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
Find four consecutive natural numbers if you know that the product of the first two is 38 less than the product of the following
Fynjy0 [20]
<span>Because the four numbers are consecutive, we can call the first one x, and the other three are x+1, x+2, and x+3, respectively. x * (x+1) = (x+2) * (x+3) - 38 x^2 + x = x^2 + 5x +6-38 x^2 + x = x^2 + 5x - 32 -4x = -32 x=8 The four numbers are 8, 9, 10, and 11 check solution: 8*9=10*11-38 72=110-38 72=72</span>
8 0
2 years ago
Read 2 more answers
A right triangle has a right exterior angle? <br> True or False?
adelina 88 [10]
False because 360-90 is 270
4 0
3 years ago
Read 2 more answers
Lisa used 1/4 cups of milk per batch using her muffin recipes. How many cups of Milan will she use when she made 6 batches of mu
marin [14]

Answer:

1 1/2

Step-by-step explanation:

1/4 cups * 6 batches = 1/4 * 6 = 6/4 = 1 2/4 = 1 1/2

7 0
3 years ago
A CD usually sells for $13.00. If the CD is 30% off, and sales tax is 8%, what is the total price of the CD, including tax?
slamgirl [31]

I think it's $10.14.

8 0
2 years ago
What do you have to do to each side to solve x – 4 ≤ 3?
VashaNatasha [74]

Answer:

x - 4 means that the answer will be greater than 3 so the answer could probably, don't take me up on it but it, should be 4 but that is just what my questions answer was. Hope it helps!!!

3 0
2 years ago
Other questions:
  • Solve the inequlity 2s+5s+12=132<br> A. s=-30<br> B. s=40<br> C. s=120<br> D. s=9
    5·1 answer
  • BRAINLIEST!!!!!!!
    12·1 answer
  • Which side is rotated around the vertex
    12·2 answers
  • What is the greatest common factor of the terms 14c to the second power D and 42 C to the third power d
    9·1 answer
  • How much bigger is 1 1/4 inch than 5/8 inch
    11·1 answer
  • Which statement describes how to solve √(3x+4)=√3x+4?
    14·2 answers
  • Round each decimal to the nearest tenth<br> 4. 13.392<br> 5. 27.149<br> 6.8.84858<br> Help!!
    14·1 answer
  • Which coordinate point represents the y -intercept of the equation 3x + 2y = 18
    11·1 answer
  • Match equivalent expressions. Numbers and letters go together
    15·1 answer
  • Luca baked 18 dozen chocolate chip cookie dozen peanut butter cookie how many cookie did Luca bake
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!