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
Damm [24]
3 years ago
15

Solve rational inequality x²+x-6/x²-3x-4≤0?​

Mathematics
2 answers:
Fittoniya [83]3 years ago
8 0

Answer:

Step-by-step explanation:

x

2

+

x

−

6

=

(

x

+

3

)

(

x

−

2

)

x

2

−

3

x

−

4

=

(

x

−

4

)

(

x

+

1

)

Each of the linear factors occurs precisely once, so the sign of the given rational expression will change at each of the points where one of the linear factors is zero. That is at:

x

=

−

3

,

−

1

,

2

,

4

Note that when

x

is large, the

x

2

terms will dominate the values of the numerator and denominator, making both positive.

Hence the sign of the value of the rational expression in each of the intervals

(

−

∞

,

−

3

)

,

(

−

3

,

−

1

)

,

(

−

1

,

2

)

,

(

2

,

4

)

and

(

4

,

∞

)

follows the pattern

+

−

+

−

+

. Hence the intervals

(

−

3

,

−

1

)

and

(

2

,

4

)

are both part of the solution set.

When

x

=

−

1

or

x

=

4

, the denominator is zero so the rational expression is undefined. Since the numerator is non-zero at those values, the function will have vertical asymptotes at those points (and not satisfy the inequality).

When

x

=

−

3

or

x

=

2

, the numerator is zero and the denominator is non-zero. So the function will be zero and satisfy the inequality at those points.

Hence the solution is:

x

∈

[

−

3

,

−

1

)

∪

[

2

,

4

)

graph{(x^2+x-6)/(x^2-3x-4) [-10, 10, -5, 5]}

Aleonysh [2.5K]3 years ago
7 0

Answer:

x ∈ [-3;-1) ∪ [2;4)

Step-by-step explanation:

\frac{x^{2}+x-6 }{x^{2}-3x-4 }\leq 0\\=> \frac{(x-2)(x+3)}{(x+1)(x-4)} \leq 0\\

we have this board:

x                          -3                    -1                      2                     4          

x - 2          -                        -                    -           0        +                     +

x+3            -         0           +                   +                      +                     +

x+1             -                      -            0      +                      +                     +

x-4            -                        -                     -                     -            0      +

\frac{(x-2)(x+3)}{(x+1)(x-4)}   +          0          -             ||        +         0        -            ||        +

from the board

=>    x ∈ [-3;-1) ∪ [2;4)

You might be interested in
Can someone help me with this?
baherus [9]

Answer:

18

Step-by-step explanation:

AB = AW + WB

But AW also equals WB because of the bisecting point

x + 6 = 3x

6 = 2x

x = 3

AW = 3 + 6 = 9

WB = 3(3) = 9

9 + 9 = 18°

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

8 0
2 years ago
Find the domain, range and if it’s a function.
Marta_Voda [28]
Domain: {-1}
Range: {0, 4, 9, 15}
Function? No

Explanation:
The domain is the x value in the given points. The only x value is -1.
The range is the y value in the given points.
You can tell if this is a function if it has repeating x values or not. Since the x value of -1 repeats, it is not a function.

Hope this helps, and please mark brainliest :)
6 0
2 years ago
How many ounces of a 15​% alcohol solution must be mixed with 4 ounces of a 20​% alcohol solution to make a 17​% alcohol​ soluti
sukhopar [10]

Answer:

6 ounces

Step-by-step explanation:

Let x = the number of ounces of the 15% alcohol solution needed to be mixed with the 4 ounces of 20% alcohol solution to obtain the 17% alcohol solution.

After converting the percentages to their decimal equivalents, set up the necessary equation as follows:

0.15x+0.20(4) = (x+4)(0.17) Simplify and solve for x.

0.15x+0.8 = 0.17x+0.68 Subtract 0.15x from both sides.

0.8 = 0.02x+0.68 Now subtract 0.68 from both sides.

0.12 = 0.02x Finally, divide both sides by 0.02

x = 6

You need to mix 6 ounces of 15% alcohol solution with 4 ounces of 20% alcohol solution to obtain 10 (x+4)ounces of 17% alcohol solution.

7 0
2 years ago
Read 2 more answers
HELP ASAP IM GIVING 40 POINTS I NEED THE AREA FROM THIS TRAPEZOID MODEL IN PICTURE
Nitella [24]

Answer:

51/2

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Ming is painting a picture. He has 2/3 pint of red paint, 2/8 pint of yellow paint and 2/6 pint of green paint. Which list order
vichka [17]

Answer:

2/3,2/6,2/8

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • What is .52,57% and 2/5 from least to greatest
    14·1 answer
  • An entrepreneur estimates his total profit (total revenue minus total cost) for his proposed company as p(x) = x3 − 4x2 + 5x − 2
    7·2 answers
  • Can u prove 1=2????????
    6·1 answer
  • (0,1)<br> (1,0.5)<br> (2,0.25)<br> (3,0.125)<br> (4,0.0625)<br> What does Y equal in this function)
    10·1 answer
  • Most analysts focus on the cost of tuition as the way to measure the cost of a college education. But incidentals, such as textb
    11·1 answer
  • A simple random sample of 72 face-to-face meetings held in March 2020 was selected, and the mean length of this sample of 72 mee
    10·1 answer
  • Given f(x) = -3x + 5, solve for x when f(x) = -4​
    9·2 answers
  • How do your write a feaction with a denominator of 20 as a decimal?​
    12·1 answer
  • I need help I don't know what to do ​
    12·1 answer
  • Complete the factoring.<br> 14x^5 = 2x^3•( ? )
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!