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Interpret this function:

The number of parking spots (y) in the local town (x) years from now can be modeled by the equation below. How many spots are there now?

y = 1000x + 6000

a.1000
b.6000

5 answers

To find the number of parking spots now, we need to evaluate the function for the value of \( x \) that represents the current time, which is \( x = 0 \).

Given the equation:

\[ y = 1000x + 6000 \]

we substitute \( x = 0 \):

\[ y = 1000(0) + 6000 \] \[ y = 6000 \]

So, the number of parking spots now is 6000.

Thus, the answer is:

b. 6000

Match the word problem to the correct equation:
Which of the answer choices represents the situation below?
Enrique's health insurance plan costs $200.00 and he spends $100.00 per doctor's visit. How much will Enrique pay for health care after a certain number of doctor's visits?

a. y = 100x + 200
b. y = 30 + 300x
c. y = 250x + 40
d. y = 300 + 30x

To analyze the situation described in the word problem, we need to identify the fixed cost and the variable cost associated with Enrique's health care expenses.

  1. Fixed Cost: His health insurance plan costs $200.00. This is a one-time payment.
  2. Variable Cost: He spends $100.00 for each doctor's visit. This cost varies based on the number of visits.

Let's denote:

  • \( y \) as the total cost Enrique pays for health care.
  • \( x \) as the number of doctor's visits.

The total cost \( y \) can be expressed as:

\[ y = \text{(fixed cost)} + \text{(cost per visit)} \times \text{(number of visits)} \]

Substituting the values we have:

\[ y = 200 + 100x \]

Now let's match this with the provided answer choices:

  • a. \( y = 100x + 200 \) (This matches our calculation, since the order of addition does not matter.)
  • b. \( y = 30 + 300x \)
  • c. \( y = 250x + 40 \)
  • d. \( y = 300 + 30x \)

From this analysis, the correct choice is:

a. \( y = 100x + 200 \)

Which of the tables is NOT a function?

Which of the tables below doesn't represent a function?

table a table b table c
x y x y x y
0 5 3 5 1 5
3 5 0 7 8 1
9 7 1 9 7 6
5 0 3 0 3 3

a. table a
b. table b
c. table c

To determine which table does not represent a function, we need to remember that, in a function, each input (or \( x \) value) must correspond to exactly one output (or \( y \) value). In other words, no two identical \( x \) values can have different \( y \) values.

Let's examine each table:

Table A:

  x      y
  0       5
  3       5
  9       7
  5       0
  • All \( x \) values (0, 3, 9, and 5) are unique, and they correspond to only one \( y \) value each. This table represents a function.

Table B:

  x      y
  3       5
  0       7
  1       9
  3       0
  • The \( x \) value of 3 corresponds to two different \( y \) values (5 and 0). This violates the definition of a function. Therefore, Table B does not represent a function.

Table C:

  x      y
  1       5
  8       1
  7       6
  3       3
  • All \( x \) values (1, 8, 7, and 3) are unique, and they correspond to only one \( y \) value each. This table represents a function.

Based on this analysis, the table that does NOT represent a function is:

b. table b