An account that yields 6% simple interest annually has $2,000
2 answers:
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Summary of even and odd functions
A function f is even if the graph of f is symmetric with respect to the y-axis. Algebraically, f is even if and only if f(-x) = f(x) for all x in the domain of f.
A function f is odd if the graph of f is symmetric with respect to the origin. Algebraically, f is odd if and only if f(-x) = -f(x) for all x in the domain of f.
From the definition itself, we see how can we test if the functions are even or odd.
- First graph (to the left)
From the graph, we see that the function is symmetric with respect to the y-axis because the left side (x<0) is a reflection (along the y-axis) of the right side (x>0), so it is an even function.
- Second graph (to the right)
From the graph, we see that the function is symmetric with respect to the origin, the left side (x<0) is a reflection (along with the origin) of the side to the right (x>0), so it is an odd function.
- First function (to the left)
The function:
is an even function because we see that:
- Second function (to the right)
The function:
is an odd function because we see that:
Summary
We have the following results:
- First function (to the left): even
- Second graph (to the right): odd
- First function (to the left): even
- Second function (to the right): odd
For this case, the first thing we must do is define variables.
We have then:
m: original quantity of merchandise sold (in $)
We then have the following idea:
(original amount) (percent) = new amount
The new amount is the amount that Jacqueline earns for 12% of the commission on sales.
We have then:
Clearing m we have:
Answer:
The equation that solves the problem is:
The amount she sold is:
This is a classic problem I think that you mean
Answer:
This problem clearly states to use proof by induction, follow the complete answer below.
Step-by-step explanation:
To prove something by induction we have to make a proposition first, in this case:
is divisible by 9
Where is the order of the proposition.
First we have to prove the first few orders, let's just check P(1):
which is clearly divisible by 9
Now let's assume that P(n) is true that means, our original proposition is true. Now let's try to find out whether P(n+1) is true:
The is divisible by 9 because we assumed that "
is divisible by 9" was a true proposition. On the other hand
has a factor of 9 regardless of n, thus is also divisible by 9 that means that P(n+1) is true and it follows that P(n) must also be true, thus proving our initial statement.