9514 1404 393
Answer:
a. x≥0, y≥0, x/3+y/4≤1
b. see attached
c. 6 square units
Step-by-step explanation:
a. We have elected to use the x- and y-axes as boundary lines of the triangle. The corresponding inequalities that place the triangle in the first quadrant are ...
x ≥ 0
y ≥ 0
We want to make a 3-4-5 right triangle, so we choose the x- and y-intercepts to be 3 and 4, respectively. The shading between the line through those points and the axes will be assured for x- and y-values less than or equal to those on the boundary line. In intercept form, the inequality is ...
x/3 +y/4 ≤ 1
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b. The graph is shown in the attachment.
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c. The legs of the right triangle have lengths 3 and 4, so the area is ...
A = 1/2bh = 1/2(3)(4) = 6 . . . square units
