - 3x⁴ - 2x - 9x² - 2) + (3x³ + 2x² - 5x - 7)
<u>Step 2: Simplify</u>
- Combine like terms (x³): -3x⁴ + 8x³ - 9x² - 2x - 5x - 2 - 7
- Combine like terms (x): -3x⁴ + 8x³ - 9x² - 7x - 2 - 7
- Combine like terms (constants): -3x⁴ + 8x³ - 9x² - 7x - 9
Answer:
see explanation
Step-by-step explanation:
Inequalities of the type | x | < a always have solutions of the form
- a < x < a
This can be extended to include expressions, that is
- 7 < 6x - 5 < 7 ( add 5 to all 3 intervals )
- 2 < 6x < 12 ( divide all 3 intervals by 6 )
-
< x < 2