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Over [174]
3 years ago
15

Consider the polynomials p(x) = 3x + 27x^2 and q(x)= 2 . Find the x -coordinate(s) of the point(s) of intersection of these two

polynomials. What is the sum of these x -coordinates? (If there is only one point of intersection, give the corresponding x -coordinate.)

Mathematics
1 answer:
Tom [10]3 years ago
4 0

Answer:

The x -coordinate(s) of the point(s) of intersection of these two polynomials are x=\frac{2}{9}\approx0.2222,\:x=-\frac{1}{3}\approx-0.3333

The sum of these x -coordinates is \frac{2}{9}+\left(-\frac{1}{3}\right)=-\frac{1}{9}

Step-by-step explanation:

The intersections of the two polynomials, p(x) and q(x), are the roots of the equation p(x) = q(x).

Thus, 3x + 27x^2=2 and we solve for x

3x+27x^2-2=2-2\\27x^2+3x-2=0\\\left(27x^2-6x\right)+\left(9x-2\right)\\3x\left(9x-2\right)+\left(9x-2\right)\\\left(9x-2\right)\left(3x+1\right)=0

Using Zero Factor Theorem: = 0 if and only if = 0 or = 0

9x-2=0\\9x=2\\x=\frac{2}{9}

3x+1=0\\3x=-1\\x=-\frac{1}{3}

The solutions are:

x=\frac{2}{9}\approx0.2222,\:x=-\frac{1}{3}\approx-0.3333

The sum of these x -coordinates is

\frac{2}{9}+\left(-\frac{1}{3}\right)=-\frac{1}{9}

We can check our work with the graph of the two polynomials.

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The first four terms of a sequence are shown below:
algol13

Answer:

Option 4 is correct.


Step-by-step explanation

Here the first term is 8 so  the first term is given by f(1) = 8

Since here the  given series is arithmetic series and here common difference is given by 5-8 = -3

Recurrence relation is given by f(n+1) - f(n) =  d

                                        where d is common difference which is given  to be  -3 .

therefore  it is given as

   f(n+1) -f(n) = -3

         f(n+1) = f(n) -3      [ adding f(n) both sides]

Since n is starting from 1 there for   its fourth option is correct

f(1) =8 and , f(n+1) = f(n) -3 ) , for n ≥1



6 0
2 years ago
Read 2 more answers
For the month of March in a certain​ city, 57​% of the days are cloudy. Also in the month of March in the same​ city, 55​% of th
kirill115 [55]

Answer:

P(F | C) = 0.96

Step-by-step explanation:

Hi!

This is a problem on conditional probability. Lets call:

C = { cloudy day }

F = { foggy day }

Then F ∩ C = { cloudy and foggy day }

You are asked for P(F | C), the probability of a day being foggy given it is cloudy. By definition:

P(F|C)=\frac{P(F\bigcap C)}{P(C)}

And the data you have is:

P(C) = 0.57\\P(F \bigcap C) =0.55

Then: P(F | C) = 0.96

3 0
3 years ago
Rewrite one tenth times x cubed times y plus two tenths times x times y squared using a common factor.
zalisa [80]

The expression which can be rewritten using a common factor is; xy/10 (x² + 2y).

<h3>What is an expression?</h3>

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We have the following information given as;

One tenth times x cubed times y plus two tenths times x times y squared using a common factor.

We know that 'times' has to be replaced with multiplication.

Now, we will change this into mathematical expression as;

x³y/ 10 + 2xy²/ 10

Now, the common factor can be ;

xy/10

The Common factor refers to the number and the variables taken as a common factor should be able to completely divide the terms given any expression.

Now, taking it as a common factor, we have the following expression:

xy/10 (x² + 2y)

Hence, the required expression is; xy/10 (x² + 2y).

To know more about factor here;

brainly.com/question/24182713

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6 0
1 year ago
a students body temperature is 98. 6 degrees Fahrenheit. what is the temperature on the Celsius scale
sleet_krkn [62]
You would take 98.6-32x.5556=37
6 0
2 years ago
Help! Please show work, and identify the solution or how many solutions there are to the system.
Sveta_85 [38]

Answer:

one solution (-3, -6)

Step-by-step explanation:

the two line cross at the point (-3, -6) and only at that one point so there is only one solution (-3, -6).

4 0
3 years ago
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