2. You start a search for a buried object by marking the center of a field as (0, 0), with coordinates giving distances in yards. Coordinates to the north or east are positive, and coordinates to the south or west are negative. You find nothing at (-10, 6), so you try a likely looking spot 3 yards to the east and 12 yards to the south of the first spot. What are the coordinates of the second spot? (1 point)
The coordinates of the second spot are ( -7, -6).
You start at (0, 0) and move 3 yards to the east, so the x-coordinate becomes -3. Then you move 12 yards to the south, so the y-coordinate becomes -12.
Therefore, the coordinates of the second spot are (-3, -12) relative to the starting point of (0, 0). To get the absolute coordinates, we add -3 to the x-coordinate of the first point (-10) and -12 to the y-coordinate of the first point (6):
-10 + (-3) = -13 (the new x-coordinate)
6 + (-12) = -6 (the new y-coordinate)
So the absolute coordinates of the second spot are (-13, -6).
You start a search for a buried object by marking the center of a field as (0, 0), with coordinates giving distances in yards. Coordinates to the north or east are positive, and coordinates to the south or west are negative. You find nothing at (–10, 6), so you try a likely looking spot 3 yards to the east and 12 yards to the south of the first spot. What are the coordinates of the second spot?
A. (–7, –6)
B. (12, –6)
C. (–13, –9)
D. (5, –3)
The correct answer is A. (-7, -6).
To get to the second spot, you move 3 yards to the east and 12 yards to the south from (-10, 6).
Moving 3 yards to the east changes the x-coordinate from -10 to -10 + 3 = -7.
Moving 12 yards to the south changes the y-coordinate from 6 to 6 - 12 = -6.
Therefore, the coordinates of the second spot are (-7, -6).
Choose the function table that matches the given rule.
Output = Input – 3
There are multiple correct answers to this question, but here's one example of a function table that matches the rule "Output = Input - 3":
| Input | Output |
|-------|--------|
| 0 | -3 |
| 1 | -2 |
| 2 | -1 |
| 3 | 0 |
| 4 | 1 |
In this table, each output (i.e. the result of "Input - 3") is equal to the input minus 3. For example, when the input is 2, the output is 2 - 3 = -1. This matches the given rule.
Question 4 of 17
Make a table and graph the function.
y = 3x + 2
A. graphThe graph shows x values of negative 2, negative 1, zero, 1, and 2. The y values are negative 4, negative 1, 2, 5, and 8. The line passes through the points left-parenthesis negative 2 comma negative 4 right-parenthesis left-parenthesis negative 1 comma negative 1 right-parenthesis left-parenthesis zero comma 2 right-parenthesis left-parenthesis 1 comma 5 right-parenthesis.
B. graphThe graph shows x values of negative 2, negative 1, zero, 1, and 2. The y values are 6, 1, 2, 3, and 8. The line passes through the points left-parenthesis negative 2 comma negative 2 right-parenthesis left-parenthesis negative 1 comma zero right-parenthesis left-parenthesis zero comma 2 right-parenthesis left-parenthesis 1 comma 4 right-parenthesis.
C. graphThe graph shows x values of zero, negative 1, 3, 1, and 2. The y values are 6, zero, 2, 3, and 8. The line passes through the points left-parenthesis negative 6 comma negative 1 right-parenthesis left-parenthesis negative 5 comma zero right-parenthesis left-parenthesis negative 4 comma 1 right-parenthesis left-parenthesis negative 3 comma 2 right-parenthesis.
A. The graph shows x values of negative 2, negative 1, zero, 1, and 2. The y values are negative 4, negative 1, 2, 5, and 8. The line passes through the points (-2, -4), (-1, -1), (0, 2), (1, 5), and (2, 8).
Solve the equation. 5x + 2 = 62
To solve the equation 5x + 2 = 62, we want to isolate the variable x on one side of the equation by itself.
First, we'll subtract 2 from both sides of the equation:
5x + 2 - 2 = 62 - 2
Simplifying the left side:
5x = 60
Next, we'll divide both sides of the equation by 5:
5x/5 = 60/5
Simplifying:
x = 12
So the solution to the equation 5x + 2 = 62 is x = 12.