Awoman leaves home and walks 3 miles west, then 2 miles southwest. how far from home is she, and in what direction must she walk to head directly home?

North-East

Step-by-step explanation:

First she walk 3 miles west and then 2 miles southwest

i.e. she is now Southwest direction with respect to initial position

she vertically 2miles below initial position

and horizontally 3+2cos45 away from initial position

Where \theta is angle made by her with horizontal

she should walk at North of east to reach directly home

answer:

given the linear inequality :

add 2y to both sides we get;

simplify:

add 12 to both sides of an equation;

simplify:

divide both sides by 2 we get;

or

the related equation for the inequality equation [1] is;

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

subtract 6 from both sides we get

multiply both sides by 2 we get;

or

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.