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3 years ago

I don’t remember how I get the answer to this. I have the answer key though. Please help, I have a test in an hour

Mathematics

2 answers:

svet-max [94.6K]3 years ago

8 0

Answer:

Correct answer: f(x) = (x - 2) · (x - 1 - 3 i) · ( x - 1 + 3 i)

Step-by-step explanation:

Given:

f(x) = x³ - 4x² + 14x - 20 polynomial on the third degree

If 2 is zero it means that the given polynomial is divisible by the binomial (x - 2)

(x³ - 4x² + 14x - 20) / (x - 2) = x² - 2x + 10

We will now factorize this polynomial:

x² - 2x + 10 = x² - 2x + 1 + 9 = (x - 1)² - ( -9) = (x - 1)² - ( -1 · 3²)

and i is an imaginary constant and i² = - 1

x² - 2x + 10 = (x - 1)² - ( 3 i )² = (x - 1 - 3 i) · ( x - 1 + 3 i)

x² - 2x + 10 = (x - 1 - 3 i) · ( x - 1 + 3 i)

where (x - 1 - 3 i) and ( x - 1 + 3 i) are conjugate complex numbers

and finally we get :

x³ - 4x² + 14x - 2 = (x -2) · (x - 1 - 3 i) · ( x - 1 + 3 i)

God is with you!!!

mrs_skeptik [129]3 years ago

5 0

Answer:

f(x) = (x -2)(x -1+3i)(x -1-3i)

Step-by-step explanation:

You can use synthetic division to find the remaining quadratic factor in the cubic. Then any of the usual means of solving the quadratic will help you find its linear factors.

In the attached, I show the synthetic division, the factoring to real numbers, and the solution that finds the complex linear factors by completing the square.

Of course, you know that for zeros a, b, and c, the linear factors are ...

f(x) = (x -a)(x -b)(x -c)

Here, we have a=2, b=1-3i, c=1+3i.

f(x) = (x -2)(x -1+3i)(x -1-3i)

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Help with question 5a

Llana [10]

This is a refreshing question!

We are given that
f(r)=ar+b, and
Sum f(r) =125 for r=1 to 5
Sum f(r) = 475 for r=1 to 10.

and we know, using Gauss's method, that
G(n)=sum (1,2,3.....n) = n(n+1)/2 or
G(n)=n(n+1)/2

Sum f(r) =125 for r=1 to 5
=>
sum=a(sum of 1 to 5) + 5b => G(5)a+5b=125 [G(5)=15]
15a+5b=125 ...................................................(1)

Similarly, Sum f(r) = 475 for r=1 to 10 => G(10)a+5b=475 [G(10)=55]
=>
55a+10b=475.................................................(2)

Solve system of equations (1) and (2)
(2)-2(1)
55-2(15)a=475-2(125) => 25a=225 =>
a=9

Substitute a=9 in 1 => 15(9)+5b=125 => 5b=-10
b=-2

Substitute a and b into f(r),
f(r)=9r-2
check: sum f(r), r=1,5 = (9-2)+(18-2)+(27-2)+(36-2)+(45-2)=135-10=125 [good]

We define the sum of f(r) for r=1 to n as
S(n)=sum f(r) for r=1 to n = 9(sum 1,2,3....n)-2n = 9n(n+1)/2-2n = 9G(n)-2n
S(n)=9n(n+1)/2-2n
checks:
S(5)=9(15)-2(5)=135-10=125 [good]
S(10)=9(55)-2(10)=495-20=475 [good]

Hence
(a)
S(n)=sum f(r) for r=1,n
= 9(sum i=1,n)+n(-2)
= 9(n(n+1)/2 -2n
=(9(n^2+n)/2) -2n

(b) sum f(r) for i=8,18
=sum f(r) for i=1,18 - sum f(r) for i=1,7
=S(18)-S(7)
=(9(18^2-18)/2-2(18))-(9(7^2-7)/2-2(7))
=1503-238
=1265

5 0

3 years ago

Which expressions are equivalent to 3(6+b)-(2b + 1)?

Anna [14]

Answer:

18+3b-2b-1

b+17

Step-by-step explanation:

$\mathrm{Using\:the\:distributive\:law}:\quad \:-\left(a+b\right)=-a-b$

$-\left(2b+1\right)=-2b-1$

$=3\left(6+b\right)-2b-1$

$=18+3b-2b-1$

$\mathrm{Group\:like\:terms}$

$=3b-2b+18-1$

$\mathrm{Subtract\:the\:numbers:}\:18-1=17$

$=3b-2b+17$

$\mathrm{Add\:similar\:terms:}\:3b-2b=b$

$=b+17$

[RevyBreeze]

7 0

2 years ago

Matthew's dad hired him to paint 6 wooden patio chairs for $125. It takes him 9 hours to paint all of the chairs. If it takes th

frozen [14]

Given:

Matthew's dad hired him to paint 6 wooden patio chairs for $125.

Time taken by him to paint all of the chairs = 9 hours.

It takes the same amount of time to paint each chair.

To find:

The fraction of an hour does it take Matthew to paint one chair

Solution:

Total time = 9 hours

Total number of chairs = 6

Now, time taken by Matthew to paint one chair is

$\dfrac{\text{Total time}}{\text{Total number of chairs}}=\dfrac{9}{6}$

$\dfrac{\text{Total time}}{\text{Total number of chairs}}=\dfrac{3}{2}$

Therefore, Mattew takes $\dfrac{3}{2}$ of an hour to paint one chair.

Thinking with a model: On dividing the total time by total number of chairs we get time taken by Mattew (in hours) to paint one chair. So, the result represents the fraction of an hour taken by Matthew to paint one chair.

8 0

3 years ago

A Web music store offers two versions of a popular song. The size of the standard version is

sashaice [31]

Let s be standard and h be high-quality versions of the song.
To figure this out, let's make a system of equations:
2.5s + 4.5h = 5740
h = 4s
First substitute the second equation into the first for h.
2.5s + 18s =5740
Then combine like terms.
20.5s = 5740
Lastly, divide each side by 20.5 to get the number of standard downloads:
s = 280
Hope this helps!

8 0

3 years ago

List the coordinates for the plotted points A, B, C, and D.

avanturin [10]

Answer:

A= (3,1) ; B=(-2,-1) ; C=(-4,1) ; D=(-4,0)

Step-by-step explanation:

Plotted points are expressed by (x,y) , where the x is equal to the value that you read on the x plot and y is equal to the value that you read on the y plot.

8 0

3 years ago