All categories

2 years ago

Which polynomial function has a root of 1 with multiplicity 2 and a root of 6 with multiplicity 1

Mathematics

2 answers:

Mashutka [201]2 years ago

7 0

Answer:

$f(x)=x^3-8x^2+13x-6$

Step-by-step explanation:

We are given information about polynomial as

a root of 1 with multiplicity 2

so, one of factor is (x-1)^2

a root of 6 with multiplicity 1

so, another factor is (x-6)^2

so, we can write polynomial as

$f(x)=(x-1)^2(x-6)$

now, we can simplify it

$f(x)=(x-1)(x-1)(x-6)$

$f(x)=(x^2-2x+1)(x-6)$

So, we get polynomial as

$f(x)=x^3-8x^2+13x-6$

aleksley [76]2 years ago

6 0

Answer: f(x) = (x – 1)(x – 1)(x – 6)

Step-by-step explanation:

You might be interested in

Answer the question in the picture

Svet_ta [14]

<h3>Answer:</h3>

left picture (bottom expression): -cot(x)
right picture (top expression): tan(x)

<h3>Step-by-step explanation:</h3>

A graphing calculator can show you a graph of each expression, which you can compare to the offered choices.

_____

You can make use of the relations ...

... sin(a)+sin(b) = 2sin((a+b)/2)cos((a-b)/2)

... cos(a)+cos(b) = 2cos((a+b)/2)cos((a-b)/2)

... cos(a)-cos(b) = -2sin((a+b)/2)sin((a-b)/2)

Then you have ...

$\dfrac{\cos{2x}-\cos{4x}}{\sin{2x}+\sin{4x}}=\dfrac{2\sin{3x}\sin{x}}{2\sin{3x}\cos{x}}=\dfrac{\sin{x}}{\cos{x}}=\tan{x}$

and ...

$\dfrac{\cos{2x}+\cos{4x}}{\sin{2x}-\sin{4x}}=\dfrac{2\cos{3x}\cos{x}}{-2\cos{3x}\sin{x}}=\dfrac{-\cos{x}}{\sin{x}}=-\cot{x}$

6 0

3 years ago

A one year member ship to your local gym costs $539. there is an initial fee of $35. write an equation tou can use to fund out h

stich3 [128]

$539 - $35 = $504

$504 : 12 = $42

Per month you pay $42.

4 0

2 years ago

Write and solve a proportion to answer the question. (Skills Review Handbook) 22. 30 is 15% of what number?

algol13

Answer:

The answer is 148.6666667

Step-by-step explanation:

1) Set a linear quation

$\frac{22.30}{x} = \frac{15}{100}$

2) Cross multiply

$15x = 22.30 \times 100$

3) Multiple the right side

$15x = 2230$

4) Divide both side by 15

$\frac{15x}{15} = \frac{2230}{15}$

5) Solve the linear equation

$x = 148.6666667$

3 0

2 years ago

A rectangle has vertices (8, 6), (4, 6), (8, −4), and (4, −4). What are the coordinates after dilating from the origin by a scal

Mama L [17]

Answer: (12,9), (6,9), (12,-6) and (6,-6)

Step-by-step explanation:

Given: The coordinates of the original rectangle are (8, 6), (4, 6), (8, −4), and (4, −4). We know that the coordinates of the image after dilation from the origin by a scale factor of k is given by:_

$(xy)\rightarrow(kx,ky)$

Then, the coordinates of the image after dilation from the origin by a scale factor of 1.5 are given by:_

(8, 6)→ $(8\times1.5,6\times1.5)=(12,9)$

(4, 6)→ $(4\times1.5,6\times1.5)=(6,9)$

(8, −4) → $(8\times1.5,-4\times1.5)=(12,-6)$

(4, −4)→ $(4\times1.5,-4\times1.5)=(6,-6)$

Hence, the coordinates of the image after dilation from the origin by a scale factor of 1.5 are (12,9), (6,9), (12,-6) and (6,-6).

3 0

3 years ago

A pile of coins, consisting of nickels, dimes, and quarters, is worth $4.55. There are 4 more dimes than nickels and 3 quarters

frozen [14]

Fun

n=number of nickles
q=number of quarters
d=number of dimes

4 more dmes than nickles, 3 more quarters than dimes
d+4=n
q=3+d

total value is 455 cents
10d+5n+25q=455
divide both sides by 5 to simplify
2d+n+5q=91

now we convert all to one coin
q=3+d and n+4=d
subsitute 3+d for q and n+4 for d

2(n+4)+n+5(3+d)=91
2(n+4)+n+5(3+n+4)=91
2(n+4)+n+5(n+7)=91
2n+8+n+5n+35=91
8n+43=91
minus 43 both sides
8n=48
divide both sides by 8
n=6

sub back
n+4=d
6+4=d
10=d

q=3+d
q=3+10
q=13

6 nickles
10 dimes
13 quarters

5 0

3 years ago