Graph and solve x+2y=4, x-2y=-8
1 answer:
Answer:
(x, y) = (-2, 3)
Step-by-step explanation:
In this form, it is easy to determine the x- and y-intercepts of each equation. That makes it easy to graph the first one, but not so easy to graph the second one on the given form.
The x-intercept is found by solving for x when y=0. In the two equations, the x-intercepts are ...
x = 4
x = -8 . . . . . . not shown on the given grid
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The y-intercepts are found by solving for y when x=0. In the two equations, the y-intercepts are ...
y = 4/2 = 2
y = -8/-2 = 4
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For the second equation, you can solve for y to put it in slope-intercept form.
x -2y = -8
x +8 = 2y . . . . . add 2y+8
y = 1/2x +4 . . . . . . . slope = 1/2, y-intercept = 4 (which we already knew)
This means the graph of the second equation will have a rise of 1 for each run of 2 units to the right. Working to the left from the y-intercept, we find another point to be (-2, 3), a point 2 left and 1 down from the y-intercept. This point is also on the line produced by the first equation, so (-2, 3) is the solution to the system.
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Answer:
407.22 foot is the boat from the base of the lighthouse
Step-by-step explanation:
Given the statement: An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression.
Let x foot be the distance of the object(boat) from the base of the lighthouse
Angle of depression =
[Alternate angle]
In triangle CAB:
To find AB = x foot.
Using tangent ratio:
Here, BC = 50 foot and
then;
or
Simplify:
AB = x = 407.217321 foot
Therefore, the boat from the base of the light house is, 407.22'
