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 and 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?
The coordinates of the second spot are (−10+3,6−12), which simplify to (-7,-6).
solve the equation. 3x + 6 = 24
To solve the equation 3x + 6 = 24, we need to isolate the variable x.
First, we can subtract 6 from both sides of the equation to get:
3x = 18
Then, we can divide both sides by 3 to get:
x = 6
Therefore, the solution to the equation 3x + 6 = 24 is x = 6.
solve the equation. x/4 + 1 = -6
To solve the equation x/4 + 1 = -6, we can start by isolating the variable x.
First, we can subtract 1 from both sides of the equation:
x/4 = -7
Next, we can multiply both sides by 4 to get rid of the fraction:
x = -28
Therefore, the solution to the equation x/4 + 1 = -6 is x = -28.
To find the coordinates of the second spot, we need to add the distances east and south from the first spot to its coordinates.
Given that the first spot is at (-10, 6), we can add 3 yards to the east, moving positively along the x-axis, and subtract 12 yards to the south, moving negatively along the y-axis.
Adding 3 yards to the x-coordinate does not change the sign, so we have -10 + 3 = -7 as the new x-coordinate.
Subtracting 12 yards from the y-coordinate changes the sign, so we have 6 - 12 = -6 as the new y-coordinate.
Therefore, the coordinates of the second spot are (-7, -6).