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
White raven [17]
3 years ago
9

consider a polynomial f(x)=ax^3 + bx^2 + x + 2/3.if x + 3 is a factor of f(x) and f(x) is divided by x + 2, then we get remainde

r as 5. find the values of a and b.
Mathematics
1 answer:
Elanso [62]3 years ago
6 0

Answer:

a = 2/27

b = 13/27

Step-by-step explanation:

The given polynomial is presented as follows;

f(x) = a·x³ + b·x² + x + 2/3

Given that x + 3 is a factor, we have;

f(-3) = 0 = a·(-3)³ + b·(-3)² - 3 +2/3 = 0

-27·a + 9·b - 3 + 2/3 = 0

-27·a + 9·b = 7/3........(1)

Also we have

(a·x³ + b·x² + x + 2/3) ÷ (x + 2) the remainder = 5

Therefore;

a·(-2)³ + b·(-2)² + (-2) + 2/3 = 5

-8·a + 4·b - 2 + 2/3 = 5

-8·a + 4·b = 2 - 2/3 = 4/3........(2)

Multiplying equation (1) by 4/9 and subtracting it from equation (2), we have;

-8·a + 4·b - 4/9×(-27·a + 9·b) = 4/3 - 4/9 × 7/3

-8·a + 12·a = 8/27

4·a = 8/27

a = 2/27 ≈ 0.0741

imputing the a value in equation (1) gives;

-27×2/27 + 9·b = 7/3

-2 + 9·b = 7/3

9·b = 7/3 + 2 = 13/3

b = 13/27 ≈ 0.481.

You might be interested in
9. Your bank account has a balance of $145.67. You make a withdrawal
Nataliya [291]
There is $103.15 in your bank account.
4 0
3 years ago
Find f(g(-4)) if f(x) =7/x+2<br> and g(x) = (x + 5)^2. Options: -5/2 , -7/2 , 37/4 , 7/3
aev [14]

Answer:

7/3

Step-by-step explanation:

f(x) =7/(x+2)

g(x) = (x + 5)^2

f(g(-4))=

First find g(-4)

g(-4) = (-4+5)^2

        =(1)^2 =1

Then find f(1)

f(1)= 7/(1+2)

   = 7/3

5 0
2 years ago
What is the equation of the line AB, if it passes through (-4,0), and is parallel to the line
Karo-lina-s [1.5K]

Rewriting the equation of the given line in slope-intercept form,

-x-4y=1\\\\-4y=x+1\\\\4y=-x-1\\\\y=-\frac{1}{4}x-\frac{1}{4}

From this, we know the slope of the given line is -1/4.

Since parallel lines have the same slope, we know the line whose equation we want to find has a slope of -1/4.

Substituting into point-slope form,

y=-\frac{1}{4}(x+4)\\\\\boxed{y=-\frac{1}{4}x-1}

6 0
2 years ago
Find the solution of the system of equations. 6x -y= 21. -5x + y= -18​
Lapatulllka [165]
First one is -6 and the second one is -3
7 0
2 years ago
A spinner with seven equal-sized sections was used to play a game.
Amiraneli [1.4K]

Answer:

cool

Step-by-step explanation:

do you need the fractions

1/7,2/7,3/7,4/7,5/7,6/7,1 or 7/7

7 0
3 years ago
Read 2 more answers
Other questions:
  • Why would a money market account require a minimum balance?
    5·1 answer
  • 2
    11·1 answer
  • HELP ASAP WILL GIVE BRAINLIEST!! What is the value of 8.25p + 3.99c, when p=12 and c=8.
    5·1 answer
  • Find the volume of a cylinder with a height of 6 cm and a radius of 3 cm.
    9·1 answer
  • Help me with this problem
    12·1 answer
  • Work out the area of this cuboid 7.5cm 2.3 cm and 5cm
    14·1 answer
  • Help help help help help help help help help help help help help​
    9·1 answer
  • Ashleigh wants to double her money. She put $5,000 in a bank account that pays 4% compounded continuously. How long will it take
    10·1 answer
  • PLSSS HELLPP MEEEEE!!
    15·1 answer
  • HURRY PLEASE <br> What is measure of
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!