The equation (x + 5) + (y + 3) = 169 models the position and range of the source of a radio signal. Describe the position of the source and the range of the signals.
How would I explain it?
To explain the position of the source and the range of the signals represented by the equation (x + 5) + (y + 3) = 169, we need to understand the equation's structure.
The equation represents a position in a two-dimensional Cartesian coordinate system, with x representing the horizontal position and y representing the vertical position. The equation (x + 5) + (y + 3) = 169 states that the sum of x plus 5 (representing a horizontal shift) and y plus 3 (representing a vertical shift) is equal to 169, which indicates the range of the signals.
To determine the position of the source, we can rearrange the equation by isolating either x or y. Let's isolate x by subtracting 5 from both sides of the equation: (x + 5) + (y + 3) - 5 = 169 - 5, which simplifies to x + y + 3 = 164.
Now, if we subtract 3 from both sides of the equation, we get x + y + 3 - 3 = 164 - 3, simplifying to x + y = 161. This equation represents a straight line that the source could potentially be located on.
As for the range of the signals, we need to determine the values of x and y that satisfy the equation. One way to find these values is by substituting different pairs of numbers into the equation and checking if they satisfy it. Another way is to plot the equation on a graph and see which points fall on the line.
Overall, the position of the source is represented by the equation x + y = 161, which lies on a straight line, and the range of the signals can be determined by finding the values of x and y that satisfy the equation (x + 5) + (y + 3) = 169.