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
11 answers
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.
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
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.
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.
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.
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
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.
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
A. infinitely many
B. zero
C. two
D. one
To determine the number of solutions in the solution set for the equation 2( x - 5 )^2 + 2 = 20, we can start by simplifying the equation:
2( x - 5 )^2 + 2 = 20
2( x - 5 )^2 = 18
( x - 5 )^2 = 9
Next, we can take the square root of both sides to solve for x:
x - 5 = ±√9
x - 5 = ±3
Now, we can solve for x in each case:
Case 1: x - 5 = 3
x = 3 + 5
x = 8
Case 2: x - 5 = -3
x = -3 + 5
x = 2
So, there are two solutions to the equation: x = 8 and x = 2.
Therefore, the correct answer is C. two.
2( x - 5 )^2 + 2 = 20
2( x - 5 )^2 = 18
( x - 5 )^2 = 9
Next, we can take the square root of both sides to solve for x:
x - 5 = ±√9
x - 5 = ±3
Now, we can solve for x in each case:
Case 1: x - 5 = 3
x = 3 + 5
x = 8
Case 2: x - 5 = -3
x = -3 + 5
x = 2
So, there are two solutions to the equation: x = 8 and x = 2.
Therefore, the correct answer is C. two.