Answer with Step-by-step explanation:
We are given that
For each real number
To prove that f is one -to-one.
Proof:Let and
be any nonzero real numbers such that
By using the definition of f to rewrite the left hand side of this equation
Then, by using the definition of f to rewrite the right hand side of this equation of
Equating the expression then we get
Therefore, f is one-to-one.
We are given the number of Blue and Purple Marbles for each of the four friends. So first we have to find the ratio of blue marbles to purple marbles for each of them.
A) Rosa
Number of blue marbles = 10
Number of purple marbles = 12
Ratio of blue to purple marbles =
B) Chi
Number of blue marbles = 5
Number of purple marbles = 6
Ratio of blue to purple marbles =
C) Alberto
Number of blue marbles = 5
Number of purple marbles = 12
Ratio of blue to purple marbles =
D) Pedro
Number of blue marbles = 10
Number of purple marbles = 6
Ratio of blue to purple marbles =
From the above calculations we can see that Pedro has the highest value of ratio for blue marbles to purple marbles. Also we can see Pedro is the only one for whom the number of blue marbles is more than the number of purple marbles. So this confirms that our calculation is correct.
Thus, the player which gets to go first is Pedro.
Answer:
The correct answer is the last option, that is,
Step-by-step explanation:
We have been given that the first runner has $112 in savings, received a $45 gift from a friend, and will save $25 each month. Therefore, amount of money in the account of first running after m months will be:
We have been given that the second runner has $50 in savings and will save $60 each month. Therefore, amount of money in the account of second running after m months will be:
In order for amount of money to be equal in accounts of both the runners, we set up:
Upon rewriting the left hand side using commutative law, we get:
Therefore, we can see that the last option is the correct answer.