f(x) = 8x^2 + 8x - 12 in vertex form

Answer:

4/18

Step-by-step explanation:

Answer:

the equation would be 9x+1=30

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

Step-by-step explanation: edge 2021

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]

For more information please refer to the link given below

https://brainly.com/question/15301188

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: I think all of the above

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

Answer:

-3

Step-by-step explanation:

Substitute -1 into the expression for every place of x, and evaluate it.

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:

a) 510000000 c) 24.4 d) 502.3

Step-by-step explanation:

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:

B

Step-by-step explanation:

hope this helped

-B

Complete Question:

Henry places x marbles into an empty bucket.  Each marble has the same weight. The weight, in ounces, of the bucket and marbles can be calculated using the expression shown: ​3x + 8

What does the term 8 represent in this expression?

Answer:

The weight of the bucket

Step-by-step explanation:

Given

[tex]Weight = 3x + 8[/tex]

Required

What does 8 represent?

The given expression illustrates the weight of the whole system i.e. bucket and marbles

i.e.

[tex]Weight = Weight\ of\ x\ marble + Weight\ of\ Bucket[/tex]

Since there are x marbles, by comparison:

[tex]Weight\ of\ x\ marble = 3x[/tex]

[tex]Weight\ of\ bucket = 8[/tex]

Hence, 8 represents the weight of the bucket

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:

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=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:

No this is not arithmetic this is geometric

Step-by-step explanation:

10 to 15 is a increase of 5

15 to 21 is a increase of 6

21 to 28 is a increase of 7 arithmetic have to have steady increases

Answer:

Hola!

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:

I say 65 hours hope it helps

Step-by-step explanation:

Answer:y=28

Step-by-step explanation:

40+3y+2y=180

Subtract 40

3y+2y=140

Combine like terms

5y=140

Divide

y=28

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!

Answer:

J.

Step-by-step explanation:

It crosses through (0,0) and has a slope of 2.5 or rather 5/2 because when the x value is at 4 the y value is at 10 that simplifies to 5/2 or 2.5.

Answer:

I think OA because you would need to know how much yarn for each cap and how many caps she will make

Answer:

The number is 623.

Step-by-step explanation:

[tex]\frac{x}{7}+3 =92\\\frac{x}{7} =89\\x=623[/tex]

Answer:

a and d are parallel

Step-by-step explanation: