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elitehairnerd1964
14.07.2019 •
Mathematics
Which of the formulas below could be a polynomial with all of the following properties: its only zeros are x = -6, -2, 2, it has y-intercept y = 4, and its long-run behavior is y rightarrow - infinity as x plusminus infinity? select every formula that has all of these properties. a. y = -4/144 (x + 6)^2 (x + 2)(x - 2) b. y = -4/192 (x + 6)(x + 2)^4 (x - 2) c. y = -4x (x + 6)(x + 2)(x - 2) d. y = -4/24 (x + 6)(x + 2)(x - 2) e. y = -4/48 (x + 6) (x + 2)^2 (x - 2) f. y = -4/48 (x + 6)(x + 2)(x - 2)^2 g. y = 4/48 (x + 6)(x + 2) (x - 2)^2
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Ответ:
A, B, and E
if I read your functions right.
Step-by-step explanation:
It's zeros are x=-6,-2, and 2.
This means we want the factors (x+6) and (x+2) and (x-2) in the numerator.
It has a y-intercept of 4. This means we want to get 4 when we plug in 0 for x.
And it's long-run behavior is y approaches - infinity as x approaches either infinity. This means the degree will be even and the coefficient of the leading term needs to be negative.
So let's see which functions qualify:
A) The degree is 4 because when you do x^2*x*x you get x^4.
The leading coefficient is -4/144 which is negative.
We do have the factors (x+6), (x+2), and (x-2).
What do we get when plug in 0 for x:
Put into calculator: 4
A works!
B) The degree is 6 because when you do x*x^4*x=x^6.
The leading coefficient is -4/192 which is negative.
We do have factors (x+6), (x+2), and (x-2).
What do we get when we plug in 0 for x:
Put into calculator: 4
B works!
C) The degree is 4 because when you do x*x*x*x=x^4.
The leading coefficient is -4 which is negative.
Oops! It has a zero at 0 because of that factor of (x) between -4 and (x+6).
So C doesn't work.
D) The degree is 3 because x*x*x=x^3.
We needed an even degree.
D doesn't work.
E) The degree is 4 because x*x^2*x=x^4.
The leading coefficient is -4/48 which is negative.
It does have the factors (x+6), (x+2), and (x-2).
What do we get when we plug in 0 for x:
Put into calculator: 4
So E does work.
F) The degree is 4 because x*x*x^2=x^4.
The leading coefficient is -4/48.
It does have factors (x+6), (x+2), and (x-2).
What do we get when we plug in 0 for x:
Put into calculator: -4
So F doesn't work.
G. I'm not going to go any further. The leading coefficient is 4/48 and that is not negative.
So G doesn't work.
Ответ:
Step-by-step explanation:
Notice that we have 3 zeros, which means there are only 3 roots, which are -6, -2 and 2, this indicates that our expression must be cubic with the binomials (x+6), (x+2) and (x-2).
We this analysis, possible choices are C and D.
Now, according to the problem, it has y-intercept at y = 4, so let's evaluate each expression for x = 0.
C.![y=-4x(x+6)(x+2)(x-2)\\y=-4(0)(0+6)(0+2)(0-2)\\y=0](/tpl/images/0087/2852/fe8b6.png)
D.Therefore, choice D is the right expression because it has all given characteristics.
Ответ:
Solve for
r
by simplifying both sides of the equation, then isolating the variable.
r
=
9
i think
Step-by-step explanation: