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Based on the Zero Product Property, which of the following statements must be true about the quadratic equation (2x−3)(x+2)=0 ?(1 point)

Responses

Both factors, (2x−3) or ​(x+2), must equal 0 for the entire function to equal 0.
Both factors, left parenthesis 2 x minus 3 right parenthesis or left parenthesis x plus 2 right parenthesis , must equal 0 for the entire function to equal 0.

No values of x will make the function equal 0.
No values of x will make the function equal 0.

Neither of the factors, (2x−3) or ​(x+2), must equal 0 for the entire function to equal 0.
Neither of the factors, left parenthesis 2 x minus 3 right parenthesis or left parenthesis x plus 2 right parenthesis , must equal 0 for the entire function to equal 0.

At least one of the factors, (2x−3) or ​(x+2), must equal 0 for the entire function to

The path of a soccer ball can be modeled by the equation h(x)=−1/2x(x−20) , where h(x) is the height of the ball, and x is the horizontal distance the ball has traveled. To determine how far the ball has traveled when it hits the ground, Leon set the height equal to 0 and obtained the equation: 0=−1/2x(x−20) . How can he use the Zero Product Property to find the horizontal distance the ball has traveled when the height of the soccer ball equals 0?(1 point)
Responses

He cannot use the Zero Product Property because the height will never be 0.
He cannot use the Zero Product Property because the height will never be 0.

Cancel out the x and then multiply −1/2 and −20.
Cancel out the x and then multiply negative Start Fraction 1 over 2 End Fraction and negative 20 .

Solve the two equations: −1/2x=0 and x−20=0.
Solve the two equations: negative Start Fraction 1 over 2 End Fraction x equals 0 and x minus 20 equals 0 .

Plug in 0 for all the x terms in the function.

Solve the factored quadratic equation 0=−1/3x(x−6) .(1 point)
Responses

The solution set is x={1/3,6}.
The solution set is x equals left brace Start Fraction 1 over 3 End Fraction comma 6 right brace .

The solution set is x={0,−6}.
The solution set is x equals left brace neagtive 0 comma negative 6 right brace .

The solution set is x={−6,3}.
The solution set is x equals left brace neagtive 6 comma 3 right brace .

The solution set is x={0,6}.

A golfer hits a golf ball toward the hole 55 yards away. The ball follows a parabolic path given by the function h(x)=−1/25x(x−45) , where h(x) is the height of the golf ball and x is the horizontal distance it has traveled. Solve the equation to determine how far the ball will have traveled when it hits the ground. How far will the ball need to roll to make it to the hole?

0=−1/25x(x−45)

(1 point)
Responses

The ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole.
The ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole.

The ball will hit the ground after it has traveled 25 yards. It will need to roll an additional 30 yards to reach the hole.
The ball will hit the ground after it has traveled 25 yards. It will need to roll an additional 30 yards to reach the hole.

The ball will hit the ground after it has traveled 30 yards. It will need to roll an additional 25 yards to reach the hole.
The ball will hit the ground after it has traveled 30 yards. It will need to roll an additional 25 yards to reach the hole.

The ball will hit the ground after it has traveled 10 yards. It will need to roll an additional 45 yards to reach the hole.

please give me an answer summary and double check

1 answer

Here’s a summary of the questions and correct answers based on the given options:

  1. Based on the Zero Product Property for the equation (2x−3)(x+2)=0:

    • Correct Response: Both factors, (2x−3) or (x+2), must equal 0 for the entire function to equal 0.

  2. How Leon can use the Zero Product Property with the equation 0=−1/2x(x−20):

    • Correct Response: Solve the two equations: −1/2x=0 and x−20=0.

  3. Solving the factored quadratic equation 0=−1/3x(x−6):

    • Correct Response: The solution set is x={0,6}.

  4. Golf ball problem with the equation 0=−1/25x(x−45):

    • Correct Response: The ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole.

Summary of Correct Answers:

  1. Both factors, (2x−3) or (x+2), must equal 0 for the entire function to equal 0.
  2. Solve the two equations: −1/2x=0 and x−20=0.
  3. The solution set is x={0,6}.
  4. The ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole.

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