Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 2, negative 1, and 2 Which of the following functions best represents the graph?

f(x) = x3 + x2 − 4x − 4
f(x) = x3 + 4x2 − x − 4
f(x) = x3 + 3x2 − 4x − 12
f(x) = x3 + 2x2 − 4x − 8

Answers

Answer 1

Answer: Based on the given intercepts, the factors of the polynomial are
f(x) = (x-2)(x+1)(x-2)
Multiplying the binomials would give us the correct answer. Multiplying the first two,
f(x) = (x2 - x - 2)(x-2)
Then multiplying the result with other binomial,
f(x) = x3 + x2 - 4x - 4

Answer 2

Answer:

Using the Factor Theorem, the function that best represents the graph is given by:

f(x) = x³ + x² - 4x - 4.

What is the Factor Theorem?

The Factor Theorem states that a polynomial function with roots $x_1, x_2, \codts, x_n$ is given by:

$f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)$

In which a is the leading coefficient

In this problem, we consider a = 1, and the roots are the x-intercepts $x_1 = -2, x_2 = -1, x_3 = 2$ , hence:

f(x) = (x + 2)(x + 1)(x - 2)

f(x) = (x² + 3x + 2)(x - 2)

f(x) = x³ + x² - 4x - 4.

More can be learned about the Factor Theorem at brainly.com/question/24380382

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Answers

Separate the quadratic functions into two individual function in x which multiply together to equal the original quadratic.
Eg: x^2-3x-10=0 can be written as (x+2)(x-5)=0
The two solutions for x can then be determined by making each bracket equal to zero.
x+2=0 so x=-2x-5=0 so x=5

Manny makes dinner using 1 box of pasta and 1 jar of sauce. If pasta is sold in packages of 10 boxes and sauce is sold in packages of 2 jars, what is the least number of dinners that Manny can make without any supplies leftover?

Answers

Answer:

10 dinners

Step-by-step explanation:

We solve using the Least Common Multiple Method.

We are told:

Pasta is sold in packages of 10 boxes Sauce is sold in packages of 2 jars.

We find the Multiples of 2 and 10

Multiples of 2:

2, 4, 6, 8, 10, 12, 14

Multiples of 10:

10, 20, 30

Therefore,

LCM(2, 10) = 10

The least number of dinners that Manny can make without any supplies leftover is 10 dinners

Ana bought a van that holds 20.75 gallons of gas and gets an average of 15.5 miles per gallon. How many miles can she expect to drive on a full tank of gas? *

Answers

The van holds 20.75 gallons.

The van gets an average of 15.5 miles per gallon.

To find your answer, multiply 20.75 by 15.5.

So, 20.75 x 15.5 = 321.625.

Round off to the nearest hundred to get 300 miles.

The dimensions of a large room are double the dimensions of a small room.Both rooms are rectangular prisms. The volume of the small room is 10 cubic
metres.
What is the volume of the large room?

Answers

The volume would be 80 cubic metres. Think about the three different dimensions for the small room as x,y and z. Therefore the volume is x*y*z= xyz. Now for the bigger room, the dimensions would be 2x,2y and 2z. Therefore, its volume would be 2x*2y*2z= 8xyz. Since xyz (volume of the smaller room)= 10 cubic metres, the bigger room's volume will be 8*10= 80 cubic metres.

What does a polygon look like? A polygon has 6 sides

Answers

Hi there!

If you're talking about the polygon, called the hexagon, which has 6 sides, the attached file is what one looks like. :)

Hope this helps!

Message me if you need anything else, I'd be happy to answer any of your questions! :D

You have a coin collection of nickels and dimes containing 63 coins. If you have$5.05, how may of each coin do you have?

Answers

Answer: 25 nickels

Step-by-step explanation:

EQUATIONS:

quantity: n + d = 63

value: 5n + 10d = 505

-------------------------

Divide thru the 2nd equation by 5 to get:

n + 2d = 101

----------------

Subtract that from the 1st equation:

-d = -38

d = 38 (# of dimes)

---------------

Substitute that into n+d=63 to solve for "n":

n + 38 = 63

n = 25 (# of nickels)

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Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 2, negative 1, and 2 Which of the following functions best represents the graph? f(x) = x3 + x2 − 4x − 4 f(x) = x3 + 4x2 − x − 4 f(x) = x3 + 3x2 − 4x − 12 f(x) = x3 + 2x2 − 4x − 8

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Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 2, negative 1, and 2 Which of the following functions best represents the graph?

f(x) = x3 + x2 − 4x − 4
f(x) = x3 + 4x2 − x − 4
f(x) = x3 + 3x2 − 4x − 12
f(x) = x3 + 2x2 − 4x − 8