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Mariana [72]
2 years ago
10

Factor f(x) = x^4 + x^3 - 8x^2 + 6x +36 completely. Show your work. Then describe what a graph of this function might look like.

Include where the graph would cross the x-axis and the y-axis. How many roots are real numbers and how many roots are imaginary numbers?
Mathematics
1 answer:
ikadub [295]2 years ago
7 0
             <span> Use the rational root theorem to find the possible rational roots. The rational roots theorem says that possible rational roots are +/- factors the constant term (36 here) divided by factors of the leading coefficient (1 here). Possible rational roots are

+/- 1, 2, 3, 4, 9, 12, 18, 36

Test each zero using the rational root test. To do this, use synthetic division to test the roots. I won't show the work here, but the roots that work are -2 and -3. As factors, this is x+2 and x+3.

From the synthetic division, we have x^2-4x+6 left over, which is irreducible.

In factored form:
f(x) = (x+2)(x+3)(x^-4x+6)

You could also use a graphing calculator to find the roots and work backwards to get the factored form too. A TI-89 Titanium would factor the polynomial and give you the above answer.</span>
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salantis [7]

The original area of a face would be a^2. Now that you added b to the edge, the new area of each face would be (a+b)^2. To find how much the are increased, subtract a^2 from (a+b)^2. (a+b)^2-(a^2)= a^2+2ab+b^2-(a^2)= 2ab+b^2= b(2a+b) So the answer is b(2a+b)

6 0
3 years ago
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The formula for the circumference of a circle is C = 2r, where r is the radius and C is the circumference. The equation solved f
Lubov Fominskaja [6]

Answer:

r = c/2pi

Step-by-step

c= pi*d

d=2r

c = 2*r*pi

6 0
2 years ago
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The graph shows the solution to which system of equations?
Sedaia [141]
So let's start by guesstimating the slopes:
the green line has a slope close to -x, but more negative than that, possibly -2; the pink line has a slope close to +x, but higher towards +2.

Next let's look at the solution: the two lines intersect at the point (1, -1).
**you could just simple plug that x (1) into all the equations, but let's rule out answers anyway. ;)

A) is incorrect because the slopes of -1 and +1 are off from out predicted -2 and +2
B) is incorrect because of a similar reason, the slopes of +3 and +1 don't make any sense
C) Ooh, we do have a +2 and -2 for the slopes, and... violà! plug in 1 for the x's and we get -1 for the y in both equations
D) slopes are closer than in A and B, but plugging in 1 doesn't get us -1

So the correct answer is:
C) y = 2x - 3 and y = −2x + 1
6 0
3 years ago
1. In AABC, if a = 8, b = 2, and c = 7. What is the value of cos C?
jenyasd209 [6]
I’m a little confused do you have a picture I could solve for cos then
4 0
3 years ago
I'm studying a new bacteria that doubles in numbers every 25 minutes. If i start with 50 bacteria, how long until i have 5 milli
dimaraw [331]

Answer:

415.63 minutes

Step-by-step explanation:

Growth can be represented by the equation A=A_0e^{rt}. We can find the rate at which it grows by using t=25 minutes and \frac{A_{0}}{A} =2 or double the amount at that time. The first step we always take is to divide A_0 by A.

[tex]\frac{A_{0}}{A}=e^{rt}\\2=e^{r(25)}

2=e^{(25)r}

To solve for r, we will take the natural log of both sides and use log rules to isolate r.

ln 2=ln e^{(25)r}\\ln 2=25r (ln e)\\\frac{ln2}{25} =r

We know lne=1 so we were able to cancel it out and divide both sides by 25.

We solve with a calculator \frac{ln2}{25} =r\\0.0277=r

We change 0.0277 into a percent by multiplying by 100 to get 2.77% as the rate.

The equation is A=A_0e^{0.0277t} .

We repeat the step above substituting A=5,000,000, A_0=50, and r=0.02777. Then solve for t.

5000000=50e^{0.0277t}\\\frac{5000000}{50} =e^{0.0277t}\\100000=e^{0.0277t}\\ln100000=lne^{0.0277t}\\ln100000=0.02777t(lne)\\\frac{ln100000}{0.0277} =t

t=415.63 minutes

6 0
3 years ago
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