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Suppose that [tex]$x$[/tex] changes by 4 (that is, [tex]\Delta x=4[/tex]). Which of the following scenarios would produce this result? Select all that apply.

A. [tex]x[/tex] changes from [tex]x_i=-8[/tex] to [tex]x_f=-4[/tex]
B. [tex]x[/tex] changes from [tex]x_i=4[/tex] to [tex]x_f=7[/tex]
C. [tex]x[/tex] changes from [tex]x_i=15[/tex] to [tex]x_j=12[/tex]
D. [tex]x[/tex] changes from [tex]x_i=5[/tex] to [tex]x_j=9[/tex]
E. [tex]x[/tex] changes from [tex]x_i=-4[/tex] to [tex]x_i=-8[/tex]

Sagot :

GinnyAnsweridn
To determine which scenarios result in a change in [tex]\(x\)[/tex] of 4, we will calculate [tex]\(\Delta x\)[/tex] for each given scenario. The change in [tex]\(x\)[/tex], [tex]\(\Delta x\)[/tex], is found by taking the absolute difference between the final value [tex]\(x_f\)[/tex] and the initial value [tex]\(x_i\)[/tex].

Let's go through each scenario step-by-step:

1. Scenario 1: [tex]\(\Delta x = x_f - x_i = -4 - (-8) = -4 + 8 = 4\)[/tex]

Here, [tex]\(\Delta x = 4\)[/tex], which matches the required change. So, this scenario is valid.

2. Scenario 2: [tex]\(\Delta x = x_f - x_i = 7 - 4 = 3\)[/tex]

Here, [tex]\(\Delta x = 3\)[/tex], which does not match the required change of 4. So, this scenario is not valid.

3. Scenario 3: [tex]\(\Delta x = x_f - x_i = 12 - 15 = -3\)[/tex]

Taking the absolute value, [tex]\(\Delta x = | -3 | = 3\)[/tex], which does not match the required change of 4. So, this scenario is not valid.

4. Scenario 4: [tex]\(\Delta x = x_f - x_i = 9 - 5 = 4\)[/tex]

Here, [tex]\(\Delta x = 4\)[/tex], which matches the required change. So, this scenario is valid.

5. Scenario 5: [tex]\(\Delta x = x_f - x_i = -8 - (-4) = -8 + 4 = -4\)[/tex]

Taking the absolute value, [tex]\(\Delta x = | -4 | = 4\)[/tex], which matches the required change. So, this scenario is valid.

Based on the calculations, the scenarios that produce the required change in [tex]\(x\)[/tex] of 4 are:
1. [tex]\(x\)[/tex] changes from [tex]\(x_i = -8\)[/tex] to [tex]\(x_f = -4\)[/tex]
2. [tex]\(x\)[/tex] changes from [tex]\(x_i = 5\)[/tex] to [tex]\(x_f = 9\)[/tex]
3. [tex]\(x\)[/tex] changes from [tex]\(x_i = -4\)[/tex] to [tex]\(x_f = -8\)[/tex]

Thus, the valid scenarios are 1, 4, and 5.
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