6.
4x^2 + 4 = 0
Divide both sides by 4
x^2 + 1 = 0
Use the quadratic formula since this cannot be factored.
x = (-b +- sqrt(b^2 - 4ac))/(2a)
x = +- sqrt(-4(1)(1))/2
x = +- sqrt(-4)/2
x = +- 2i/2
x = +- i
x = i or x = -i
Quicker solution:
If you have x^2 = number, then
x = +- sqrt(number)
Once you get to
x^2 + 1 = 0
Subtract 1 from both sides
x^2 = -1
Apply the quick method
x = +- sqrt(-1)
x = +- i
8.
2x^2 + 50 = 0
Divide both sides by 2
x^2 + 25 = 0
Subtract 25 from both sides
x^2 = -25
Apply quick method
x = +- sqrt(25)
x = +- 5i
x = 5i or x = -5i
Answer:
The answer is the last one.
Step-by-step explanation:
They paid $24.10 dollars, they paid $1.25 each and they paid $2.70 per mile. So, we subtract 2.50 from 24.10, since Landis and her father went together. And then, we divide our answer by 2.70.
24.10 - 2.50 = 21.60
21.60/2.70 = 8
They drove 8 miles.
Answer:
<h2>There is a 9% of chances that all three selections are apples.</h2>
Step-by-step explanation:
We know that there are 6 apples, 5 oranges and 1 pear, which gives a total of 12 fruits, that's total number of possible outcomes, the denominator of the simple probability.
Now, his friend selects three fruits with three trials without replacement, that means we need to find the probability of each even and then multiply them, because they are independent events.
Notice that we calculated the total probability using the same expression. The important thing is that you need to decrease the number of events and the total number of outcomes at each selection, because after his friends picks one apple, he doesn't put it back in the bag.
Therefore, there is a 9% of chances that all three selections are apples.
(We multiplies the number by 100 to express it in percentage)
Answer:
Oh I find all my inspiration thinkin' about you
Step-by-step explanation:
The generic equation of a third degree polynomial is given by:
y = ax ^ 3 + bx ^ 2 + cx + d
We must make a system of equations to find the values of a, b, c, d.
We have then:
For (1, 3):
3 = a (1) ^ 3 + b (1) ^ 2 + c (1) + d
3 = a + b + c + d
For (2, -2):
-2 = a (2) ^ 3 + b (2) ^ 2 + c (2) + d
-2 = 8a + 4b + 2c + d
For (3, -5):
-5 = a (3) ^ 3 + b (3) ^ 2 + c (3) + d
-5 = 27a + 9b + 3c + d
For (4.0):
0 = a (4) ^ 3 + b (4) ^ 2 + c (4) + d
0 = 64a + 16b + 4c + d
We obtain the following system of equations:
3 = a + b + c + d
-2 = 8a + 4b + 2c + d
-5 = 27a + 9b + 3c + d
0 = 64a + 16b + 4c + d
Whose solution is:
a = 1
b = -5
c = 3
d = 4
The polynomial will then be:
y = x ^ 3 - 5x ^ 2 + 3x + 4
Answer:
y = x ^ 3 - 5x ^ 2 + 3x + 4
