In rectangle KLMN, KM = 6x + 16, and LN = 49. Find the value of x.​

Given:

Zero: 2, multiplicity: 3

Zero: 0, multiplicity: 2

Degree: 5

Leading coefficient = 1

To find:

The polynomial function.

Solution:

The general form of a polynomial is

[tex]P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}[/tex]

where, a is a constant, [tex]c_1,c_2,...,c_n[/tex] are zeroes with multiplicity [tex]m_1,m_2,...,m_n[/tex].

Using the given information and the general form of a polynomial, we get

[tex]P(x)=a(x-2)^{3}(x-0)^{2}[/tex]

[tex]P(x)=ax^2(x^3-6x^2+12x-8)[/tex]

[tex]P(x)=a(x^5-6x^4+12x^3-8x^2)[/tex]

Leading coefficient is 1, so the value of a is also 1.

[tex]P(x)=1(x^5-6x^4+12x^3-8x^2)[/tex]

[tex]P(x)=x^5-6x^4+12x^3-8x^2[/tex]

Therefore, the required polynomial is [tex]P(x)=x^5-6x^4+12x^3-8x^2[/tex].

The polynomial for the conditions with leading coefficient 1 that has the given zeros, multiplicities, and degree. Zero: 2, multiplicity: 3 Zero: 0, multiplicity: 2 Degree: 5 is given as

[tex]\rm\bold{ y(x) = 1\times (x-2)^3(x-0)^2 }[/tex]

According to the given condition

The given conditions to write the polynomial equations are as follows

Zero 2  and Multiplicity 3

Zero 0 and Multiplicity 2  

Degree of polynomial expression  = 5

Leading coefficient of polynomial expression = 1

Let us consider the polynomial equation has only one variable and hence in general form we can write the equation of polynomial as follows

[tex]\rm y (x) = a(x-\alpha)^m (x-\beta)^n........(1)\\Where \\a = Leading \; coefficient\; of\; polynomial\; expression \\\alpha ,\beta = Roots \; of \; the\; polynomial\; expression\\m\; and \; n \; are \; multiplicities \; of \; the \; roots \; \alpha,\beta \; respectively\\Degree = m+n[/tex]

From the general form of polynomial expression as shown in equation (1) we can write

Polynomial expression for the given  conditions is formulated in equation (2)

[tex]\rm y(x) = 1\times (x-2)^3(x-0)^2 .......(2)[/tex]

So the polynomial for the conditions given in question is expressed as

[tex]\rm\bold{ y(x) = 1\times (x-2)^3(x-0)^2 }[/tex]

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Answer:

Henry's mom spent $17.70 on lemonade.

Step-by-step explanation:

6 x 2.95 = 17.7

Answer: I think all of the above

Step-by-step explanation:maybe there traveling so…

Answer:

for the domain, find the point on the farthest side (the left) and the closest (the right)

so for yours it would be [-3,2]

it's brackets because the points are closed.

for the range, same thing but for the y intercept.

so it's [-2,4]

there's your answer!

Question:

You flip a fair coin ; What is P(heads)? If necessary, round your answer to 2 decimal places​

Answer:

[tex]P(Head) =0.50[/tex]

Step-by-step explanation:

Given:

A fair coin

Required

Determine [tex]P(Head)[/tex]

A coin has two faces (Head (1) and Tail (1) )

i.e. 1 head and 1 tail

Both of which have equal probability, which is calculated as follows:

[tex]P(Head) = P(Tail) = \frac{1}{1 + 1}[/tex]

[tex]P(Head) = P(Tail) = \frac{1}{2}[/tex]

[tex]P(Head) = P(Tail) = 0.5[/tex]

Hence:

[tex]P(Head) =0.50[/tex]

Answer: Its 0.50

Step-by-step explanation:

Answer:

Step-by-step explanation:

800+20%

20%= (20/100)

800/100=8*20=160

add to original price= 800+160=960

Answer:

Each bag is $1.50. 11 bags would cost $16.50.

Answer:

Each bag would cost 1.50$.

15.00$ / 10 = 1.5$

1.5 = 1.50

______________________

11 bags:

1.5 x 11 = 16.5

16.5 = 16.50$

11 bags would cost 16.50$

Answer:

D

Step-by-step explanation:

sry if im wrong i tried

Answer:

0; 1; 2; 3. The slopes are 2, 0, 1, 3 from top to bottom, but from least to greatest it is 0, 1, 2, 3

Answer:

think 2 could be wrong

Brainlest pls

Step-by-step explanation:

x

Answer:

2      3    0   -4    8

+            6    12   16

       3    6     8    24

A：3x^3+6x^2+8x+24/x-2

Answer:

(3x^4-4x^2+8x-1)÷(x-2)

Answer:

y=2x

it already gives you that in 2 hours four inches of snow has fallen. to find one hour you would basically just divide it in half

Answer:

a and d are parallel

Step-by-step explanation:

Answer: I believe it is 3.75-

Step-by-step explanation:

David: 3.25

Jenny: 2.25 more than Dan

Dan: 1.75 less than David

  3.25

-  1.75

_______

  1.50

Dan spent 1.50

  1.50

+ 2.25

 3.25

_______

$7.00

Answer:

CB = 13.75

Step-by-step explanation:

Since we know that A, B, and C are the midpoint of the sides, we know that line CB is proportional to QR (by 2)..

So, 27.5/2 = 13.75

Answer:

1/3 or 3.33

Step-by-step explanation:

There are 6 sides to dice, and to land on one side is a 1/6th of a chance. to land on 2 possible sides, you do 1/6+1/6 which equals 2/6 which is equivalent to 1/3 or 3.33 as a decimal.

I hope this helps and good luck!

Answer:

1/3 or 3.3333333333333333333 repeating

Step-by-step explanation:

A normal dice has 6 sides. You are asking the probability of getting two of them. 2 ÷ 6 = 1/3, or 33.3 repeating

I Hope That This Helps! :)

Answer:

y=1/4x-7; can't put graph on here

Step-by-step explanation:

m=y2-y1/x2-x1

m=-8+6/-4-4=-2/-8=1/4

put it in point-slope form with (4,-6) as the base

y-y1=m(x-x1)

y+6=1/4(x-4)

y+6=1/4x-1

y=1/4x-7

Answer:

the equation would be 9x+1=30

Answer:

Work shown below;

Step-by-step explanation:

Factor by grouping:

[tex]x^{3}+5 x^{2}-6x-30\\(x^{3}+5 x^{2}) (-6x-30)\\x^{2} (x+5)-6(x+5)\\(x^{2}-6 )(x+5)[/tex]

Answer: the length of GH is half the length of KL

Step-by-step explanation: edge 2021

Answer:

1. 2

2.circle

3.b tan t

Step-by-step explanation:

The slope of the equations x = 1 + 3t and y = -1 + 6t is 6, the equations x = 5 cos t and y = 5 sin t describe a circle and if x = a sec t is one of the parametric equations, the other will be y =b tan t

Two or more expressions with an Equal sign is called as Equation.

The equation x = 1 + 3t and y = -1 + 6t can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

In this case, m = 6, which is the slope of the line.

The equations x = 5 cos t and y = 5 sin t describe a circle.

These equations define the parametric form of a circle with a radius of 5 centered at the origin.

if x = a sec t is one of the parametric equations, the other will be y =b tan t

Hence, the slope of the equations x = 1 + 3t and y = -1 + 6t is 6, the equations x = 5 cos t and y = 5 sin t describe a circle and if x = a sec t is one of the parametric equations, the other will be y =b tan t

To learn more on Equation:

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Answer:What’s the question that we have to answer?

Step-by-step explanation:

Answer: it would be 2 1/3 cups

Step-by-step explanation:

Answer:

you have to divide the gallons with the money per gallon

Step-by-step explanation:

Answer:

$842.40

Step-by-step explanation:

2.70 x 312

Answer:

That would be -14.

Step-by-step explanation:

Answer:

it's -14 when u evaluate a-2x

Answer:

5.35*2+x=16 and the answer is $.35

Step-by-step explanation:

5.35*2+x=16

10.70+x=16

-10.70     -10.70

x=5.30

5.30/15= about .35

Answer

$12.65/15

Step-by-step explanation:

$16.00-$5.35=$12.65

This means that $12.65/15 is the cost of each apple.

Answer:

A. -3 < x < 1

General Formulas and Concepts:

Step-by-step explanation:

"When is the function decreasing" is saying when the graph is going down.

Calculus-wise, we are finding when the slope of the tangent line is negative.

From the graph, we see it decreasing from -3 to 1. Everywhere else is increasing.

Therefore, our interval decreasing is from (-3, 1).

Answer:

Step-by-step explanation:

She has 200

80 deposit - 200= 120 left to spend

80+30h=200

If she has 120 left to spend at 30 hr, she could have the boat for 4 hrs

80+30h=200 subtract 80 from both sides

30h=120 divide by the 30

h=4

Answer:

0 is rational

5 rational so u are correct

Step-by-step explanation:

Step-by-step explanation:

0 is Rational

5 is Rational is you are correct

Answer:

Sorry.........................