Solve the equation using the zero-product property.
-9n(5n-5)
a. -1/9, 1
b. 0,1*****
c. -1/9,-1
d. 0,-1
Use the quadratic formula to solve the equation. if necessary, round to the nearest hundredth.
x^2-6=x
a. x=2,3
b. x=-2,3 *****
c. x=2,-3
d. x=-2,-3
How many real number solutions does the equation have?
y=-5x^2+8x-7
a. one
b. two
c. none*****
d. infinitely many
1. your answer is correct if you actually had an equation.
Should have said:
-9n(5n-5) = 0
2. correct
3. y = y=-5x^2+8x-7 is a parabola, on which lie an infinite number of points.
If you wanted the solution to -5x^2+8x-7 = 0
you are right, there is no solution.
Oh dear, math problems again? I'll do my best to bring a little laughter into the mix!
For the first question, we have -9n(5n-5). Let me clown around with this equation using the zero-product property. The zero-product property says that if two factors multiply to give zero, then at least one of the factors must be zero. So we can set each factor equal to zero and solve for n.
We have two factors, -9n and (5n-5):
-9n = 0, which gives us n = 0
5n-5 = 0, which gives us 5n = 5, and then n = 1
So the correct answer is b. 0,1. What a colorful solution!
Now let's move on to the next question, where we need to use the quadratic formula to solve the equation x^2-6=x. Are you ready for some clownish calculations?
First, we rearrange the equation to get x^2 - x - 6 = 0. Now we can apply the quadratic formula:
x = (-(-1) ± √((-1)^2 - 4(1)(-6))) / (2(1))
Simplifying this funny-looking formula, we get:
x = (1 ± √(1 + 24)) / 2
x = (1 ± √25) / 2
x = (1 ± 5) / 2
So the solutions are x = (1 + 5) / 2 = 6/2 = 3, and x = (1 - 5) / 2 = -4/2 = -2.
The correct answer is b. x = -2,3. Clowning around with math can be quite silly!
Lastly, let's tackle the question about the number of real number solutions in the equation y = -5x^2 + 8x - 7. Hold on tight, we're about to dive into the world of solutions!
To determine the number of real number solutions, we can look at the discriminant, which is the part under the square root in the quadratic formula. The discriminant is b^2 - 4ac.
In this case, a = -5, b = 8, and c = -7. Let's calculate the discriminant:
b^2 - 4ac = 8^2 - 4(-5)(-7)
= 64 - 140
= -76
Uh-oh, negative discriminant! That means we have no real number solutions. So the correct answer is c. none. Sometimes math can surprise us with its clownish tricks!
I hope I brought a smile to your face with my wacky explanations. Remember, math is serious, but it's okay to have a little fun along the way!
To solve the equation -9n(5n-5) using the zero-product property:
-9n(5n-5) = 0
We set each factor equal to zero and solve for n:
-9n = 0 or 5n-5 = 0
For the first factor, -9n = 0, we divide by -9 to isolate n:
n = 0/(-9) ⇒ n = 0
For the second factor, 5n - 5 = 0, we add 5 to both sides and then divide by 5 to solve for n:
5n = 5
n = 5/5 ⇒ n = 1
Therefore, the solutions to the equation are n = 0 and n = 1. The correct answer is b. 0,1.
To solve the equation x^2 - 6x = 0 using the quadratic formula:
We recognize that the equation is in the form ax^2 + bx + c = 0, where a = 1, b = -6, and c = 0.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac))/(2a)
By substituting the values into the formula, we have:
x = (-(-6) ± √((-6)^2 - 4(1)(0)))/(2(1))
= (6 ± √(36))/2
= (6 ± 6)/2
This simplifies to:
x = (6 + 6)/2 = 12/2 = 6
x = (6 - 6)/2 = 0/2 = 0
Therefore, the solutions to the equation are x = 6 and x = 0. The correct answer is b. x = -2,3.
For the equation y = -5x^2 + 8x - 7, to determine the number of real number solutions:
We can observe that this equation is a quadratic equation in the form ax^2 + bx + c.
In general, a quadratic equation in the form ax^2 + bx + c = 0 can have one of three types of solutions:
1. Two distinct real number solutions
2. One repeated real number solution
3. No real number solutions
To determine which type of solution this equation has, we can use the discriminant, given by b^2 - 4ac.
If the discriminant is positive, then the equation has two distinct real number solutions.
If the discriminant is zero, then the equation has one repeated real number solution.
If the discriminant is negative, then the equation has no real number solutions.
For our equation y = -5x^2 + 8x - 7, the discriminant is:
b^2 - 4ac = (8)^2 - 4(-5)(-7) = 64 - 140 = -76
Since the discriminant is negative (-76), the equation has no real number solutions. The correct answer is c. none.
To solve the equation -9n(5n-5) using the zero-product property, we set each factor equal to zero and solve for n:
-9n = 0, gives n = 0
5n - 5 = 0, gives n = 1
Combining the solutions, we get n = 0, 1. Therefore, the correct answer is b. 0, 1.
To solve the equation x^2 - 6 = x using the quadratic formula, we rearrange the equation to have zero on one side:
x^2 - x - 6 = 0
Now we can use the quadratic formula, which states that if we have an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac))/(2a)
In our equation, a = 1, b = -1, and c = -6:
x = (-(-1) ± √((-1)^2 - 4(1)(-6)))/(2(1))
x = (1 ± √(1 + 24))/2
x = (1 ± √25)/2
x = (1 ± 5)/2
This gives us two solutions: x = (1 + 5)/2 = 6/2 = 3, and x = (1 - 5)/2 = -4/2 = -2.
So, the correct answer is b. x = -2, 3.
To determine how many real number solutions the equation y = -5x^2 + 8x - 7 has, we can use the discriminant. The discriminant is the value inside the square root in the quadratic formula, given by b^2 - 4ac.
In our equation, a = -5, b = 8, and c = -7:
Discriminant = 8^2 - 4(-5)(-7)
= 64 - 140
= -76
Since the discriminant is negative, it means that there are no real number solutions to the equation. Therefore, the correct answer is c. none.