Answer:
(x, y) = (-1, -3) or (4, 12)
Step-by-step explanation:
A graphing calculator can show the solutions to this system.
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You can equate expressions for y and solve for x.
3x = x^2 -4
x^2 -3x = 4 . . . . add 4-3x
x^2 -3x +2.25 = 6.25 . . . . complete the square by adding (-3/2)^2 where -3 is the coefficient of x.
(x -1.5)^2 = 2.5^2 . . . . . . rewrite as squares
x -1.5 = ±2.5 . . . . . . . . . . take the square root
x = 1.5 ± 2.5 = -1, +4
y = 3x = -3, +12, respectively
Solutions are ...
(x, y) = (-1, -3) . . . . and . . . . (4, 12)
4500 feet
Step-by-step explanation:
We can begin by finding x using the tangent rule;
The tangent of the angle = the length of the opposite side / the length of the adjacent side
Tan 35 = 3500 / x
X = 3500 / tan 35
X = 3500 / 0.7
X = 5000
Now that we have x we can calculate the value of ? using the same tangent rule;
Tan 42 = ? / 5000
? = tan42 * 5000
? = 0.9 * 5000
? = 4500
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