Answer:
21
Step-by-step explanation:
Answer:
The expression that represents the given sequence is 5+6(n-1). Option C (not labeled).
Explanation:
<u>Arithmetic Sequences</u>
In an arithmetic sequence, each term can be obtained by adding or subtracting a fixed number to the previous term. That fixed number is called the common difference.
We are given the following sequence:
5, 11, 17, 23, 29, ...
Each term is located in a position starting from n=1. Let's test each option:
A For n=1 we should have the first term (5). Substituting n=1 into the general equation: 5+6(n+1) = 5+6(1+1) = 5+12 = 17. Since the resulting term is not 5, this option is incorrect.
B For n=1, 6+5(n+1)= 6+5(2)=16. This option is incorrect.
C (not labeled) For n=1, 5+6(n-1)=5+6(1-1)=5+0=5. The first term is correct. Let's test for the second term (n=2):
5+6(2-1)=5+6=11. Correct. For n=3
5+6(3-1)=5+12=17. Correct.
We can see the terms are increasing by 6, and the given sequence is also increasing by 6. Thus, This option is correct.
D For n=1, 6+5 (n-1)=6+0=6. This option is incorrect.
Answer:
D. -18x-6
Step-by-step explanation:
The Distributive property is all you do is time -3 to both the 6 and the 2 and you will get your answer. -18x-6.
Answer:
x = -1 ± 2i
Step-by-step explanation:
The standard form of a quadratic equation is ax² + bx + c = 0, and the quadratic formula is x= [−b ± √(b
² - 4ac) ] / 2a
In this case, a = 1, b = 2 and c = 5. Now you have to substitute in the quadratic formula:
x= [−b ± √(b
² - 4ac) ] / 2a
x= [−2 ± √(2
² - 4*1*5) ] / 2*1
x= [−2 ± √(4 - 20) ] / 2
x= [−2 ± √(-16) ] / 2
Since the square root is negative, you have to use imaginary numbers to continue solving the equation. Remmber that √(-1) = i.
x= [−2 ± √(-16) ] / 2
x= [−2 ± √(16)i ] / 2
x= [−2 ± 4i ] / 2
x1 = [−2 + 4i ] / 2
x1 = -1 + 2i
x2 = [−2 - 4i ] / 2
x2 = -1 - 2i
So the answers of x are -1 ± 2i