Use the table to answer the question. x Substituted Evaluate True Statement? 12 24 36 48 When set off, a certain firework follows the path of the quadratic function h=−2536x2+1623x , where: h= the height of the firework in feet. x= the horizontal distance it travels in feet. To determine how far the firework will travel before reaching the ground, determine which value of x in table is a solution to the equation 0=−2536x2+1623x . (1 point) Responses 36 feet 36 feet 48 feet 48 feet 12 feet 12 feet 24 feet 24 feet Skip to navigation
To determine how far the firework will travel before reaching the ground, we need to find the value of x in the table that is a solution to the equation 0 = -2536x^2 + 1623x.
From the table, we can see that when x = 36, the value of h is 0. Therefore, the firework will travel 36 feet before reaching the ground.
The correct answer is: 36 feet.
To determine how far the firework will travel before reaching the ground, we need to find the value of x that makes the equation 0=−2536x^2+1623x true.
Looking at the table, we can see that when x = 36 feet, the equation becomes:
0 = -2536(36)^2 + 1623(36)
Simplifying the equation, we get:
0 = -2536(1296) + 58548
0 = -3306816 + 58548
0 = -3248268
As the equation does not evaluate to true when x = 36 feet, we can conclude that 36 feet is not a solution to the equation.
Similarly, we can observe that the equation does not evaluate to true for any of the other values of x in the table. Therefore, there is no solution in the provided table to determine how far the firework will travel before reaching the ground.
To determine which value of x in the table is a solution to the equation 0 = -2536x^2 + 1623x, we need to substitute each value of x from the table into the equation and evaluate if the statement is true.
Let's go through the process step by step:
1. Substitute x = 12 into the equation:
0 = -2536(12)^2 + 1623(12)
0 = -2536(144) + 1623(12)
0 = -365184 + 19476
0 = -345708
Since the statement is not true, we can conclude that x = 12 feet is not a solution to the equation.
2. Substitute x = 24 into the equation:
0 = -2536(24)^2 + 1623(24)
0 = -2536(576) + 1623(24)
0 = -1460736 + 38952
0 = -1421784
Again, the statement is not true, so x = 24 feet is not a solution.
3. Substitute x = 36 into the equation:
0 = -2536(36)^2 + 1623(36)
0 = -2536(1296) + 1623(36)
0 = -3292416 + 58428
0 = -3233988
Once again, the statement is not true, so x = 36 feet is not a solution either.
4. Lastly, substitute x = 48 into the equation:
0 = -2536(48)^2 + 1623(48)
0 = -2536(2304) + 1623(48)
0 = -5865984 + 77844
0 = -5782140
As before, the statement is not true for x = 48 feet.
Therefore, none of the values in the table (12, 24, 36, or 48) are solutions to the equation 0 = -2536x^2 + 1623x.