6x^2 + 4(x^2 - 1) =
6x^2 + 4x^2 - 4 =
10x^2 - 4 <===
The simplest form of
6
2
is
3
1
.
Steps to simplifying fractions
Find the GCD (or HCF) of numerator and denominator
GCD of 6 and 2 is 2
Divide both the numerator and denominator by the GCD
6 ÷ 2
2 ÷ 2
Reduced fraction:
3
1
Therefore, 6/2 simplified to lowest terms is 3/1.
Answer:
x = -2, x = 3 − i√8, and x = 3 + i√8
Step-by-step explanation:
g(x) = x³ − 4x² − x + 22
This is a cubic equation, so it must have either 1 or 3 real roots.
Using rational root theorem, we can check if any of those real roots are rational. Possible rational roots are ±1, ±2, ±11, and ±22.
g(-1) = 18
g(1) = 18
g(-2) = 0
g(2) = 12
g(-11) = 1782
g(11) = 858
g(-22) = -12540
g(22) = 8712
We know -2 is a root. The other two roots are irrational. To find them, we must find the other factor of g(x). We can do this using long division, or we can factor using grouping.
g(x) = x³ − 4x² − 12x + 11x + 22
g(x) = x (x² − 4x − 12) + 11 (x + 2)
g(x) = x (x − 6) (x + 2) + 11 (x + 2)
g(x) = (x (x − 6) + 11) (x + 2)
g(x) = (x² − 6x + 11) (x + 2)
x² − 6x + 11 = 0
Quadratic formula:
x = [ 6 ± √(36 − 4(1)(11)) ] / 2
x = (6 ± 2i√8) / 2
x = 3 ± i√8
The three roots are x = -2, x = 3 − i√8, and x = 3 + i√8.
A
This is like a base form of a prime polynomial
X^2+x+1
Answer:
<em>On time: 0.67</em>
<em>Late: 0.33</em>
Step-by-step explanation:
<u>Probabilities</u>
One approach to estimating the probability of occurrence of an event is to record the number of times that event happens (e) and compare it with the total number of trials (n).
The probability can be estimated with the formula:

And the probability that the event doesn't occur is
Q = 1 - P
Paulo arrives on time to school e=53 times out of n=79 times. The probability that he arrives on time is:

P = 0.67
And the probability he arrives late is:
Q = 1 - 0.67 = 0.33