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What polynomial expressions equal 8x^3+64?

Natali5045456 [20]

Answer:

$\displaystyle \boxed{8[x + 2][x^2 - 2x + 4]}$

Step-by-step explanation:

Use the Difference of Cubes [(a³ - b³)(a² + 2ab + b²)] to figure this out:

$\displaystyle 8x^3 + 64 \\ 8[x^3 + 8] \\ \\ x + 2 = \sqrt[3]{x^3 + 8}$

Then, since the divisor\factor is in the form of x - c, use what is called Synthetic Division. Remember, in this formula, −c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:

−2| 1 0 0 8

↓ −2 4 −8

___________

1 −2 4 0 → ${x}^{2} - 2x + 4$

You start by placing the c in the top left corner, then list all the coefficients of your dividend [x³ + 8]. You bring down the original term closest to c then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x², the −2x follows right behind it, then 4, giving you the other factor of $x^2 - 2x + 4$ , attaching this to the first two factors you started out your work on:

$\displaystyle \boxed{8[x + 2][x^2 - 2x + 4]}$

I am joyous to assist you anytime.

6 0

3 years ago

Is the rate of change of the function 5? On a coordinate plane, a line with positive slope goes through points (negative 2, 0) a

Rashid [163]

Answer:

C

Step-by-step explanation:

the slope is 2/3

4 0

3 years ago

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The table below shows the radius y, in inches, created by growing algae in x days: Time (x) (days) 1 4 7 10 Radius (y) (inches)

tatuchka [14]

PART A:
Given the table below showing the radius y, in inches, created by growing algae in x days.

Time (x) (days): 1 4 7 10
Radius (y) (inches): 1 8 11 12

We can find the find the correlation coeficient of the data using the table below:
$\begin{center}
\begin{tabular}
{|c|c|c|c|c|}
x & y & x^2 & y^2 & xy \\ [1ex]
1 & 1 & 1 & 1 & 1\\
4 & 8 & 16 & 64 & 32\\
7 & 11 & 49 & 121 & 77\\
10 & 12 & 100 & 144 & 120\\ [1ex]
\Sigma x=22 & \Sigma y=32 & \Sigma x^2=166 & \Sigma y^2=330 & \Sigma xy=230
\end{tabular}
\end{center}$

Recall that the correlation coefitient is given by the equation:
$r= \frac{n(\Sigma xy)-(\Sigma x)(\Sigma y)}{ \sqrt{(n\Sigma x^2-(\Sigma x)^2)(n\Sigma y^2-(\Sigma y)^2)} } \\ \\ = \frac{4(230)-(22)(32)}{ \sqrt{(4(166)-(22)^2)(4(330)-(32)^2)} } = \frac{920-704}{ \sqrt{(664-484)(1,320-1,024)}} \\ \\ = \frac{216}{ \sqrt{180(296)}} = \frac{216}{ \sqrt{53,280} } = \frac{216}{230.8} =0.94$

[Notice: even without using the formular to find the value of the correlation coeficient, it can be seen that the value of y strictly increases as the valu of x increases. This means that the value of the correlation coeficient is closer to +1 and from the options the value that is closest to +1 is 0.94]

From the value of the correlation coeffeicient, it can be deduced that the radius of the algae has a strong positive relationship with the time.

Recall the for the value of the correlation coeficient closer to +1, the relationship is strong positive, for the value closer to -1, the value is strong negative and for the values closer to zero, either way of zero is a weak positive if it is positive and weak negative if it is negative.

PART B:
Recall that the slope of a straight line passing through two points
$(x_1,y_1)$ and $(x_2,y_2)$
is given by
$m= \frac{y_2-y_1}{x_2-x_1}$

Thus the slope of the graph of radius versus time between 4 and 7 days, [i.e. the line passes through points (4, 8) and (7, 11)] is given by
$m= \frac{11-8}{7-4}= \frac{3}{3} =1$

The value of the slope means that the radius of the algea grows by 1 inch evry day between day 4 and day 7.

PART C:
We can say that the data above represent both correlation and causationg.

Recall that correlation expresses the relationship between two variables while causation expresses that an event is as a result of another event.

From the information above, we have seen that there is a relationship (correlation) between the passing of days and the growth in the radius of the algae.

Also we can conclude that the growth in the radius of algae is a function of the passing of days, i.e. the growth in the radius of algae is as a result of the passing of days.

Therefore, the data in the table represent both correlation and causation.

6 0

3 years ago

Bill mixes candy costing 45cents per pound with candy costing 65cents a pound. A 7-pound box of the mix costs $3.65. How much of

Len [333]

Answer:

Bill should use 4.5 pounds of the candy costing 45 cents and 2.5 pounds of the candy costing 65 cents.

Step-by-step explanation:

With the information provided, you can say that the sum of the pounds of each type of candy is equal to 7, which can be expressed as:

x+y=7

Also, the statement indicates the 7 pound box costs $3.65 and you can say that the sum of the results of multiplying the price of each candy for the number of pounds is equal to $3.65, which is:

0.45x+0.65y=3.65

You have the following equations:

x+y=7 (1)

0.45x+0.65y=3.65 (2)

Now, you have to solve for x in (1):

x=7-y (3)

Then, you have to replace (3) in (2):

0.45(7-y)+0.65y=3.65

3.15-0.45y+0.65y=3.65

0.20y=0.50

y=0.50/0.20

y=2.5

Finally, you can replace the value of y in (3) to find x:

x=7-y

x=7-2.5

x=4.5

According to this, the answer is that Bill should use 4.5 pounds of the candy costing 45 cents and 2.5 pounds of the candy costing 65 cents.

4 0

3 years ago

Determine whether each sum or product is even or odd. 10,481 + 4,569

lianna [129]

Answer:

even

Step-by-step explanation:

6 0

3 years ago

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