The explicit function is (b) f(n) = -4(n - 1) + 3; the seventh term is -21
<h3>How to determine the explicit form?</h3>
The given parameters are:
- First term of the sequence, a = 3
- Common difference of the sequence, d = -4
The explicit form is for an arithmetic function.
An arithmetic function has an explicit form represented as:
f(n) = a + (n -1) * d
Substitute the values of n and a in the above equation
f(n) = 3 + (n -1) * -4
Evaluate the product i.e. multiply -4 by (n - 1)
f(n) = 3 -4(n - 1)
Rewrite the equation as
f(n) = -4(n - 1) + 3
The seventh term is then calculated as:
f(n) = -4(n - 1) + 3
Substitute 7 for n in the above equation
f(7) = -4(7 - 1) + 3
Evaluate
f(7) = -21
Hence, the explicit function is (b) f(n) = -4(n - 1) + 3; the seventh term is -21
Read more about arithmetic sequence at:
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0.025 ÷ 0.5 = 0.05
lol very quick answer but yea
answer: 0.05
Louis is walking at 4 mph. If Louis can walk 2 miles in 30 minutes, she can then walk 4 miles in an hour if you double the amount of time she is walking from 30 to 60, so you would also double the distance. She is walking at 4 miles per hour.
Solve for v by simplifying both sides of the equation, then isolating the variable.
v = -1
A) zeroes
P(n) = -250 n^2 + 2500n - 5250
Extract common factor:
P(n)= -250 (n^2 - 10n + 21)
Factor (find two numbers that sum -10 and its product is 21)
P(n) = -250(n - 3)(n - 7)
Zeroes ==> n - 3 = 0 or n -7 = 0
Then n = 3 and n = 7 are the zeros.
They rerpesent that if the promoter sells tickets at 3 or 7 dollars the profit is zero.
B) Maximum profit
Completion of squares
n^2 - 10n + 21 = n^2 - 10n + 25 - 4 = (n^2 - 10n+ 25) - 4 = (n - 5)^2 - 4
P(n) = - 250[(n-5)^2 -4] = -250(n-5)^2 + 1000
Maximum ==> - 250 (n - 5)^2 = 0 ==> n = 5 and P(5) = 1000
Maximum profit =1000 at n = 5
C) Axis of symmetry
Vertex = (h,k) when the equation is in the form A(n-h)^2 + k
Comparing A(n-h)^2 + k with - 250(n - 5)^2 + 1000
Vertex = (5, 1000) and the symmetry axis is n = 5.
