Answer: 742
<u>Step-by-step explanation:</u>
The given sequence {27, 31, 35, ... } provides the following information:
- the first term (a₁) = 27
- the difference (d) = 4
We can use the information above to find the explicit rule of the sequence:
We can use the explicit rule to find the 14th term (a₁₄)
Next, we can input the first and last term of the sequence into the Sum formula:
3 - (5x + 4/5) = x/2
3 - 5x - 4/5 = x/2
3 - 4/5 = x/2 + 5x
15/5 - 4/5 = x/2 + 5x
11/5 = x/2 + 5x.....multiply both sides by 10
22 = 5x + 50x
22 = 55x
22/55 = x
2/5 = x
The correct answer is:
[C]: "
a = ± 
" .
<span>
___________________________________________________________Explanation: _________________________________________________________We are given:
_________________________________________________________ </span>
→ "
25 = a² + b² " ; Solve for "
a" ;
_________________________________________________________ → To solve for "
a" ; we want to isolate "
a" on one side of the equation.
_________________________________________________________We can rewrite: "
25 = a² + b² " ;
as: " a² + b² = 25 " .
_________________________________________________________
Then, we can subtract "
b² " from each side of the equation; as follows:
_________________________________________________________
→ " a² + b² − b² = 25 − b² " ;
to get:
_________________________________________________________ → " a² = 25 − b² " ;
_________________________________________________________ → Now, take the square root of EACH SIDE of the equation ;
to isolate "
a" on one side of the equation; & to solve for the value(s) of "
a" ;
_________________________________________________________ → √(a²) =
;
to get:
_____________________________________________________ → a = | | ;
→ a = ± ;
→ which is:
Answer choice: [C]: "
a = ± " .
______________________________________________________
