Answer:
D. 
Step-by-step explanation:
The period of the functions 
is 
The period of the function 
is ALWAYS 
In your case, you have function 
and this function has the period
You need to find the function that will have the period that is half of 
so
So, correct choice is
(x - 1)(x - 2)(x + 2)
note that the sum of the coefficients 1 - 1 - 4 + 4 = 0
thus x = 1 is a root and (x - 1 ) is a factor
dividing x³ - x² - 4x + 4 by (x - 1)
x³ - x² - 4x + 4 = (x - 1)(x² - 4 ) (note (x² - 4 ) is a difference of squares )
x³ - x² - 4x + 4 = (x - 1)(x - 2)(x + 2)
(x - 1)(x - 2)(x + 2 ) =0
x - 1 = 0 ⇒ x = 1
x - 2 = 0 ⇒ x = 2
x + 2 = 0 ⇒ x = - 2
solutions are x = 1 or x = ± 2
Answer:
f(x) = 4x^2 + 2x - 4.
Step-by-step explanation:
Let the quadratic function be y = f(x) = ax^2 + bx + c.
For the point (-2, 8) ( x = -2 when y = 8) we have:
a(-2)^2 + (-2)b + c = 8
4a - 2b + c = 8 For (0, -4) we have:
0 + 0 + c = -4 so c = -4. For (4, 68) we have:
16a + 4b + c = 68
So we have 2 systems of equations in a and b ( plugging in c = -4):
4a - 2b - 4 = 8
16a + 4b - 4 = 68
4a - 2b = 12
16a + 4b = 72 Multiplying 4a - 2b = 12 by 2 we get:
8a - 4b = 24
Adding the last 2 equations:
24a = 96
a = 4
Now plugging a = 4 and c = -4 in the first equation:
4(4) - 2b - 4 = 8
-2b = 8 - 16 + 4 = -4
b = 2.
Considering that the p-value associated for a r<em>ight-tailed test with z = 2.115</em> is of 0.0172, it is found that it is significant at the 5% level, but not at the 1% level.
<h3>When a measure is significant?</h3>
- If p-value > significance level, the measure is not significant.
- If p-value < significance level, the measure is significant.
Using a z-distribution calculator, it is found that the p-value associated for a r<em>ight-tailed test with z = 2.115</em> is of 0.0172, hence, this is significant at the 5% level, but not at the 1% level.
More can be learned about p-values at brainly.com/question/16313918
Answer: 72 gallons
Step-by-step explanation: I added 5 and 3 then multiplied by 9.
