Question

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={0,−6}. The solution set is x equals left brace neagtive 0 comma negative 6 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={−6,3}.

Answer 1

To solve the factored quadratic equation \(0 = -13x(x - 6)\), we need to set the factors equal to zero.

1. The first factor is \(-13x\): \[ -13x = 0 \] Dividing both sides by -13 gives us: \[ x = 0 \]

2. The second factor is \((x - 6)\): \[ x - 6 = 0 \] Adding 6 to both sides gives us: \[ x = 6 \]

Now, we have two solutions: \[ x = 0 \quad \text{and} \quad x = 6 \]

Thus, the solution set is: \[ x = {0, 6} \]

The correct response is: The solution set is \(x = {0, 6}\).

Answer 2

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 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 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 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.

Answer 3

To determine how far the golf ball will travel when it hits the ground, we need to solve the equation given by the parabolic function:

\[ 0 = -125x(x - 45) \]

This equation can be factored into two parts:

1. \( -125x = 0 \)
2. \( x - 45 = 0 \)

Setting each factor to zero gives:

1. From \(-125x = 0\): \[ x = 0 \]

2. From \(x - 45 = 0\): \[ x = 45 \]

So, the ball will hit the ground when \(x = 45\) yards.

Next, we need to find out how far the ball will need to roll to reach the hole, which is 55 yards away.

To find the additional distance the ball needs to roll: \[ \text{Distance to the hole} - \text{Distance traveled} = 55 - 45 = 10 \text{ yards} \]

Thus, the golf ball will hit the ground after traveling 45 yards, and it will need to roll an additional 10 yards to reach the hole.

The correct response is: 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.