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fomenos
3 years ago
12

What is the completely factored form of f(x)=x3+5x2+4x−6?

Mathematics
1 answer:
Gre4nikov [31]3 years ago
3 0
f(x)=x^3+5x^2+4x-6
f(-3)=(-3)^3+5(-3)^2+4(-3)-6=0\implies x+3\text{ is a factor of }f(x)

Synthetic division yields

-3  |  1   5   4   -6
.    |      -3  -6    6
- - - - - - - - - - - - -
.    |  1   2  -2    0

which translates to

\dfrac{x^3+5x^2+4x-6}{x+3}=x^2+2x-2

with remainder 0. Now by the quadratic formula,

x^2+2x-2=0\implies x=\dfrac{-2\pm\sqrt{2^2-4(1)(-2)}}2=-1\pm\sqrt3

and so

f(x)=x^3+5x^2+4x-6=(x+3)(x-(-1+\sqrt3))(x-(-1-\sqrt3))
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Tan 48 degrees 19'23"
asambeis [7]

Answer:

Step-by-step explanation:

y = tan(48 + 19/60 + 23/3600)

y = tan(48.323055555...)

y = 1.1232851096924531815531574029372...

3 0
2 years ago
Some algae contains up to 50% oil by weight. How much oil is in a 7.3-ounce sample of this type of algae?
frutty [35]

Answer: 3.65

Step-by-step explanation:

This question is asking basically what is 50% or 1/2 of 7.3.

Let's expand the number 7.3

Then, we end up getting 7.30.

We have to find 1/2 of 7.30.

\frac{1}{2} of 7.30 = 3.65

Hope this helps you!

5 0
3 years ago
Ten times a number increased by eighty four equals 194. what is the number
steposvetlana [31]

Answer: x = 11

Step-by-step explanation:

10x+84=194

10x = "10 times a number"

+84 = "increased by eighty four"

=194 = "equals 194"

10x+84=194

Subtract 84

10x = 110

Divide by 10

x = 11

<em>Hope it helps <3</em>

4 0
3 years ago
Read 2 more answers
claudia is making a gelatin desseert for a party.She plans on making 12 servings for every 5 people.If each pan claudia uses to
prisoha [69]
First we need to find the total amount of servings needed.

(x2) 12 servings/5 people (x2)
        24 servings/10 people

Now we can find the amount of pans needed

24 servings/8 servings (1 pan)
=3 pans

She needs at least 3 pans
5 0
3 years ago
PLS HELP THIS IS A TEST
Pie

Answer:

D: 7

Step-by-step explanation:

1.75 (7) + 4.50

12.25 + 4.50

= 16.75

16.75 < 20

8 0
3 years ago
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