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$(x-4)(x-5)=0$ $\newline$ If $x=s$ and $x=t$ are the solutions to the given equation, which of the following is equal to the value of $|s-t|$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-9$ $\newline$ (B) $-1$ $\newline$ (C) $1$ $\newline$ (D) $9$

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Transformations of absolute value functions: translations and reflections

Full solution

Q.

(x-4)(x-5)=0

\newline

If

x=s

and

x=t

are the solutions to the given equation, which of the following is equal to the value of

|s-t|

?

\newline

Choose

1

answer:

\newline

(A)

-9

\newline

(B)

-1

\newline

(C)

1

\newline

(D)

9

Factorize and Solve: We are given the equation $(x-4)(x-5)=0$ . To find the solutions, we set each factor equal to zero and solve for $x$ . $\newline$ $(x-4) = 0$ or $(x-5) = 0$ $\newline$ Solving each equation gives us the solutions: $\newline$ $x = 4$ or $x = 5$
Assign Solutions: Now, we assign the solutions to $s$ and $t$ as given in the problem: $\newline$ $s = 4$ and $t = 5$
Calculate Absolute Value: We need to find the absolute value of the difference between $s$ and $t$ , which is $|s-t|$ . $\newline$ Calculate $|s-t|$ : $\newline$ $|s-t| = |4-5| = |-1|$
Final Result: The absolute value of $-1$ is $1$ , so $|s-t| = 1$ .

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