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Let’s check out your problem:

(x-4)(x-5)=0
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| ?
Choose 1 answer:
(A) -9
(B) -1
C 1

$(x-4)(x-5)=0$ $\newline$ 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 $1$

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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

Find Solutions: First, we need to find the solutions to the equation $(x-4)(x-5)=0$ . The equation is already factored, so we can set each factor equal to zero to find the solutions. $(x-4) = 0$ or $(x-5) = 0$ Solving each equation for $x$ gives us the solutions: $x = 4$ or $x = 5$
Identify Solutions: Now, we have the solutions $x = 4$ and $x = 5$ . According to the problem, $x = s$ and $x = t$ are the solutions, so we can say: $s = 4$ and $t = 5$
Calculate Absolute Value: We need to find the absolute value of the difference between $s$ and $t$ , which is $|s-t|$ . Substitute the values of $s$ and $t$ into the expression: $|s-t| = |4-5|$
Calculate Absolute Value: We need to find the absolute value of the difference between $s$ and $t$ , which is $|s-t|$ . $\newline$ Substitute the values of $s$ and $t$ into the expression: $\newline$ $|s-t| = |4-5|$ Calculate the value of $|4-5|$ : $\newline$ $|4-5| = |-1|$ $\newline$ The absolute value of $-1$ is $1$ . $\newline$ $t$ $0$

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