All categories

2 months ago

Complete the sentence below. If (3x2 + 22x + 7) ÷(x + 7) = 3x + 1, then (x + 7)(???????) =???? .

Mathematics

2 answers:

Zina [12.3K]2 months ago

7 0

Response: The outcome is $(x+7)(3x+1)=33x^2+22x+7.$

Detailed explanation: Suppose that

$(3x2 + 22x + 7) \div(x + 7) = 3x + 1,$

we need to finalize the subsequent sentence:

$(x+7)(???)=???$

We have the polynomial division algorithm as follows

$\textup{If }a(x)\times b(x)=c(x),\\\textup{then, we have }\\\\\dfrac{c(x)}{b(x)}=a(x)~~~~~\textup{or}~~~~~~c(x)\div b(x)=a(x).$

In this equation, a(x) denotes the quotient, b(x) indicates the divisor, and c(x) stands for the dividend.

Using this principle in the current problem, it results in

$\textup{since }(3x2 + 22x + 7) \div(x + 7) = 3x + 1,\\\\\textup{so, }\\\\(x+7)(3x+1)=3x^2+22x+7=0.$

Consequently, the full sentence would be

$(x+7)(3x+1)=3x^2+22x+7=0.$

zzz [12.3K]2 months ago

3 0

Response:

3x+1, 3x^2+22x+7, and closure

Detailed explanation:

You might be interested in

David read 69 books in a 12-month period. Sarah read 54 books in the same period of time. How many more books per month did Davi

tester [12383]

David has read 15 additional books.

3 0

2 months ago

Read 2 more answers

About ten percent of users do not close Windows properly. Suppose that Windows is installed in a public library that is used by

lawyer [12517]

Answer:

Refer to the explanation

Step-by-step explanation:

As approximately 10% of users fail to close Windows properly, we determine:

The likelihood that a user neglects to shut down Windows correctly is $p=0.1;$
The likelihood that a user shuts the Windows properly is $q=1-p=1-0.1=0.9.$

A. On average,

one in ten users does not close Windows correctly;
10 out of 100 users fail to close Windows correctly.

B. The likelihood that precisely 8 out of the next 10 users will close Windows correctly is

$C^{10}_8\cdot q^{8}p^{10-8}=\dfrac{10!}{8!(10-8)!}\cdot (0.9)^8\cdot (0.1)^2=45\cdot (0.9)^8\cdot (0.1)^2\approx 0.1937$

6 0

3 months ago

Which equation represents a proportional relationship with a constant of proportionality of 14? y = x + 14 y = 14x 14y = x y = x

tester [12383]

The equation that demonstrates a proportional relationship, maintaining a constant of proportionality equal to 14, is: Here, and are proportional with a constant of proportionality of 14.

6 0

2 months ago

Read 2 more answers

While driving from his home to his workplace, Chris has to pass through two traffic lights. The general probability of getting a

AnnZ [12381]

These occurrences are unlikely to take place!

I hope this is helpful

6 0

2 months ago

Read 2 more answers

What is the main reason Dylan uses the word uses the word “lonesome” to describe Hattie Carroll’s death?

lawyer [12517]

The correct answer is B. No one stood up for her

The song primarily addresses the racism prevalent in our nation. Dylan highlights that the murderer was not penalized initially; he was released on the night of the homicide due to his wealth, and during the trial, he received only a six-month term instead of a meaningful punishment. Hattie Carroll was largely overlooked in this scenario.

8 0

3 months ago