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
Ymorist [56]
3 years ago
15

Which of the following shows the graph of the inequality y> -2x + 9

Mathematics
1 answer:
VashaNatasha [74]3 years ago
3 0

Answer:

(7/3,3)

Step-by-step explanation:

first part is -3 < 2/(3x-9).

second part is 2/(3x-9) < -1.

there is a third piece that needs to be evaluated, which is where the vertical asymptote lies.

the vertical asymptote lies at x = 3.

when x < 3, the graph of 2/(3x-9) is negative and stays negative.

when x > 3, the graph of 2/(3x-9) is positive and stays positive.

this is clear from the equation, because when x > 3, (3x-9) is positive, and 2 is positive and therefore the fraction is positive.

this is also clear from the equation, because when x < 3, (3x-9) is negative, and therefore 2/(3x-9) is negative because the numerator is positive and the denominator is positive and therefore the fraction is negative.

what this tells you is that 2/(3x-9) is greater than -3 when x is greater than 3.

what this also tells you is that 2/(3x-9) is not smaller than -1 when x is greater than 3.

if you solve the equations for when -3 = 2/(3x-9) and when -1 = (2/(3x-9), you will find that:

-3 = 2/(3x-9) when x = 25/9 which is equal to 2.778 rounded to 3 decimal places.

-1 = 2/(3x-9) when x = 7/3 which is equal to 2.333 rounded to 3 decimal places.

at x = 25/9, 2/(3x-9) = -3

when x < 25/9, 2/(3x-9) > -3.

when x > 25/9, 2/(3x-9) < -3.

however, when x > 3, 2/(3x-9) becomes positive and is therefore greater than -3 all over again.

therefore 2/(3x-9) is greater than -3 when x is smaller than 25/9 and when x is greater than 3.

this satisfies the inequality of -3 < 2/(3x-9).

the other inequality that needs to be satisfied is 2/(3x-9) < -1.

you know that 2/(3x-9) = -1 when x = 7/3.

if you look at the interval between x = 7/3 and x = 3, you will see that 3/(3x-9) is less than -1.

for example, when x = 8/3, which is greater than 7/3 and less than 3, 2/(3x-9 is equal to -30 which is clearly less than -1.

when x is less than 7/3, 2/(3x-9) is greater than -1.

 

for example, when x is equal to 6/3, which is less than 7/3, 2/(3x-9) is equal to -2/3 which is greater than -1.

therefore when x > 7/3 and < 3, y = 2/(3x-9) is less than -1.

what you really want to do is graph the equality points where the graph shows equality, and then look at the intervals between those points.

the following graph shows you what i mean.

i graphed 4 equations.

first equation is y = 2/(3x-9)

second equation is y = -3

third equation is y = -1

fourth equation is x = 3.

you can see from the graph that y = -3 is smaller than y = 2/(3x-9) when x is smaller than 25/9 and when x is greater than 3.

you can also see from the graph that y = (3x-9) is smaller than y = -1x is greater than 7/3 and when x is smaller than 3.

those are your solutions.

-3 < 2/(3x-9) when x < 25/9 or when x > 3.

in interval notation, this would be x = (minus infinity, 25/9) union (3, plus infinity).

You might be interested in
Select The correct Description giving brainliest PLZ HELP
Alika [10]

Answer: C

Step-by-step explanation:

6 0
2 years ago
What is 257,650 rounded to the nearest ten
den301095 [7]
The answer is 257,650
5 0
3 years ago
Read 2 more answers
Adam put $100 in a savings account. After 10 years, he had $1649 in the account. What rate of interest did he earn? Use the form
Rina8888 [55]

Answer:

Step-by-step explanation: C. 28%

A = Pe^{rt}

1649 = 100 \cdot e^{10r}\\16.49 = e^{10r}\\\ln{16.49} = 10r\\r = \frac{\ln{16.49}}{10} = 0.28\\

7 0
2 years ago
Factorise fully 9x squared - 6xy
prisoha [69]
3x(3x-2y) 

you have to find a common factor between the two numbers. in this case it's three, so you just divide each number by three.
4 0
2 years ago
Put these decimals in order from least to greatest.<br> 8.009<br> 8.90<br> 8.09<br> 8.913
vagabundo [1.1K]

Answer:

8.009, 8.09, 8.90, 8.913

3 0
3 years ago
Other questions:
  • PLEAsE HELP[<br> simplify:<br> (3x^4y^4)(5x^4) / 20xy^2
    7·1 answer
  • 0.067 as a fraction
    5·2 answers
  • What is the solution of the system?<br> 10x – 2y = 24<br> 6x+2y = 8
    15·1 answer
  • Can someone help me in geometry
    10·2 answers
  • Solve for x in the equation? <br><br> a/(2x-c) = -1
    11·2 answers
  • Please help me idk this
    6·2 answers
  • Help Please I will Give Brainliest if Correct!!
    5·2 answers
  • The cost of 7 apples is $2.10. What is the constant of proportionality that relates to the number of apples ,x, to the cost in d
    8·1 answer
  • Write and solve an equation to answer question 28 is 35% of what number
    15·1 answer
  • PLZ HELP ill give brainliest​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!