x Substituted Evaluate True Statement? 12 24 36 48 When set off, a certain firework follows the path of the quadratic function h=−25/36 x^2+16 2/3x , 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=−25/36 x^2+16 2/3x .
36 feet
48 feet
24 feet
12 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=−25/36 x^2+16 2/3x true.
Let's substitute each value of x from the table into the equation and see which one makes it true.
For x = 36:
0 = -25/36 * 36^2 + 16 2/3 * 36
0 = -25/36 * 1296 + 16 2/3 * 36
0 = -900 + 600
0 ≠ -300
For x = 48:
0 = -25/36 * 48^2 + 16 2/3 * 48
0 = -25/36 * 2304 + 16 2/3 * 48
0 = -1600 + 800
0 ≠ -800
For x = 24:
0 = -25/36 * 24^2 + 16 2/3 * 24
0 = -25/36 * 576 + 16 2/3 * 24
0 = -400 + 400
0 = 0
For x = 12:
0 = -25/36 * 12^2 + 16 2/3 * 12
0 = -25/36 * 144 + 16 2/3 * 12
0 = -100 + 200
0 ≠ -100
Therefore, the only value of x in the table that makes the equation 0=−25/36 x^2+16 2/3x true is x = 24 feet.
To determine which value of x in the table is a solution to the equation 0=−25/36 x^2+16 2/3x, we need to substitute each value of x in the equation and evaluate if the equation is true.
Let's substitute and evaluate each value:
For x = 12 feet:
0 = (-25/36)(12)^2 + (16 2/3)(12)
0 = (-25/36)(144) + (16 2/3)(12)
0 = -100 + 40
0 ≠ -60
For x = 24 feet:
0 = (-25/36)(24)^2 + (16 2/3)(24)
0 = (-25/36)(576) + (16 2/3)(24)
0 = -400 + 320
0 ≠ -80
For x = 36 feet:
0 = (-25/36)(36)^2 + (16 2/3)(36)
0 = (-25/36)(1296) + (16 2/3)(36)
0 = -900 + 960
0 = 60
For x = 48 feet:
0 = (-25/36)(48)^2 + (16 2/3)(48)
0 = (-25/36)(2304) + (16 2/3)(48)
0 = -1600 + 960
0 = -640
Based on the evaluation, the only value of x in the table that is a solution to the equation 0=−25/36 x^2+16 2/3x is x = 36 feet.
To determine which value of x in the table is a solution to the equation 0 = -25/36 x^2 + 16 2/3x, we need to substitute each value from the table into the equation and check if the equation evaluates to 0.
Let's substitute each value one by one and see which one gives us a true statement.
1. For x = 12 feet:
Replace x with 12 in the equation: 0 = -25/36 * (12)^2 + 16 2/3 * 12
Simplify the equation: 0 = -25/36 * 144 + 16 2/3 * 12
Calculate: 0 = -100 + 200
The equation does not evaluate to 0, so x = 12 feet is not a solution.
2. For x = 24 feet:
Replace x with 24 in the equation: 0 = -25/36 * (24)^2 + 16 2/3 * 24
Simplify the equation: 0 = -25/36 * 576 + 16 2/3 * 24
Calculate: 0 = -400 + 400
The equation does evaluate to 0. Therefore, x = 24 feet is a solution.
3. For x = 36 feet:
Replace x with 36 in the equation: 0 = -25/36 * (36)^2 + 16 2/3 * 36
Simplify the equation: 0 = -25/36 * 1296 + 16 2/3 * 36
Calculate: 0 = -900 + 800
The equation does not evaluate to 0, so x = 36 feet is not a solution.
4. For x = 48 feet:
Replace x with 48 in the equation: 0 = -25/36 * (48)^2 + 16 2/3 * 48
Simplify the equation: 0 = -25/36 * 2304 + 16 2/3 * 48
Calculate: 0 = -1600 + 1600
The equation does evaluate to 0. Therefore, x = 48 feet is a solution.
Based on our calculations, the values of x that are solutions to the equation are 24 feet and 48 feet.