To determine which graph represents the number of half-days and full-days that Brad must work to earn more than 40 hours of job shadowing, let's establish a few variables:
- Let \( x \) be the number of half-days Brad works.
- Let \( y \) be the number of full-days he works.
The total number of hours he earns can be represented by the equation:
\[ 4x + 8y > 40 \]
This can be simplified:
\[ x + 2y > 10 \]
To create a graph of this inequality, we can first find the boundary line by setting the equation equal to 10:
\[ x + 2y = 10 \]
Next, we can find the intercepts:
-
When \( x = 0 \): \[ 0 + 2y = 10 \Rightarrow y = 5 \] (This gives the point (0, 5))
-
When \( y = 0 \): \[ x + 2(0) = 10 \Rightarrow x = 10 \] (This gives the point (10, 0))
Now, we can plot the line connecting the points (0, 5) and (10, 0).
To determine the region that satisfies the inequality \( x + 2y > 10 \), we will shade above the line since we want all the combinations of half-days and full-days that result in more than 40 hours.
If you have options A, B, C, D, and you want to know which represents this inequality correctly, look for a graph that:
- Has a line passing through points (0, 5) and (10, 0).
- Shows shading above this line, indicating the area where the values of \( x \) and \( y \) satisfy \( x + 2y > 10 \).
Without seeing the graphs W, X, Y, and Z, I can't specify exactly which one corresponds to this condition, but it would be the one fitting the criteria stated above. If you can provide the descriptions of each graph, I can help you identify the correct one!
1 answer