B. The equation has two real solutions.
To find the solutions to the quadratic equation x^2 = 4x - 5, we can rearrange it to x^2 - 4x + 5 = 0 and then use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = -4, and c = 5. Plugging in these values, we get:
x = (4 ± √((-4)^2 - 4(1)(5))) / (2(1))
x = (4 ± √(16 - 20)) / 2
x = (4 ± √(-4)) / 2
Since the square root of a negative number is not real, the equation has two complex solutions.
Consider the quadratic equation x^2 = 4x-5. How many solutions does the equation have?
A. The equation has one real solution.
B. The equation has two real solutions.
C. The equation has no real solutions.
D. The number of solutions cannot be determined.
5 answers
An astronaut drops a rock into a crater on the moon. The distance, d(t), in meters, the rock travels after t seconds can be modeled by the function d(t) = 0.8t^2. What is the average speed, in meters per second, of the rock between 5 and 10 seconds after it was dropped?
To find the average speed of the rock between 5 and 10 seconds, we need to find the total distance the rock traveled during this time and then divide by the total time.
The distance traveled by the rock after 5 seconds:
d(5) = 0.8(5)^2
d(5) = 0.8(25)
d(5) = 20 meters
The distance traveled by the rock after 10 seconds:
d(10) = 0.8(10)^2
d(10) = 0.8(100)
d(10) = 80 meters
So, the total distance traveled between 5 and 10 seconds is:
Total distance = d(10) - d(5)
Total distance = 80 - 20
Total distance = 60 meters
The total time taken is 10 - 5 = 5 seconds.
Average speed = Total distance / Total time
Average speed = 60 meters / 5 seconds
Average speed = 12 meters per second
Therefore, the average speed of the rock between 5 and 10 seconds after it was dropped is 12 meters per second.
The distance traveled by the rock after 5 seconds:
d(5) = 0.8(5)^2
d(5) = 0.8(25)
d(5) = 20 meters
The distance traveled by the rock after 10 seconds:
d(10) = 0.8(10)^2
d(10) = 0.8(100)
d(10) = 80 meters
So, the total distance traveled between 5 and 10 seconds is:
Total distance = d(10) - d(5)
Total distance = 80 - 20
Total distance = 60 meters
The total time taken is 10 - 5 = 5 seconds.
Average speed = Total distance / Total time
Average speed = 60 meters / 5 seconds
Average speed = 12 meters per second
Therefore, the average speed of the rock between 5 and 10 seconds after it was dropped is 12 meters per second.
What are the roots of the equation x^2+6x-9=0?
A. 3±6√2
B. -3±6√2
C.3±3√2
D.-3±3√2
A. 3±6√2
B. -3±6√2
C.3±3√2
D.-3±3√2
To find the roots of the equation x^2 + 6x - 9 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = 6, and c = -9. Plugging these values into the formula, we get:
x = (-6 ± √(6^2 - 4(1)(-9))) / (2(1))
x = (-6 ± √(36 + 36)) / 2
x = (-6 ± √72) / 2
x = (-6 ± 6√2) / 2
x = -3 ± 3√2
Therefore, the roots of the equation x^2 + 6x - 9 = 0 are:
D. -3 ± 3√2
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = 6, and c = -9. Plugging these values into the formula, we get:
x = (-6 ± √(6^2 - 4(1)(-9))) / (2(1))
x = (-6 ± √(36 + 36)) / 2
x = (-6 ± √72) / 2
x = (-6 ± 6√2) / 2
x = -3 ± 3√2
Therefore, the roots of the equation x^2 + 6x - 9 = 0 are:
D. -3 ± 3√2
1 answer