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Naddik [55]
2 years ago
10

One of the factors of the polynomial x3 − 5x2 is x + 3. What is the other factor?

Mathematics
2 answers:
olya-2409 [2.1K]2 years ago
8 0
The answer is letter c. x2-8x+24-[72/(x+3)]. If you do not know how to solve this using the long division method, you can always evaluate the options through the process of elimination first. Since the degree of the other factor is already 1 (x to the power of 1), you know that option d. is not the correct answer because you know that the other factor must be raised to the power of 2. That leaves us with a, b and c. Working backwards and multiplying the given factor (x+3) with the factor in b, gives us x3-5x2+72. So from there, you know that you have to eliminate 72, which can be removed when it is subtracted by itself. Letter c does just that. Try multiplying (x+3) and option c for yourself :).
sesenic [268]2 years ago
3 0

Answer:

Option C is correct.

Step-by-step explanation:

Given polynomial : x³ - 5x²

Factors of given polynomial = x + 3

Let, p(x) = x³ - 5x²

To get other factor of p(x), we divide p(x) by given factor.

On division we get,

Quotient = x² - 8x + 24

Remainder = -72

So another factor is x^2-8x+24-\frac{72}{x+3}

Therefore, Option C is correct.

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Describe the following variation: y/x2=5
Firdavs [7]
We are asked to describe the variation \displaystyle{ \frac{y}{x^2}=5, 

that is y=5x^2

for x≠0, in which case x=y=0, we distinguish the following intervals:

I   = (-infinity, -1]
II  = (-1, 0)
III = (0, 1)
III = [1, infinity)

Case I, consider the cases (examples)   x= -5, and x= -6

5(-6)^2\ \textgreater \ 5(-5)^2, so we can conclude that the greater the x, the smaller the y.

Case II, consider x= -1/2 < x=-1/3

5(-\frac{1}{2})^2= \frac{5}{4}\\\\ 5(-\frac{1}{3})^2= \frac{5}{9}\\\\\frac{5}{9}\ \textless \  \frac{5}{4}

thus, the greater the x, the smaller the y.


Case III, consider the cases (examples)   x= 5, and x= 6

5(6)^2\ \textgreater \ 5(5)^2, so we can conclude that the greater the x, the greater the y.

Case III, consider x= 1/3 < x=1/2

5(\frac{1}{2})^2= \frac{5}{4}\\\\ 5(\frac{1}{3})^2= \frac{5}{9}\\\\\frac{5}{9}\ \textless \ \frac{5}{4}

thus, the greater the x, the greater the y.


Conclusion:

y=0 only if x is 0. Otherwise y>0 always:

for x<0,   x and y are inversely proportional

for x>0,   x and y are directly proportional.


Remark, an other possible consideration in cases could be x<0 and x>0 only.


Remark, 
another approach is considering the graph of y=5x^2, which is a parabola, with the vertex at (0, 0) opening upwards.

From the graph we can find the same conclusion. That is we can see that the farer we get away from the y-axis, in both direction, the larger the values of y become.

4 0
3 years ago
How do i solve the circumference with the diameter of 1.3?
Contact [7]

Answer:

Inputs:

Radius (r):

0.65

or

Diameter (d):

1.3

or

Area (A):

1.327

Unit of Lenght:

centimeter

Calculate Circumference

Result:

The circumference of a circle with diameter 1.3 is 4.084(*)

Formulas:

r = 0.65

d = 1.3

C = 4.08

C = 2·π·r C = π·d C = √4·π·A π = 3.1415

A = area of the circle

C = circumference or perimeter

r = radius, d = diameter

Step-by-step Solution:

Circumference of a cicle in terms of radius:

Circumference = 2·π·r = 2·3.14·0.65 = 4.09(*)

In terms of diameter:

Circumference = π·d = 3.14·1.3 = 4.08(*)

In terms of area:

Circumference C = √4·π·A = √4·π·1.33 = 4.09(*)

(*) 4.084 cm exactly or limited to de precision of this calculator (13 decimal places).

Note: for simplicity, the operations above were rounded to 2 decimal places and π was rounded to 3.14.

A circumference of 4.084 centimeters is equal to:

4.084E-5 kilometers (km)

0.04084 meters (m)

40.84 millimeters (mm)

2.53768E-5 miles (mi)

0.0446632 yards (yd)

0.13399 feet (ft)

1.60787 inches (in)

8 0
2 years ago
Read 2 more answers
When registering their cars, owners must identify the color that covers the largest portion of the vehicle. In one region, the p
Blababa [14]

Answer:

0.41 probability

Step-by-step explanation:

0.22 + 0.19 = 0.41

3 0
3 years ago
7(4g) + 3(5h) +2(-3g) g=1/2, h=1/3
cluponka [151]

Answer:16

Step-by-step explanation:

4 0
2 years ago
What is the slope of the line that goes through the points (12,-18) (-15,-18)
AnnZ [28]

Hi!

Step-by-step explanation:

SLOPE=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}

\frac{(-18)-(-18)}{(-15)-12}=\frac{0}{-27}=0

<u><em>Slope is 0.</em></u>

<u><em>The answer is 0.</em></u>

Hope this helps!

Have a nice day! :)

:D

-Charlie

Thank you!

4 0
2 years ago
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