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navik [9.2K]
3 years ago
9

The polynomial x^3+8 is equal to

Mathematics
2 answers:
Veseljchak [2.6K]3 years ago
6 0

Answer:

(x + 2)(x² - 2x + 4)

Step-by-step explanation:

x³ + 8 ← is a sum of cubes, which factors in general as

• a³ + b³ = (a + b)(a² - ab + b²)

x³ = (x)³ ⇒ a = x and 8 = 2³ ⇒ b = 2

x³ + 8 = (x + 2)(x² - 2x + 4) ← in factored form


skad [1K]3 years ago
4 0

Answer:

x^{3} +8=(x+2)(x^{2} -2x+4)

Step-by-step explanation:

The binomial can be factored by the binomial form by trinomial. This binomial is a sum of cubes, whose general form presents the following result.

(x^{3} +y^{3} )=(x+y)(x^{2} -xy+y^{2} )

Substituting the values ​​of x and y we will have

x^{3} =x^{3} ;     y^{3} =8

Obtaining the cubic roots of each variable

x=x; y=2

So

x^{3} +8=(x+2)(x^{2} -2x+4)

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3
Bas_tet [7]

Answer:

<em>The height of the candle after 23 hours is 20.4 centimeters</em>

Step-by-step explanation:

<u>Mathematical Modeling</u>

To model a real-life situation, a mathematical model can be built in such a way it accurately represents the variables measured in the system.

This problem requires to build a model for the height of a candle as a linear function of the time it has been burning. If the time is expressed in hours and the height is in centimeters, then the linear function can be written as:

H(t)=mt+b

Where m and b are constants we need to find. We are provided two points of reference: After 15 hours of burning, the candle has a height of 22 centimeters. This is the point (15,22).

We also know after 27 hours of burning, the height is 19.6 cm. This is the point (27,19.6). This data is enough to accurately define the function. Let's substitute the first point:

22=15m+b\qquad\qquad [1]

Substituting the second point:

19.6=27m+b\qquad\qquad [2]

Subtracting [1] - [2]:

22-19.6=15m-27m

\Rightarrow 12m=-2.4

Solving for m:

m=-2.4/12=-0.2

Using this value in [1]:

22=15(-0.2)+b

22=-3+b

Solving for b:

b=25

The function is now complete:

H(t)=-0.2t+25

Finally, substitute t=23:

H(23)=-0.2(23)+25=20.4

The height of the candle after 23 hours is 20.4 centimeters

7 0
3 years ago
Tadeo Volunteered at the library six times as many hours over the weekend as Dylan. Together they volunteer at a total of 14 hou
LuckyWell [14K]

Answer:

<em>Tadeo Volunteered for 12 hours while Dylan volunteered for 2 hours</em>

Step-by-step explanation:

Let the total number of hours Tadeo volunteered be x

Let the total number of hours Dylan volunteered be y

If together they volunteer at a total of 14 hours, then;

x + y = 14 ...... 1

If<em> </em>Tadeo Volunteered at the library six times as many hours over the weekend as Dylan, then;

x = 6y

Substitute x = 6y into 1;

6y + y = 14

7y = 14

y = 14/7

y = 2

Since x = 6y

x = 6(2)

x = 12

<em>Hence Tadeo Volunteered for 12 hours while Dylan volunteered for 2 hours</em>

4 0
3 years ago
DO NOW: What is the surface area of the cube? 4 in 4 in 4 in​
ikadub [295]

Answer:

96 in^2.

Step-by-step explanation:

It has 6 surfaces each of area 4*4 = 16

Answer is 6*16 = 96.

7 0
2 years ago
Does anyone know this? Please help! ASAP!!!
Fudgin [204]
The answers:
a=4
b=5
c=6
d=1
8 0
2 years ago
Read 2 more answers
0.008 is 1 tenth of what decimal
shepuryov [24]
0.08, Hope it helped
3 0
3 years ago
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