All categories

3 years ago

Write a rational inequality with the solution: (-2,-1)U(1, oo)

Mathematics

1 answer:

serg [7]3 years ago

4 0

Answer:

$\displaystyle \frac{x^2+3x+2}{1-x}$

Step-by-step explanation:

Rational Inequality

We are given the solution of rational inequality:

(-2,-1) U (1,∞)

The first set suggests a limited zone than can be obtained by a quadratic equation of the form:

$(x-a)(x-b)$

Where a and b are the roots of the equation, which coincide with the endpoints of the interval. Thus, to get the interval, we can use:

$(x+2)(x+1)$

Operating:

$x^2+3x+2$

The second set is an open infinite interval, that can be modeled as a third binomial that changes signs in x=1 and is in the denominator, so x=1 is not included.

Thus, one possible inequality is:

$\mathbf{\displaystyle \frac{x^2+3x+2}{1-x}$

You might be interested in

How do I solve The sum of a number and 3 is subtracted from 10 the result is 5

meriva

State the given in the question

Given that the sum of a number and 3 is subtracted from, the result is 5

State what is to be found in the question

We are to find the number. In other to achieve this, we would follow the steps below:

Step 1: Represent the number with an unknown

Let x represent the number

Step 2: Interpret the given statement mathematically

If x is the number, then the sum of the number and 3 would be

$x+3$

Then the sum of a number and 3 subtracted from 10 would be

$10-(x+3)$

Finally, when the sum of a number and 3 subtracted from 10, the result is 5, would be

$10-(x+3)=5$

Step 3: Solve for x in the mathematical interpretation of the given statement

The value of x is as calculated as shown below:

$\begin{gathered} 10-(x+3)=5 \\ \text{Open the bracket or the parenthesis} \\ 10-x-3=5 \\ \text{collect like terms} \\ 10-3-5=x \\ 7-5=x \\ 2=x \\ \text{Therefore:} \\ x=2 \end{gathered}$

Hence, the number is 5

4 0

1 year ago

I’m confused on this one

dedylja [7]

It's a parallelogram so if one angle is 90 degrees they all will be because of transverse angles and all that good stuff.

So we're given the diagonal of a rectangle and one side and we're asked to find the other. The diagonal of a rectangle is the hypotenuse of the right triangle whose legs are the sides of the rectangle. So this is a Pythagorean Theorem question in disguise:

$AB^2 + AD^2 = BD^2$