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maxonik [38]
3 years ago
5

Find an expression for a cubic function f if f(4) = 96 and f(-4) = f(0) = f(5) = 0. Part 1 of 4 A cubic function generally has t

he form f(x) = ax3 + bx2 + cx + d. If we know that for some x-value x = p we have f(p) = 0, then it must be true that x − p is a factor of f(x). Since we are told that f(5) = 0, we know that x-5 Correct: Your answer is correct. seenKey x-5 is a factor. Part 2 of 4 Similarly, since f(−4) = 0, then f(x) has the factor x+4 Correct: Your answer is correct. seenKey x+4 , and since f(0) = 0, then f(x) has the factor x Correct: Your answer is correct. seenKey x .
Mathematics
1 answer:
Bezzdna [24]3 years ago
4 0

Given a polynomial p(x) and a point x_0, we have that

p(x_0) = 0 \iff (x-x_0) \text{\ divides\ } p(x)

We know that our cubic function is zero at -4, 0 and 5, which means that our polynomial is a multiple of

(x+4)(x)(x-5) = x(x+4)(x-5)

Since this is already a cubic polynomial (it's the product of 3 polynomials with degree one), we can only adjust a multiplicative factor: our function must be

f(x) = ax(x+4)(x-5),\quad a \in \mathbb{R}

To fix the correct value for a, we impose f(4)=96:

f(4) = 4a(4+4)(4-5) = -32a = 96

And so we must impose

-32a=96 \iff a = -\dfrac{96}{32} = -3

So, the function we're looking for is

f(x) = -3x(x+4)(x-5)=-3x^3+3x^2+60x

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Inessa [10]

Answer:

0.05, 0.5, 0.507, 0.57, 0.577

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
A survey with a two-point scale was conducted in an organization. It concluded that 85% of the respondents were unsatisfied with
Morgarella [4.7K]

Answer:

Number of the peoples were satisfied with the career guidance are 300 .

Step-by-step explanation:

Formula

Percentage = \frac{Part\ value\times 100}{Total\ value}

As given

A survey with a two-point scale was conducted in an organization.

It concluded that 85% of the respondents were unsatisfied with the career guidance they were provided.

If 2,000 people participated in the survey.

Total value = 2000

Percentage = 85%

Putting all the values in the formula

85 = \frac{Part\ value\times 100}{2000}

Part\ value= \frac{2000\times 85}{100}

Part\ value= \frac{170000}{100}

Part value = 1700

i.e

People not satisfied by the career guidance = 1700

People satisfied by the career guidance = Total people participated in survey  - People not satisfied by the career guidance .

Putting the values in the above

                                                                  = 2000 - 1700

                                                                  = 300

Therefore the number of the peoples were satisfied with the career guidance are 300 .


5 0
3 years ago
Read 2 more answers
What is 233 x 234 ???
andre [41]

Answer:

the answer is 54522

Step-by-step explanation:

hope it helps

7 0
3 years ago
Read 2 more answers
HELP ASAP!!!!! Given: Point B is on the perpendicular bisector of AC¯¯¯¯¯. BD¯¯¯¯¯ bisects AC¯¯¯¯¯ at point D. Prove: B is equid
Harlamova29_29 [7]

Answer:  Missing parts are,

In first blank,  AD\cong DC,

In second blank, SAS postulate

In third blank, CPCTC postulate

Step-by-step explanation:

Since, Here D is the mid point on the line segment AC.

And BD is a perpendicular to the line AC.

Therefore, In triangles ADB and CDB ( shown in figure)

AD\cong DC ( By the definition of mid point)

\angle BDA\cong \angle BDC ( right angles )

BD\cong BD ( reflexive)

Thus, By SAS ( side angle side )postulate,

\triangle ADB\cong \triangle CDB

So, by CPCTC( Corresponding parts of congruent triangles are congruent)

AB\cong CB

Now, By definition of congruent segment,

AB=CB

By definition of equidistant,

B is equally far from both A and C.




7 0
3 years ago
Read 2 more answers
If JM = 5x – 8 and LM = 2x - 6, which expression represents JL?
Anastasy [175]

Answer:

3x-2

Step-by-step explanation:

JK =JL+LM

5x-8=JL +(2x -6)

JL = 5x-8 -2x+6

JL = 3x-2

6 0
3 years ago
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