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
Is this graph linear or exponential
barxatty [35]
Its a graph linear i believe
3 0
3 years ago
For which value of x is ABCD a kite?
Anit [1.1K]

Answer:

83

Step-by-step explanation:

x+7+90

x=83

5 0
2 years ago
A kayak rental company charges $25.00 to rent a kayak and $3.50 for each half hour it is used.
pogonyaev

Answer:

Option D (r(t) = 3.50t +25 ; r(8) = 53)

Step-by-step explanation:

The fixed cost to rent the kayak $25. This is the cost which remains fixed irrespective of the usage of the kayak. The variable cost of using the kayak is the cost which depends on the usage of the kayak. It is mentioned that the kayak is used for 4 hours and the company charges $3.5 for every half hour. The cost function is given by:

r(t) = 25 + 3.5t ; there r is the total cost of using the kayak and t is the number of half-hours the kayak is used.

4 hours means that there are 8 half-hours. Therefore, t=8. Put t=8 in r(t).

r(8) = 25 + 3.5*(8) = 25 + 28 = 53.

Therefore, Option D is the correct answer!!!

3 0
3 years ago
Read 2 more answers
The coordinates of the following points represent the vertices of a rectangle. W: (3,3) X: (8,3) Y: (8,7) Z: (3,7) What is the p
anygoal [31]

Answer:

18

Step-by-step explanation:

The answer is B, 18

7 0
3 years ago
Read 2 more answers
Marissa is drawing coins from a bag that contains 5 pennies (yellow), 4 nickels (green), 5 dimes
Anna007 [38]

Answer:

\frac{4}{16}=\frac{1}{4}=0.25=25\%

Step-by-step explanation:

Total number of coins in the bag = 5 + 4 + 5 + 2 = 16 coins

Number of nickels in the bag = 4

We have to find the probability that Marissa draws a nickels from the bag.

Probability is defined as the ratio of Number of "Favorable Outcomes" to "Total number of possible outcomes"

In this case total number of possible outcomes is the total number of coins which is 16.

Favorable/Desires outcome is drawing a Nickle from the bag which are 4 in number. So, number of favorable outcomes is 4

Therefore, the probability that she will draw a nickel = \frac{4}{16}=\frac{1}{4}=0.25=25\%

7 0
3 years ago
Other questions:
  • What is the GCF of 33,55,132
    8·1 answer
  • Artie can travel 120.25 miles on 6.5 gallons of gas.
    8·2 answers
  • Please look at the picture. Choices: A: 6 B: 10 C: 12 D: 14
    10·1 answer
  • Convert y= 2x(x-6)-5 to vertex form.
    7·1 answer
  • Triangle A B C is shown. The length of A B is 16, the length of B C is 14, and the length of A C is 12.
    10·2 answers
  • Express the following<br> ratio in its simplest<br> terms: 4 weeks 6 days
    8·2 answers
  • HI ANYONE PLEASE HELP ME IF YOU CAN,
    6·1 answer
  • I NEED CORRECT ANSWER ​
    14·1 answer
  • The number of pizzas y you need for a party is proportional to the number of people x attending the party. You will need 2 pizza
    15·1 answer
  • The county fair charges $1.00 per rode and an additional $3.00 to get in the fair. Write an equation to represent the total cost
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!