Question

current skill $ the variables a, b, c, and d are graphed on the number line shown. a c b d 0 use the number line to help you answer the questions in the chart. expression answer a - c d - a b - d c - d 123 abc 0 1 2 3 4 + - * ÷ 5 6 7 8 9 = . , $ x y π < ≤ > ≥ % : skill code: 1800002

Explanation:

Step1: Analyze positions on number line

From the number line, \(a\) is negative (left of 0), \(c\), \(b\), \(d\) are positive (right of 0), with \(a < 0 < c < b < d\) (assuming equal spacing, let's assign values: let each tick be 1 unit. So \(a=-4\), \(c = 2\), \(b = 3\), \(d = 4\) (since from \(a\) to 0: 4 ticks, 0 to \(c\): 2 ticks, \(c\) to \(b\):1 tick, \(b\) to \(d\):1 tick).

Step2: Calculate \(a - c\)

Substitute \(a=-4\), \(c = 2\): \(a - c=-4 - 2=-6\)? Wait, no, maybe spacing: Let's re - assign. Let the distance from \(a\) to 0 be 4 units (so \(a=-4\)), 0 to \(c\) is 2 units (\(c = 2\)), \(c\) to \(b\) is 1 unit (\(b = 3\)), \(b\) to \(d\) is 1 unit (\(d = 4\)). Then \(a - c=-4-2=-6\)? Wait, but maybe the number of ticks: from \(a\) to 0: 4 intervals, 0 to \(c\): 2 intervals, \(c\) to \(b\):1, \(b\) to \(d\):1. So \(a=-4\), \(c = 2\), \(b = 3\), \(d = 4\).

Step3: Calculate \(d - a\)

\(d - a=4-(-4)=8\)

Step4: Calculate \(b - d\)

\(b - d=3 - 4=-1\)

Step5: Calculate \(c - d\)

\(c - d=2 - 4=-2\)

Wait, maybe my initial value assignment is wrong. Let's look at the number line: The number line has \(a\) at the leftmost, then 0, then \(c\), \(b\), \(d\) in order. Let's count the number of units between them. Let the distance from \(a\) to 0 be 4 units (so \(a=-4\)), 0 to \(c\) is 2 units (\(c = 2\)), \(c\) to \(b\) is 1 unit (\(b = 3\)), \(b\) to \(d\) is 1 unit (\(d = 4\)).

So:

• \(a - c\): \(a\) is negative, \(c\) is positive, so \(a - c\) is negative. \(a=-4\), \(c = 2\), \(a - c=-4 - 2=-6\)
• \(d - a\): \(d = 4\), \(a=-4\), \(d - a=4-(-4)=8\)
• \(b - d\): \(b = 3\), \(d = 4\), \(b - d=3 - 4=-1\)
• \(c - d\): \(c = 2\), \(d = 4\), \(c - d=2 - 4=-2\)

Answer:

For \(a - c\): \(-6\) (if our value assignment is correct), for \(d - a\): \(8\), for \(b - d\): \(-1\), for \(c - d\): \(-2\) (assuming the number of intervals as above). But maybe the actual answer depends on the correct spacing. If we assume each small tick is 1 unit, then:

• \(a - c\): Let \(a=-4\), \(c = 2\), so \(a - c=-6\)
• \(d - a\): \(d = 4\), \(a=-4\), so \(d - a = 8\)
• \(b - d\): \(b = 3\), \(d = 4\), so \(b - d=-1\)
• \(c - d\): \(c = 2\), \(d = 4\), so \(c - d=-2\)

(Note: The answer may vary slightly depending on the exact unit assignment, but the method is to use the position on the number line to determine the sign and magnitude of the numbers and then perform subtraction.)