This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the inequalities that determine the unshaded regions for each graph: a) Step 1: Identify the horizontal lines that form the boundaries of the unshaded region. The unshaded region is bounded by the line y=0 from below and y=3 from above. Step 2: Determine the inequalities for the unshaded region. The region below y=0 is shaded, meaning y ≥ 0 is unshaded. The region above y=3 is shaded, meaning y ≤ 3 is unshaded. Combining these, the unshaded region is between y=0 and y=3, inclusive. 0 ≤ y ≤ 3 b) Step 1: Identify the vertical lines that form the boundaries of the unshaded region. The unshaded region is bounded by the line x=-2 from the left and x=2 from the right. Step 2: Determine the inequalities for the unshaded region. The region to the left of x=-2 is shaded, meaning x ≥ -2 is unshaded. The region to the right of x=2 is shaded, meaning x ≤ 2 is unshaded. Combining these, the unshaded region is between x=-2 and x=2, inclusive. -2 ≤ x ≤ 2 c) Step 1: Identify the diagonal line that forms the boundary. The line passes through (0,0), (1,1), (2,2), which is the line y=x. Step 2: Determine the inequality for the unshaded region. The region below the line y=x is shaded. This means the unshaded region is above or on the line y=x. y ≥ x d) Step 1: Identify the diagonal line that forms the boundary. The line passes through (-3,3), (0,0), (3,-3). The slope is (0-3)/(0-(-3)) = (-3)/(3) = -1. The y-intercept is 0. So the equation of the line is y=-x. Step 2: Determine the inequality for the unshaded region. The region above the line y=-x is shaded. This means the unshaded region is below or on the line y=-x. y ≤ -x Last free one today — make it count tomorrow, or type /upgrade for unlimited.