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
Step 1: Identify the first inequality from the dashed line. The dashed line represents the equation y = x + 5. Since the line is dashed, the inequality is strict (< or >). The shaded region is below this line. To confirm, we can test a point in the shaded region, for example, (0,0). Substituting (0,0) into y < x + 5: 0 < 0 + 5 0 < 5 (True). So, the first inequality is y < x + 5. Step 2: Identify the second inequality from the solid line. The solid line represents the equation 8x + 9y = 5. Since the line is solid, the inequality is non-strict ( or ). The shaded region is above this line. To confirm, we can test a point in the shaded region, for example, (-5, 5) (which is clearly in the shaded region). Substituting (-5, 5) into 8x + 9y 5: 8(-5) + 9(5) 5 -40 + 45 5 5 5 (True). So, the second inequality is 8x + 9y 5. Step 3: Combine the inequalities to represent the shaded region. The shaded region is the intersection of the two inequalities. The region represented on the number plane is: y < x + 5 \\ 8x + 9y 5 Send me the next one 📸