Devon drank 5/6 of her juice. What is this amount as a decimal?

Question 14 of 25What is the complete factorization of the polynomial below?x³+x² + 4x+4O A. (x-1)(x+2)(x+2)B. (x + 1)(x + 2)(x

mote1985 [20]

GIVEN:

We are given the following polynomial;

$x^3+x^2+4x+4$

Required;

We are required to factorize this polynomial completely.

Step-by-step explanation;

To factorize this polynomial, we start by grouping;

$(x^3+x^2)+(4x+4)$

We now take the common factor in each group;

$\begin{gathered} x^2(x+1)+4(x+1) \\ \\ (x^2+4)(x+1) \end{gathered}$

Next, we factorize the first parenthesis. To do this we set the equation equal to zero and solve for x as follows;

$\begin{gathered} x^2+4=0 \\ \\ Subtract\text{ }4\text{ }from\text{ }both\text{ }sides: \\ \\ x^2=-4 \\ \\ Take\text{ }the\text{ }square\text{ }root\text{ }of\text{ }both\text{ }sides: \\ \\ x=\pm\sqrt{-4} \\ \\ x=(\pm\sqrt{-1}\times\sqrt{4}) \\ \\ x=\pm2i \end{gathered}$

Therefore, the factors of the other parenthesis are;

$(x+2i)(x-2i)$

Therefore, the complete factorization of the polynomial is;

ANSWER:

$(x+1)(x+2i)(x-2i)$

Option C is the correct answer.

4 0

7 months ago

a rectangular prism has a volume of 300 cm squared if the scale factor of the second rectangular prism is 3.5 what is the volume

velikii [3]

Volume of rectangular prism= 30 cm³
Formula for volume of rectangular prism:
V=whl
Scale factor of second prism= 3.5
Which is 3 and a half times greater than the 1st one.
So volume of 2nd prism = 3. 5 x 300
V= 1050 cm³

Answer: Volume of second Rectangular Prism is 1050 cm³

6 0

2 years ago

I need help with this question please

ludmilkaskok [199]

Answer:

62

Step-by-step explanation:

The enclosing rectangle is 24 units long and 12 units high. Its area is ...

(24 units)(12 units) = 288 square units

The white circles obviously cover more than half the area, so the only viable answer choice is 62.

__

If you want to go to the trouble to actually figure it out, you can find the area of each circle using the area formula ...

A = πr² = (3.14)(6²) = 113.04

Then both circles have an area of 2×113.04 = 226.08, and the shaded area is the difference between that and the rectangle area:

shaded area = 288 -226.08 = 61.92 ≈ 62

5 0

2 years ago

What is the solution to -x2 + 5x - 10 = 0?

Korolek [52]

Answer:

No solution

Explanation

−x^2+5x−10=0

Step 1: Use quadratic formula with a=-1, b=5, c=-10.

you plug it in as shown below

and simplify

when you simplify

you get

as shown below

This is no solution....

7 0

2 years ago

What is. <br> m + 0.6 = 2.6

professor190 [17]

Answer:

m=2

Step-by-step explanation:

STEP 1 : m+0.6=2.6

move constant to the right-hand side and change it's sign m=2.6-0.6

STEP 1: m=2.6-0.6

subtract the numbers m=2

5 0

2 years ago