Answer:
2
Step-by-step explanation:
118 × 3 = 354 feet ( Path A)
180 × 3 = 540 feet ( Path B)
Path B as it is closer to 500 feet than path A
The numerators in each term are consecutive integers ≥ 6. If n = 1 refers to the first term, then the numerator of the n-th term would be n + 5.
The denominators are consecutive odd integers ≥ 7. Odd numbers take the form 2k - 1, where k is any integer, and 2k - 1 = 7 when k = 4. But we want our sequence to start at n = 1, so we replace k here with n + 3. Then the denominator of the n-th term would be 2 (n + 3) - 1, or 2n + 5.
The odd-indexed terms are negative, while the even-indexed terms are positive. We can account for the sign of the term by multiplying by (-1)ⁿ.
Taking everything together, it follows that the n-th term in the sequence is

To add fractions, find the LCD and then combine.
Exact form:
9/2
Decimal form:
4.5
Mixed number form:
4 1/2
So, answer is
4 1/2
Hope this helps!
Answer:
x = 12
, y = -3
Step-by-step explanation:
Solve the following system:
{2 x + 7 y = 3 | (equation 1)
x = -4 y | (equation 2)
Express the system in standard form:
{2 x + 7 y = 3 | (equation 1)
x + 4 y = 0 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{2 x + 7 y = 3 | (equation 1)
0 x+y/2 = -3/2 | (equation 2)
Multiply equation 2 by 2:
{2 x + 7 y = 3 | (equation 1)
0 x+y = -3 | (equation 2)
Subtract 7 × (equation 2) from equation 1:
{2 x+0 y = 24 | (equation 1)
0 x+y = -3 | (equation 2)
Divide equation 1 by 2:
{x+0 y = 12 | (equation 1)
0 x+y = -3 | (equation 2)
Collect results:
Answer: {x = 12
, y = -3