1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
A rabbit can run 35 miles per hour.A fox can run 21 miles in half an hour.Which animal is faster and how much
Pachacha [2.7K]

Answer:


Step-by-step explanation:

The fox is faster. Because he is a fox.


Also because he can (assuming he doesn't fatigue or get caught by hounds in the second half of the hour) run 42 miles in 1 hour.


The rabbit runs 35 miler per hour.


Velocity = Distance/time


Fox velocity = 21 miles/0.5 hour


Dividing by 0.5 is the same as multiplying by 2, so...


Fox velocity = 42 miles/hour

6 0
3 years ago
The dress store is having a sale where all merchandise is 1/4 off. A woman buys $48 of merchandise at a sale price.
Fantom [35]

Answer:$36 depending on what question is i just assuming how much she has to pay

Step-by-step explanation:

48 divded by 4 is 12. $48-$12 is $36. The $12 is the 1/4 discount.

7 0
3 years ago
SYSTEMS OF LINEAR EQUATIONS - Tell whether the ordered pair is a soulution if the given system: (2,-4); {y - 2x = -8, 4y + 13x =
Leviafan [203]
No, it is not. Because it doesn't satisfy the first equation.
6 0
3 years ago
Eli ran for 27 minutes. He stopped running 5:42 what time did Eli start running
geniusboy [140]
5:15 because 42-27 is 15
6 0
2 years ago
Read 2 more answers
A cell phone factory has a cost of production C(x) = 66x + 30,000 where x is the total number of attendees at the concert . The
dimulka [17.4K]

Answer:

8000-8500

Step-by-step explanation:

I can't manage to figure out the exact number without multiple choice answers. That is the closest I could get to finding out the answer. Good Luck!

8 0
2 years ago
Other questions:
  • What is the answer to 2(5x-8)+6=11
    7·1 answer
  • EASY MATH, GOOD QUALITY PHOTO! <br><br><br><br><br>Answer for OR4 B Please!
    5·2 answers
  • What is the equation of the following graph in vertex form?
    15·1 answer
  • A professor must randomly select 4 students to participate in a mock debate. There are 15 students in his class. In how many dif
    12·1 answer
  • -3(3x+8)&gt;-9x+4 always or never true?
    12·1 answer
  • Pls help me with this question
    12·1 answer
  • Find the equation of the line
    14·1 answer
  • Pls help me with this
    9·2 answers
  • What is the least common denominator for 5 and 16
    8·2 answers
  • PLEASE HELP 50 POINTS I WILL GIVE BRAINLIEST
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!