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(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 (D) 9

(x−4)(x−5)=0 (x-4)(x-5)=0 \newlineIf x=s x=s and x=t x=t are the solutions to the given equation, which of the following is equal to the value of ∣s−t∣ |s-t| ?\newlineChoose 11 answer:\newline(A) −9-9\newline(B) −1-1\newline(C) 11\newline(D) 99

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Full solution

Q. (x−4)(x−5)=0 (x-4)(x-5)=0 \newlineIf x=s x=s and x=t x=t are the solutions to the given equation, which of the following is equal to the value of ∣s−t∣ |s-t| ?\newlineChoose 11 answer:\newline(A) −9-9\newline(B) −1-1\newline(C) 11\newline(D) 99
  1. Find Solutions: We need to find the solutions to the equation (x−4)(x−5)=0(x-4)(x-5)=0.\newlineThe equation is already factored, so we can use the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero.\newlineSetting each factor equal to zero gives us two equations:\newline11. x−4=0x - 4 = 0\newline22. x−5=0x - 5 = 0
  2. Apply Zero Product Property: Solve the first equation x−4=0x - 4 = 0 for xx.\newlineAdding 44 to both sides of the equation gives us:\newlinex=4x = 4\newlineThis is our first solution, so we can say s=4s = 4.
  3. Solve Equation 11: Solve the second equation x−5=0x - 5 = 0 for xx.\newlineAdding 55 to both sides of the equation gives us:\newlinex=5x = 5\newlineThis is our second solution, so we can say t=5t = 5.
  4. Solve Equation 22: Now we need to find the absolute value of the difference between ss and tt, which is ∣s−t∣|s-t|.\newlineSubstitute s=4s = 4 and t=5t = 5 into the expression ∣s−t∣|s-t|:\newline∣s−t∣=∣4−5∣|s-t| = |4-5|
  5. Calculate Absolute Difference: Calculate the value of ∣4−5∣|4-5|.\newline∣4−5∣=∣−1∣|4-5| = |-1|\newlineThe absolute value of −1-1 is 11, so ∣4−5∣=1|4-5| = 1.

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