x Substituted Evaluate True Statement? 12 24 36 48 When set off, a certain firework follows the path of the quadratic function h=−25/36x^2+162/3x , 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=−25/36x^2+162/3x .
36 feet
48 feet
24 feet
12 feet
To determine which value of x is a solution to the equation 0=−25/36x^2+162/3x, we substitute each value of x given in the table.
For x = 36 feet:
0 = -25/36(36)^2 + 162/3(36)
0 = -25/36(1296) + 162/3(36)
0 = -25/36(1296) + 54(36)
0 = -900 + 1944
0 = 1044
Since 0 does not equal 1044, x = 36 feet is not a solution.
For x = 48 feet:
0 = -25/36(48)^2 + 162/3(48)
0 = -25/36(2304) + 162/3(48)
0 = -25/36(2304) + 54(48)
0 = -1600 + 2592
0 = 992
Since 0 does not equal 992, x = 48 feet is not a solution.
For x = 24 feet:
0 = -25/36(24)^2 + 162/3(24)
0 = -25/36(576) + 162/3(24)
0 = -25/36(576) + 54(24)
0 = -400 + 1296
0 = 896
Since 0 does not equal 896, x = 24 feet is not a solution.
For x = 12 feet:
0 = -25/36(12)^2 + 162/3(12)
0 = -25/36(144) + 162/3(12)
0 = -25/36(144) + 54(12)
0 = -100 + 648
0 = 548
Since 0 does equal 548, x = 12 feet is a solution.
Therefore, the firework will travel 12 feet before reaching the ground.
To determine which value of x in the table is a solution to the equation 0 = (-25/36)x^2 + (162/3)x, we can substitute each value in the equation and see which one makes it true.
Let's substitute x = 36 into the equation:
0 = (-25/36)(36)^2 + (162/3)(36)
0 = (-25/36)(1296) + (162/3)(36)
0 = -900 + 1944
0 = 1044
Since the equation is not true when x = 36, let's try the next value.
Let's substitute x = 48 into the equation:
0 = (-25/36)(48)^2 + (162/3)(48)
0 = (-25/36)(2304) + (162/3)(48)
0 = -1600 + 2592
0 = 992
Again, the equation is not true when x = 48. Let's move on to the remaining values.
Let's substitute x = 24 into the equation:
0 = (-25/36)(24)^2 + (162/3)(24)
0 = (-25/36)(576) + (162/3)(24)
0 = -400 + 432
0 = 32
Finally, let's substitute x = 12 into the equation:
0 = (-25/36)(12)^2 + (162/3)(12)
0 = (-25/36)(144) + (162/3)(12)
0 = -100 + 216
0 = 116
Therefore, the true statement is that the firework will travel 12 feet before reaching the ground.
To determine which value of x in the table is a solution to the equation 0 = -25/36x^2 + 162/3x, we substitute each value of x from the table into the equation and check if the equation equals zero.
Let's evaluate for each value of x in the table:
1. When x = 12:
0 = -25/36 * 12^2 + 162/3 * 12
0 = -25/36 * 144 + 162/3 * 12
0 = -25/36 * 144 + 54 * 12
0 = -25 * 4 + 648
0 = -100 + 648
0 = 548
2. When x = 24:
0 = -25/36 * 24^2 + 162/3 * 24
0 = -25/36 * 576 + 162/3 * 24
0 = -25/36 * 576 + 54 * 24
0 = -25 * 16 + 1296
0 = -400 + 1296
0 = 896
3. When x = 36:
0 = -25/36 * 36^2 + 162/3 * 36
0 = -25/36 * 1296 + 162/3 * 36
0 = -25/36 * 1296 + 54 * 36
0 = -25 * 36 + 1944
0 = -900 + 1944
0 = 1044
4. When x = 48:
0 = -25/36 * 48^2 + 162/3 * 48
0 = -25/36 * 2304 + 162/3 * 48
0 = -25/36 * 2304 + 54 * 48
0 = -25 * 64 + 2592
0 = -1600 + 2592
0 = 992
From the calculations, we can see that the equation is only equal to zero when x = 36 feet.
Therefore, the firework will travel 36 feet before reaching the ground.