Question

A. Write a system of inequalities that defines a shaded region that looks like a

right triangle?

b. Graph your system from part (a)?

c. What is the area of the triangle you drew with your system of inequalities in
parts (a) and (b)?​

Answer 1

Answer - 6 square units is answer

Answer 2

9514 1404 393

Answer:

a. x≥0, y≥0, x/3+y/4≤1

b. see attached

c. 6 square units

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