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 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 equal 0. At least one 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. 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.
At least one of the factors, (2x-3) or (x+2), must equal 0 for the entire function to equal 0.
The path of a soccer ball can be modeled by the equation h(x)=−12x(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=−12x(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 Plug in 0 for all the x terms in the function. Plug in 0 for all the x terms in the function. Cancel out the x and then multiply −12 and −20. Cancel out the x and then multiply negative Start Fraction 1 over 2 End Fraction and negative 20 . 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. Solve the two equations: −12x=0 and x−20=0.
To find the horizontal distance the ball has traveled when the height of the soccer ball equals 0, Leon can use the Zero Product Property by solving the equation -12x(x-20) = 0.
Solve the factored quadratic equation 0=−13x(x−6) .(1 point) Responses The solution set is x={0,6}. The solution set is x equals left brace 0 comma 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={13,6}. 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={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)=−125x(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=−125x(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 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. 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. 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.
To determine how far the ball will have traveled when it hits the ground, we need to solve the equation -125x(x-45) = 0.
Factoring the equation, we have x(x-45) = 0.
Applying the Zero Product Property, we have x = 0 and x-45 = 0.
Solving for x, we find x = 0 and x = 45.
Therefore, the ball will hit the ground after it has traveled 45 yards.
To reach the hole, the ball will need to roll an additional distance of 55 - 45 = 10 yards.
Hence, the ball will need to roll an additional 10 yards to reach the hole.