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

Answers

Answer 1

Answer:

Applying division signal rules, from the graphs of both functions, it is found that the solution of the inequality is:

$x \in [-3,-1) \cup [2,4)$

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A fraction, which represents a division, is negative if the numerator and the denominator have different signals. Thus, to solve this inequality, we have to study the signals of the numerator and the denominator.

The numerator is: $f(x) = x^2 + x - 6$

It is the first graph appended at the end of this answer.
From the graph, we have that it is negative or zero on [-3,2], and positive on the rest of the interval.

The denominator is: $g(x) = x^2 - 3x - 4$

It is the second graph appended at the end of this answer.
The denominator cannot be zero, so we consider only the interval (-1,4), in which it is negative.

Numerator positive, denominator negative: On interval [2,4).
Denominator positive, numerator negative. On interval [-3,-1).

Thus, the solution is:

$x \in [-3,-1) \cup [2,4)$

A similar problem is given at brainly.com/question/14361489

Answer 2

Answer:

Answer:

x ∈ [-3;-1) ∪ [2;4)

Step-by-step explanation:

$(x^(2)+x-6 )/(x^(2)-3x-4 )\leq 0\n=> ((x-2)(x+3))/((x+1)(x-4)) \leq 0\n$

we have this board:

x -3 -1 2 4

x - 2 - - - 0 + +

x+3 - 0 + + + +

x+1 - - 0 + + +

x-4 - - - - 0 +

$((x-2)(x+3))/((x+1)(x-4))$ + 0 - || + 0 - || +

from the board

=> x ∈ [-3;-1) ∪ [2;4)

Related Questions

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It takes 12 hours to clean the windows of a certain office building. During the first day of cleaning, the workers were able to clean for 9 hours. If the variable t stands for the amount of time the workers have left to clean the windows, which of the following choices is the most reasonable value for t?A. 3 hours B. 1 hour C. 30 hours D. 20 hours
Which is the correct input-output table for the function ?f(x)=3/x+4

={125},={#125}andQ={#125},
finda. ∪ b. ∩ c. d.

Answers

Answer:

h3llo

Step-by-step explanation:

hey the answer is in your heart

One of the factors of the polynomial x3 − 5x2 is x + 3. What is the other factor?a. x2-8x+24+(72/x+3)
b. x2-8x+24
c. x2-8x+24-(72/x+3)
d. x3-8x2+24x-72

Answers

The answer is letter c. x2-8x+24-[72/(x+3)]. If you do not know how to solve this using the long division method, you can always evaluate the options through the process of elimination first. Since the degree of the other factor is already 1 (x to the power of 1), you know that option d. is not the correct answer because you know that the other factor must be raised to the power of 2. That leaves us with a, b and c. Working backwards and multiplying the given factor (x+3) with the factor in b, gives us x3-5x2+72. So from there, you know that you have to eliminate 72, which can be removed when it is subtracted by itself. Letter c does just that. Try multiplying (x+3) and option c for yourself :).

Answer:

Option C is correct.

Step-by-step explanation:

Given polynomial : x³ - 5x²

Factors of given polynomial = x + 3

Let, p(x) = x³ - 5x²

To get other factor of p(x), we divide p(x) by given factor.

On division we get,

Quotient = x² - 8x + 24

Remainder = -72

So another factor is $x^2-8x+24-(72)/(x+3)$

Therefore, Option C is correct.

Rachel's cell phone company charges $0.10 per minute . She used 350 minutes last month and paid $84. Write and solve a linear equation to fins what her bill will be if she uses 300 minutes next month .

Answers

300 min = $X
350 min = $84
now cross multiply
350 * x = 300*84
x = 25200/350
x = $72 Answer

Question: Michelle is making goodie bags for Christmas filled with chocolate and candy. Chocolates cost $2.50 per lb and candy cost $3.00 per lb. Michelle spent a total of $40 on 20 lbs of candy. How much of each kind of candy did she purchase ?

Answers

Michelle purchased 5 lbs of chocolates and 5 lbs of candy.

Let assume Michelle purchased x lbs of chocolates and y lbs of candy.

According to the given information,

Michelle spent a total of $40 on 20 lbs of candy.

So, the equation can be set up as:

Equation 1: 2.50x + 3.00y = 40

As, the totalweight of candy is 20 lbs, so we have:

Equation 2: x + y = 15

From equation 2: x = 15 - y

Substitute the value of x= 15 - y into Equation 2 as

2.5(15-y) + 3y = 40

37.5 - 2.5y + 3y= 40

0.5y = 2.5

y= 5

Substituting y= 5 into the second equation

x + 5 = 10

x = 10 -5

x = 5

Thus, 5 lbs of chocolates and 5 lbs of candy were bought.

Learn more about Equation here:

brainly.com/question/29657983

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The question attached have incorrect values, the correct question is

Michelle is making goodie bags for Christmas filled with chocolate and candy. Chocolates cost $2.50 per lb and candy cost $3.00 per lb. Michelle spent a total of $40 on 15 lbs of candy. How much of each kind of candy did she purchase ?

the answer will be 80

How would the domain and range of the function
1
y = -x-6 be determined? Explain.