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
qaws [65]
3 years ago
15

Consider the cubic function f(x) = x^3 + ax^2 + bx + 4 where (a) and (b) are constants. When f(x) is divided by x-3, the remaind

er is 10. When f (x) is divided by x+1, the remainder is 6.
Show that a = -1 and b = -4
Mathematics
1 answer:
Debora [2.8K]3 years ago
8 0

Answer:

see explanation

Step-by-step explanation:

Using the Remainder theorem

If f(x) is divided by (x - h) then f(h) = remainder, thus

f(3) = 3³ + a(3)² + b(3) + 4 = 10, that is

27 + 9a + 3b + 4 = 10

9a + 3b + 31 = 10 ( subtract 31 from both sides )

9a + 3b = - 21 → (1)

f(- 1) = (- 1)³ + a(- 1)² + b(- 1) + 4 = 6, that is

- 1 + a - b + 4 = 6

a - b + 3 = 6 ( subtract 3 from both sides )

a - b = 3 → (2)

Rearrange (2) expressing a in terms of b

a = 3 + b → (3)

Substitute a = 3 + b into (1)

9(3 + b) + 3b = - 21 ← distribute and simplify left side

27 + 9b + 3b = - 21

12b + 27 = - 21 ( subtract 27 from both sides )

12b = - 48 ( divide both sides by 12 )

b = - 4

Substitute b = - 4 into (3)

a = 3 - 4 = - 1

Hence a = - 1 and b = - 4

You might be interested in
Please answer this question below.
Katarina [22]
In a theatre room, there are 4 rows of  chairs. There are 4 columns of chairs. How many chairs are there in the theatre room?

4x4=16 

There are 16 chairs in the theatre room.
5 0
3 years ago
Read 2 more answers
Which of the following functions gives the length of the base edge, a(v), of a right square pyramid that is 8 inches tall as a f
Reil [10]

Answer:

\large\boxed{a(V)=\sqrt{\dfrac{3V}{8}}}

Step-by-step explanation:

The formula of a volume of a square pyramid:

V=\dfrac{1}{3}a^2h

a - base edge

h - height of a pyramid

We have H = 8in.

Substitute and solve for a:

\dfrac{1}{3}a^2(8)=V\\\\\dfrac{8}{3}a^2=V\qquad\text{multiply both sides by}\ \dfrac{3}{8}\\\\\dfrac{3\!\!\!\!\diagup^1}{8\!\!\!\!\diagup_1}\cdot\dfrac{8\!\!\!\!\diagup^1}{3\!\!\!\!\diagup_1}a^2=\dfrac{3}{8}V\\\\a^2=\dfrac{3V}{8}\Rightarrow a=\sqrt{\dfrac{3V}{8}}

3 0
3 years ago
Circle F is congruent to circle J, and ZEFD = ZGJH.<br> m ZDFE = 80'. What is the measure of H?
djyliett [7]

Answer:

50 deg

Step-by-step explanation:

The circles are congruent, so all radii of both circles are congruent.

The given central angles are congruent, so the triangles are congruent by SAS.

Since each triangle has 2 congruent sides (the radii), opposite angles are congruent.

m<DFE = m<J = 80 deg

m<H = m<G = x

m<H + m<G + m<J = 180

x + x + 80 = 180

2x + 80 = 180

2x = 100

x = 50

m<H = 50

6 0
3 years ago
Read 2 more answers
HELP ME PLEASE!!!!!!
Free_Kalibri [48]

Step-by-step explanation:

$9.99 + $0.35t <= $12

$0.35t <= $2.01

t <= 5.74

The most number of toppings would be 5.

4 0
3 years ago
Read 2 more answers
Lexi is rehydrating after an intense workout. She
Anuta_ua [19.1K]

Answer:

Step-by-step explanation:

89

535

hhyoljy,osl

2

32323

5 0
3 years ago
Other questions:
  • What is 10+10x20 please help
    5·2 answers
  • Identify the period for the trigonometric function: f (t) = −2sec(t).
    6·1 answer
  • Please help me please!!!!!!!
    14·1 answer
  • Suppose Country A has a high average wage level and a high level of output per person, while Country B has a low average wage le
    7·1 answer
  • How much interest would $2,000 earn in one year at the rate of 1.2%?
    11·1 answer
  • Prove that \P(A) \cup \P(B) \subseteq \P(A \cup B) and find a counter-example to show that we don't always have equality
    8·1 answer
  • The line plot below shows the lengths of bolts Mr. Slivka found in his drawer. He needs 16 bolts that are longer than 1 inch for
    15·1 answer
  • Does the greater than or less than
    5·1 answer
  • Solve using Pythagoras Theorem (please)​
    10·1 answer
  • Which of the following statements accurately describe the dilation shown? Select all that apply.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!