1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Maksim231197 [3]
3 years ago
11

Find the numbers a, b and c if the polynomial x3−18x2+24xb−c is the cube of the binomial x+2a.

Mathematics
1 answer:
mojhsa [17]3 years ago
6 0

Answer:

a=-3\\ \\b=\dfrac{9}{2}\\ \\c=216

Step-by-step explanation:

Use formula

(u+v)^3=u^3+3u^2v+3uv^2+v^3.

Hence,

(x+2a)^3=x^3+3x^2\cdot 2a+3x\cdot (2a)^2+(2a)^3=x^3+6ax^2+12a^2x+8a^3.

This expression is equal to

x^3-18x^2+24bx-c,

so we can equate the coefficients at powers of x:

x^3:\ 1=1\\ \\x^2:\ 6a=-18\Rightarrow a=-3\\ \\x:\ 12a^2=24b\Rightarrow b=\dfrac{9}{2}\\ \\1=x^0:\ 8a^3=-c\Rightarrow c=-8\cdot (-3)^3=216.

You might be interested in
Given f(x) = 18x + 8, find x when f(x)= 14.
Naddika [18.5K]

The answer is 0.3 (1/3.)

Proof?

f(0.3) = 18(0.3) + 8

f(0.3) = 6 + 8

f(0.3) = 14

14 = 14

⭐ Please consider brainliest! ⭐

✉️ If any further questions, inbox me! ✉️

8 0
2 years ago
Jane ordered a few moving boxes from a local store as she is relocating to Atlanta. She returned 28 damaged boxes. She allotted
kherson [118]

Answer:

17

Step-by-step explanation:

7 0
2 years ago
Two likes that do not intersect are parallel <br><br> Always? <br> Sometimes?<br> Or<br> Maybe?
earnstyle [38]

Answer:

sometimes

Step-by-step explanation: They may not intersect at first but they may be put on a slight angle to where they may intersect in the longrun.

3 0
3 years ago
NEED HELP FAST! 50 POINTS see the image below
ale4655 [162]

Answer:

90 in²

Step-by-step explanation:

First,check the figure I provided .

Area of the figure = area1 + area2 + area3 + area4

= (3×2) + (7×7) + (7×2) + (7×6)÷2

= 6 + 49 + 14 + 21

= 90

4 0
1 year ago
The circumference of a circle is 3pi in. What is the area of the circle?
Nezavi [6.7K]

Answer:

A = 2.25 pi in^2

Step-by-step explanation:

The circumference of a circle is 3pi

so d = 3

Area of circle = pi r^2

r = 3/2 = 1.5

A = (1.5)^2 pi

A = 2.25 pi in^2

3 0
2 years ago
Other questions:
  • 43 5/12 x 11 Please help
    15·1 answer
  • If there is 15,000 gallons of water in your basement, how long will it take the 2,500 gph
    13·2 answers
  • What is the square root of -1?<br> Т -<br> ОООО<br> Т -
    6·2 answers
  • Justin walked 3 miles north and 6 miles west. starting from the same point, tina walked 2 miles south and 4 miles east. how far
    14·1 answer
  • The height of a right rectangular prism is 3 units greater than the length of the base. The edge length of the square base is x
    10·1 answer
  • specialty T-shirts are being sold online for $30 each plus a one-time handling fee of $2.75 . The total cost is a function of th
    15·1 answer
  • A scientist changes the temperature of a solution at a rate of
    6·1 answer
  • (1/?) Please tell me if these are corect or wrong, If it's wrong, tell me what number I should change
    10·2 answers
  • 13
    6·1 answer
  • Evaluate each expression using the order of operations 35-14/2+8 to the power of 2
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!