All categories

3 years ago

What is the solution set of the quadratic inequality x^2+x-2>0?

Mathematics

2 answers:

vekshin13 years ago

8 0

Answer is A.

The values of x must be greater than or equal to 1 and the value of x must be less than or equal to -2.

x >= 1.....x <= -2

Please see attachment!

Svetradugi [14.3K]3 years ago

8 0

Answer: The solution set is $(-\infty, -2)\cup (1, \infty).$

Step-by-step explanation: We are given to find the solution set of the following quadratic inequality:

$x^2+x-2>0.$

The solution is as follows:

$x^2+x-2>0\\\\\Rightarrow x^2+2x-x-2>0\\\\\Rightarrow x(x+2)-1(x+2)>0\\\\\Rightarrow (x+2)(x-1)>0.$

We know that if 'a' and 'b' are two numbers such that a × b > 0, then either both 'a' and 'b' are greater than 0 or both of them are less than 0.

Therefore, we have

either

$x+2>0,~~~x-1>0\\\\\Rightarrow x>-2,~~~~x>1\\\\\Rightarrow x>1,$

$x+2$

Thus, the required solution set is x < -2 and x > 1. We can also write the solution set in terms of intervals as $(-\infty, -2)\cup (1, \infty).$

You might be interested in

A rectangle has perimeter 28cm. Its area is 42sq.cm. Determine the dimensions of the rectangle. Include a diagram in your soluti

yawa3891 [41]

The dimensions of the rectangle are: b=9.65 cm and h=4.35 cm or b=4.35 cm and h= 9.65 cm.

<h3>Quadrilaterals</h3>

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.

The area of a rectangle is equal to base x height (A=bh). The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2b+2h.

<h3>System of Linear Equations</h3>

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

The question gives:

Perimeter=28cm

Area= 42 cm²

If the perimeter is the sum of all sides of the rectangle, you have:

Perimeter= 2b+2h=28

If the area of the rectangle is 42cm², you have:

Area=bh=42 cm²

You can write a system of linear equations.

2b+2h=28 (1)

bh=42 (2)

From equation 2, you have $b=\frac{42}{h}$ . Then, you can replace it in equation 1.

$2*\frac{42}{h}+2h=28 \\ \\ 84+2h^2=28h\\ \\ 2h^2-28h+84=0 \; dividing\; by\; 2\\ \\ h^2-14h+42=0$

Now, you should solve the quadratic equation.

$h_{1,\:2}=\frac{-\left(-14\right)\pm \sqrt{\left(-14\right)^2-4\cdot \:1\cdot \:42}}{2\cdot \:1}$

$h_{1,\:2}=\frac{-\left(-14\right)\pm \:2\sqrt{7}}{2\cdot \:1}$

$h_1=\frac{-\left(-14\right)+2\sqrt{7}}{2\cdot \:1}=7+\sqrt{7}=9.65 cm$

$h_2=\frac{-\left(-14\right)-2\sqrt{7}}{2\cdot \:1}=7-\sqrt{7}=4.35cm$

If h1=9.65 cm, then $b_1=\frac{42}{9.65} =4.35 cm$ , and if h2=4.35 cm, then $b_1=\frac{42}{4.35} =9.65 cm$ .

Read more about the quadratic function here:

brainly.com/question/1497716

#SPJ1

8 0

2 years ago

these are the means and standard deviations for samples of building heights in two different cities. city a city b mean: 120 ft

Kazeer [188]

The average building height and the standard deviation for two separate cities' samples are shown. The true statements are:

City A’s heights are more spread out than city B’s heights.

City A has a lower average height than city B.

<h3>What is average?</h3>

In daily life, an average is a number chosen to represent a group of numbers; it is often the sum of the numbers divided by the total number of numbers in the group (the arithmetic mean). The average of the integers 2, 3, 4, 7, and 9, for instance, is 5, which equals 25. An average could alternatively be another statistic like the median or mode, depending on the situation. The median is sometimes used in place of the mean since the mean would be unnaturally high if it included the personal incomes of a few billionaires. The median is the amount below which 50% of personal incomes fall and above which 50% of personal incomes rise.

To learn more about average ,visit:

brainly.com/question/15570401

#SPJ4

4 0

1 year ago

The table below represents the function F

nikklg [1K]

Answer:

C. 2^x+1

Step-by-step explanation:

Graph

6 0