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Snezhnost [94]
3 years ago
8

Solving Rational Inequalities and use sign diagram to sketch the graph. Image attached for better understanding.

Mathematics
1 answer:
Digiron [165]3 years ago
6 0

Answer:

x ∈ (-∞, -1) ∪ (1, ∞)

Step-by-step explanation:

To solve this problem we must factor the expression that is shown in the denominator of the inequality.

So, we have:

x ^ 2-1 = 0\\x ^ 2 = 1

So the roots are:

x = 1\\x = -1

Therefore we can write the expression in the following way:

x ^ 2-1 = (x-1)(x + 1)

Now the expression is as follows:

\frac{(x-2) ^ 2}{(x-1) (x + 1)}\geq0

Now we use the study of signs to solve this inequality.

We have 3 roots for the polynomials that make up the expression:

x = 1\\x = -1\\x = 2

We know that the first two are not allowed because they make the denominator zero.

Observe the attached image.

Note that:

(x-1)\geq0 when x\geq-1

(x + 1)\geq0 when x\geq1

and

(x-2) ^ 2 is always \geq0

Finally after the study of signs we can reach the conclusion that:

x ∈ (-∞, -1) ∪ (1, 2] ∪ [2, ∞)

This is the same as

x ∈ (-∞, -1) ∪ (1, ∞)

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If 12 children represents 12.5% of the people attending a concert, how many people are attending the concert
NeTakaya

96 people are attending the concert.

Step-by-step explanation:

Given,

Number of children at concert = 12

This represents 12.5% of the people attending concert.

Let,

p be the total people attending concert.

12.5% of p = 12

\frac{12.5}{100}*p=12\\0.125p=12

Dividing both sides by 0.125

\frac{0.125p}{0.125}=\frac{12}{0.125}\\p=96

96 people are attending the concert.

Keywords: percentage, division

Learn more about division at:

  • brainly.com/question/317601
  • brainly.com/question/306772

#LearnwithBrainly

7 0
3 years ago
What is the geometric mean of 4 and 10
GalinKa [24]

Answer: 6.3

Step-by-step explanation:

The formula for geometric mean is given as :

G.m = \sqrt{pq}

Therefore , the geometric mean between 4 and 10 will be :

G.m = \sqrt{4(10)}

      = \sqrt{40}

      = 2\sqrt{10}

     = 6.3

8 0
3 years ago
Y = -2x2 + 10 y = -2x – 2
34kurt

Answer:

x = 6

y = - 14

Step-by-step explanation:

\left \{y=-2x2 + 10y} \atop {y=-2x -2}} \right.

  1. -2x × 2 + 10 = - 2x - 2
  2. x = 6
  3. y = -2 × 6 - 2 = - 14
4 0
2 years ago
Read 2 more answers
Divide 4 1/4 by 2. ​
Aleonysh [2.5K]
I’m pretty sure it’s 2 1/8
5 0
2 years ago
The distance to the nearest exit doir is no more than 150 feet. Use d to represent the distance in feet to the nearest exit door
il63 [147K]

Answer: d\leq150

Step-by-step explanation:

1. You have the following information given in the problem:

- The distance to the nearest exit door is no more than 150 feet.

-  d represents the distance to the nearest exit door, in feet.

2. Therefore, keeping the information above on mind, you know that the  distance to the nearest exit door (d) must be less than or equal to 150 feet, then, you can express this as following:

d\leq150

5 0
3 years ago
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