This is an arithmetic sequence, since it's pattern is +4.
n1 = 1
d = 4
n = 1 + (n-1)(4) <-------------- This is the formula for the nth term of the sequence.
Answer:
The answer is False,
Step-by-step explanation:
The answer is False because in some expressions if there are parentheses and there is a subtraction problem in the parentheses but there is an addition problem in front of the parentheses that does not exactly mean that you do the addition first, this is because the subtraction is inside the parentheses and so since the subtraction is in parentheses it is done fist.
Answer:
5 * 5 * 5 * 5
Step-by-step explanation:
Use the rules of Indices.
5⁶⁻²
= 5⁴
Answer: The number of $12 tickets and $15 sold are 120 and 180 respectively.
Step-by-step explanation:
The given equation is:
12x + 15y = 4140 .....(1)
Where,
x stands for $12 tickets and y stands for $15 tickets
According to the question:
x + y = 300 ....(2)
Now solving equation 1 and 2.
From equation 2:
x = 300 - y
Now putting this expression in equation 1.
12x + 15y = 4140
12(300 - y) + 15y = 4140
3600 - 12y + 15y = 4140
3600 + 3y = 4140
3y = 4140 - 3600
3y = 540
y = 180
And,
x = 300 - y = 300 - 180 = 120
The number of $12 tickets sold = x = 120
The number of $15 tickets sold = y = 180
Thus, the number of $12 tickets and $15 sold are 120 and 180 respectively.
Since f(x) is (strictly) increasing, we know that it is one-to-one and has an inverse f^(-1)(x). Then we can apply the inverse function theorem. Suppose f(a) = b and a = f^(-1)(b). By definition of inverse function, we have
f^(-1)(f(x)) = x
Differentiating with the chain rule gives
(f^(-1))'(f(x)) f'(x) = 1
so that
(f^(-1))'(f(x)) = 1/f'(x)
Let x = a; then
(f^(-1))'(f(a)) = 1/f'(a)
(f^(-1))'(b) = 1/f'(a)
In particular, we take a = 2 and b = 7; then
(f^(-1))'(7) = 1/f'(2) = 1/5
