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____ [38]
3 years ago
8

find the root(s) of f (x) = (x + 5)3(x - 9)2(x + 1). 50 POINTS!!!!!!! -5 with multiplicity 3 5 with multiplicity 3 -9 with multi

plicity 2 9 with multiplicity 2 -1 with multiplicity 0 -1 with multiplicity 1 1 with multiplicity 0 1 with multiplicity 1
Mathematics
2 answers:
Dmitrij [34]3 years ago
8 0

Answer:

The answer to this question can be described as follows:

-5 with multiplicity 3

9 with multiplicity 2

-1 with multiplicity 1

Step-by-step explanation:

Given:

\Rightarrow f (x) = (x + 5)^3(x - 9)^2(x + 1)

Solve the above equation:

\Rightarrow f (x) = (x + 5)(x + 5)(x + 5)(x - 9)(x - 9)(x + 1)\\

The roots of the polynomial are as follows:

 \Rightarrow (x-x_1)(x-x_2)(x-x_3)......(x-x_n)\\\\\Rightarrow  x_1,x_2,x_3.........x_n

That's why the roots are:

5 with multiplicity 3

9 with multiplicity 2

-1 with multiplicity 1

AysviL [449]3 years ago
5 0

Answer:

answer:

a. -5 with multiplicity 3  

d. 9 with multiplicity 2

f. -1 with multiplicity 1

Step-by-step explanation:

You might be interested in
Y=3/4 x-4
pochemuha

Answer:

see graph of y=3/4 x-4

Step-by-step explanation:

Assuming you mean

y = \frac34x - 4

Below is a graph of that one. The slope is 3/4 and the interception with the y axis is at y=-4. The equation is in its normal form y=ax+b with a=3/4 (slope) and b=-4 (y intercept), so no conversion needed.

You have to be careful on how you write these equations down. It might very well be that you meant:

y = \frac{3}{4x-4} or y = \frac{3}{4x} - 4

However, those are more complex so I'm hoping for the first one... ;-)

8 0
3 years ago
Marsha wants to determine the vertex of the quadratic function f(x) = x2 – x + 2. What is the function’s vertex?
BaLLatris [955]

Answer:

Vertex = (\frac{1}{2},\frac{7}{4})

Step-by-step explanation:

Given

f(x) = x^2 - x +2

Required

The vertex

We have:

f(x) = x^2 - x +2

First, we express the equation as:

f(x) = a(x - h)^2  +k

Where

Vertex = (h,k)

So, we have:

f(x) = x^2 - x +2

--------------------------------------------

Take the coefficient of x: -1

Divide by 2: (-1/2)

Square: (-1/2)^2

Add and subtract this to the equation

--------------------------------------------

f(x) = x^2 - x +2

f(x) = x^2 - x + (-\frac{1}{2})^2+2  -(-\frac{1}{2})^2

f(x) = x^2 - x + \frac{1}{4}+2  -\frac{1}{4}

Expand

f(x) = x^2 - \frac{1}{2}x- \frac{1}{2}x + \frac{1}{4}+2  -\frac{1}{4}

Factorize

f(x) = x(x - \frac{1}{2})- \frac{1}{2}(x - \frac{1}{2})+2  -\frac{1}{4}

Factor out x - 1/2

f(x) = (x - \frac{1}{2})(x - \frac{1}{2})+2  -\frac{1}{4}

f(x) = (x - \frac{1}{2})^2+2  -\frac{1}{4}

f(x) = (x - \frac{1}{2})^2+ \frac{8 -1 }{4}

f(x) = (x - \frac{1}{2})^2+ \frac{7}{4}

Compare to: f(x) = a(x - h)^2  +k

h = \frac{1}{2}

k = \frac{7}{4}

Hence:

Vertex = (\frac{1}{2},\frac{7}{4})

8 0
3 years ago
Read 2 more answers
It takes 20 hours and $400 to interview a candidate
erma4kov [3.2K]

Answer:

Not sure what this question is asking but for the hourly rate, the answer is $20.

Step-by-step explanation:

You can write an equation as 20x=400.

Simply solve it by dividing each side by 20 to find the hourly rate in dollars per hour.

You get x=20 as your answer so 20 dollars per hour!

Hope this helps! :)

3 0
3 years ago
Which expression represents the quotient of the model shown? -x2 O x + 3 x - 3 lolo o O -X-3 -x + 3​
Bess [88]

Answer:

<h3>-x+3</h3>

Step-by-step explanation:

Given the expression

-x^2 + x + 3 x - 3

Factorize

(-x^2 + x) + (3 x - 3)

-x(x-1)+3(x-1)

= (x-1)(-x+3)

Hence one of the quotient is -x+3

3 0
3 years ago
What is the next number in this sequence? 100,10,1___,...
maw [93]
.1 or 1/10
Vote me brainliest!
6 0
3 years ago
Read 2 more answers
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