1. Simplify ((-2x^4y^7)/(x^5))^3. Assume all variables are nonzero.
A: (-8y^21)/(x^3)
2. Simplify 3x(5y + 4) - 2xy - 10x + 6x^2
A: 13xy + 2x + 6x^2 or 6x^2 + 13xy + 2x
3. Evaluate (2.0 x 10^-7)/(8.0 x 10^-9). Write the answer in scientific notation.
A: 0.25 x 10^2
4. Evlauate f(x) = 8 - 4x for f(0), f(1/2), and f(-2).
A: 8, 6, 16
5. Determine whether the relation is a function.
A: ?
6. A commuter has $75. Each day's commute costs $3.50. Write a function to represent the total amount the commuter has remaining after d days. What is the value of the function for an input of 5, and what does it represent?
A: ?
5. Determine whether the relation is a function: from last name to age.
A: ?
#1 ok
#2 ok
#3 right value, but not scientific notation
#4 ok
#5 Well, if it is a function, then no last name maps to more than one age. What do you think?
#6 r(d) 75.00-3.50d
I think you can answer the other parts of this one, no?
5. To determine whether the given relation is a function, we need to check if each input value has a unique output value. The relation is typically presented as a set of ordered pairs, where the first number represents the input (x-coordinate) and the second number represents the output (y-coordinate).
To analyze the given relation and determine if it is a function, we can look for any repeated x-values. If there are no repeated x-values, then the relation is a function. However, if there are any repeated x-values, then the relation is not a function.
Unfortunately, the specific relation is not provided, so we cannot determine whether it is a function or not.
6. To write a function that represents the total amount the commuter has remaining after d days, we can use the equation:
f(d) = 75 - 3.50d
Here, f(d) represents the remaining amount of money the commuter has after d days, and the equation subtracts the cost of the commute from the initial amount.
For an input of 5, we can substitute d = 5 into the equation:
f(5) = 75 - 3.50(5)
= 75 - 17.50
= 57.50
The value of the function for an input of 5, which is 57.50, represents the remaining amount of money the commuter has after 5 days of commuting.