dominick is training for a race. he spends 0.75 hours running each time he runs and 1.5 hours swimming each…

dominick is training for a race. he spends 0.75 hours running each time he runs and 1.5 hours swimming each time he swims. this week, he spent more than 6 hours training for the race. which graph represents his possible training times this week?

dominick is training for a race. he spends 0.75 hours running each time he runs and 1.5 hours swimming each time he swims. this week, he spent more than 6 hours training for the race. which graph represents his possible training times this week?

Answer

Answer:

The correct graph is the one where the shaded region is above the dashed line (0.75x + 1.5y = 6) in the first quadrant (assuming standard graph labeling where (x =) number of runs, (y =) number of swims).

Explanation:

Step 1: Define Variables

Let (x =) number of runs, (y =) number of swims.
Total training time: (0.75x + 1.5y).

Step 2: Set Up Inequality

Time spent is more than 6 hours:
(0.75x + 1.5y > 6).

Step 3: Simplify Inequality

Divide by 0.75:
(x + 2y > 8).

Step 4: Identify Boundary Line

Boundary line: (x + 2y = 8) (dashed since inequality is strict).

Step 5: Determine Shaded Region

Test point ((0,0)): (0 + 0 = 0 \not> 8), so shade opposite side of origin.
Shaded region is above the line in the first quadrant (non-negative (x, y)).