On a road map 1 inch represents 1,500 miles. How many miles represent 4 inches?
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<h3>Answer:</h3>
(-4, 15), (1.5, 4)
<h3>Step-by-step explanation:</h3>This is easily solved using a graphing calculator. (See attached.)
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Algebraically, the solution is found by equating the expressions for y:
... -2x +7 = y = 2x² +3x -5
... 2x² +5x -12 = 0 . . . . rearranged to standard form
... (2x -3)(x +4) = 0 . . . . factor
The x-values of the points of intersection are those that make these factors be zero:
... 2x-3 = 0 ⇒ x = 3/2
... x+4 = 0 ⇒ x = -4
The linear equation is the easiest to use to find the corresponding y-values.
... for x = 3/2, y = -2(3/2) +7 = 4
... for x = -4, y = -2(-4) +7 = 15
The points of intersection are (-4, 15) and (3/2, 4).