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: ?
For question 5, to determine whether a relation is a function, we need to check if each input value has a unique output value.
To do this, we can look at the given relation and see if any input value repeats with a different output value. If there are no repetitions, then the relation is a function. If there is at least one instance where an input value has multiple corresponding output values, then the relation is not a function.
Without the specific relation given, it is not possible to determine whether it is a function or not. Could you please provide the specific relation?
Regarding question 6, let's create the function as described.
The total amount the commuter has remaining after d days can be represented by the function:
Remaining amount = 75 - 3.50 * d
To find the value of the function for an input of 5, we substitute d = 5 into the function:
Remaining amount = 75 - 3.50 * 5
Remaining amount = 75 - 17.50
Remaining amount = 57.50
So, for an input of 5, the value of the function is 57.50. This represents the amount of money the commuter has remaining after 5 days of commuting.