Determine whether the values -1 and 7.3 are solutions to the quadratic equation 3x^2 - 4x - 4 = 3
To determine whether -1 and 7.3 are solutions to the quadratic equation 3x^2 - 4x - 4 = 3, we need to substitute each value into the equation and see if it equals 3.
For -1:
3(-1)^2 - 4(-1) - 4 = 3
3(1) + 4 - 4 = 3
3 + 4 - 4 = 3
3 = 3
Since -1 satisfies the equation, it is a solution.
For 7.3:
3(7.3)^2 - 4(7.3) - 4 = 3
3(53.29) - 29.2 - 4 = 3
159.87 - 29.2 - 4 = 3
159.87 - 33.2 = 3
126.67 = 3
Since 7.3 does not satisfy the equation, it is not a solution.
Therefore, -1 is a solution to the quadratic equation 3x^2 - 4x - 4 = 3, but 7.3 is not.
Determine whether the values -1 and 7/3 are solutions to the quadratic equation 3x^2 - 4x - 4 = 3
To determine whether -1 and 7/3 are solutions to the quadratic equation 3x^2 - 4x - 4 = 3, we need to substitute each value into the equation and see if it equals 3.
For -1:
3(-1)^2 - 4(-1) - 4 = 3
3(1) + 4 - 4 = 3
3 + 4 - 4 = 3
3 = 3
Since -1 satisfies the equation, it is a solution.
For 7/3:
3(7/3)^2 - 4(7/3) - 4 = 3
3*(49/9) - (28/3) - 4 = 3
(147/9) - (84/9) - (36/9) = 3
(147 - 84 - 36)/9 = 3
(27/9) = 3
3 = 3
Since 7/3 satisfies the equation, it is also a solution.
Therefore, both -1 and 7/3 are solutions to the quadratic equation 3x^2 - 4x - 4 = 3.
Use the table to answer the question.
When set off, a certain firework follows the path of the quadratic function h = -25/36x^2, 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 the table is a solution to the equation 0 = -25/36x^2 + 16 2/3x.
A. 12 feet
B. 36 feet
C. 48 feet
D. 24 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 = -25/36x^2 + 16 2/3x true.
By looking at the table, we can see that the equation is equal to 0 at x = 12 feet.
Therefore, the firework will travel 12 feet before reaching the ground.
The correct answer is A. 12 feet.
Ariel is trying to determine of x = -3 is a solution to the quadratic -3x^2 - 9x = 0. Which explanation demonstrates the correct reasoning?
A. Yes, x = -3 is a solution because substituting it back into the equation results in the following: x = -3, substituted -3(-3)^2 - 9(-3) = 0, evaluate 54 = 0, its a true statement.
B. No, x = -3 is not a solution because substituting it back into the equation results in the following: x = -3, substituted -3(-3)^2 - 9(-3) = 0, evaluate 54 not equal to 0, its a false statement
C. Yes, x = -3 is a solution because substituting it back into the equation results in the following: x = -3, substituted -3(-3)^2 - 9(-3) = 0, evaluate 0 = 0, its a true statement.
D. No, x = -3 is not a solution because substituting it back into the equation results in the following: x = -3, substituted -3(-3)^2 - 9(-3) = 0, evaluate 54 not equal to 0, its a false statement.
The correct reasoning is option D.
No, x = -3 is not a solution because substituting it back into the equation results in the following: x = -3, substituted -3(-3)^2 - 9(-3) = 0, evaluate 54 not equal to 0, it's a false statement.
When we substitute x = -3 into the equation -3x^2 - 9x = 0, we get:
-3(-3)^2 - 9(-3) = 0
-3(9) + 27 = 0
-27 + 27 = 0
0 = 0
Since the equation is true when x = -3, it is a valid solution.
Show how many solutions are in the solution set for the equation 3x^2 = 21
A. infinitely many
B. two
C. zero
D. one
To determine the number of solutions in the solution set for the equation 3x^2 = 21, we need to solve the equation.
We can start by dividing both sides of the equation by 3:
x^2 = 7
Next, we take the square root of both sides to isolate x:
x = ±√7
The equation has two solutions, x = √7 and x = -√7.
Therefore, the correct answer is B. two.
Show how many solutions are in the solution set for 2( x - 5 )^2 + 2 = 20
A. infinitely many
B. zero
C. two
D. one