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
qwelly [4]
3 years ago
5

The sides of a triangle are 1, x, and x2. what are possible values of x?

Mathematics
1 answer:
Whitepunk [10]3 years ago
7 0
The sides of the triangle are given as 1, x, and x².

The principle of triangle inequality requires that the sum of the lengths of any two sides should be equal to, or greater than the third side.

Consider 3 cases
Case (a):  x < 1,
      Then in decreasing size, the lengths are 1, x, and x².
      We require that x² + x ≥ 1
      Solve x² + x - 1 = 
      x = 0.5[-1 +/- √(1+4)] = 0.618 or -1.618.
      Reject the negative length.
     Therefore, the lengths are 0.382, 0.618 and 1.

Case (b): x = 1
   This creates an equilateral triangle with equal sides
    The sides are 1, 1 and 1.

Case (c): x>1
  In increasing order, the lengths are 1, x, and x².
  We require that x + 1 ≥ x²
  Solve x² - x - 1 = 0
  x = 0.5[1 +/- √(1+4)] = 1.6118 or -0.618
  Reject the negative answr.
 The lengths are 1, 1.618 and 2.618.

Answer:
The possible lengths of the sides are
(a) 0.382, 0.618 and 1
(b) 1, 1 and 1.
(c) 2.618, 1.618 and 1.

You might be interested in
Use the distributive property to write an equivalent expression.<br> 9(8w + 4)
Harlamova29_29 [7]

Answer:

72w+36

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
What radius of a circle is required to inscribe a regular hexagon with an area of 210.44 cm2 and an apothem of 7.794 cm
alekssr [168]
We know that

[area of a regular hexagon]=6*[area of one <span>equilateral triangle]
</span>210.44=6*[area of one equilateral triangle]
[area of one equilateral triangle]=210.44/6-----> 35.07 cm²

[area of one equilateral triangle]=b*h/2
h=7.794 cm
b=2*area/h------> b=2*35.07/7.794------>b= 9 cm

the length side of a regular hexagon is 9 cm
<span>applying the Pythagorean theorem
</span>r²=h²+(b/2)²------>r²=7.794²+(4.5)²------> r²=81--------> r=9 cm

<span>this last step was not necessary because the radius is equal to the hexagon side------> (remember the equilateral triangles)
</span>
the answer is
the radius is 9 cm
8 0
3 years ago
a college student needs 11 classes that are worth a total of 40 credits in order to complete her degree. The college offers both
Rasek [7]
I’m not entirely sure but I think it’s D
8 0
3 years ago
Factorise<br><br> x^3 - 2x^2 -x+2
tankabanditka [31]

Answer:

Solution given:

x^3 - 2x^2 -x+2

take common from two each term

x²(x-2)-1(x-2)

take common again and keep left one on other bracket

<u>(x-2)(x²-1) or (x-1)(x+1)(x-2)</u> is a required answer.

note:using formula a²-b²=(a+b)(a-b) for x²-1.

5 0
3 years ago
Read 2 more answers
The sum of 3 consecutive even numbers is 42. The sum can be respresented by n+(n+2)+(n+4)=42. What does n represent?
Eva8 [605]

Answer:

13

Step-by-step explanation:

n+(n+2)+(n+4)=42

3n+6=42

3n=42-6=36

3n=36

n=13

13+14+15=42

6 0
3 years ago
Other questions:
  • Which of the following is an example of combination?
    11·1 answer
  • An object is dropped from a building and allowed to freefall to the ground. The height of the object over time is shown in the t
    12·1 answer
  • performance task applying probability concepts i need the work shown w answers any help is appreciated :)
    11·1 answer
  • If OB= 17 and AB = 30, then OR =
    8·2 answers
  • How many roots does y=x5−4x2+3x have?
    6·1 answer
  • What is a number greater than 25 that has more factors than the number 21
    9·1 answer
  • IF YOU GET IT RIGHT THeN YOULL GET BRAINLIEST
    10·2 answers
  • A circle is divided into 18 equal parts. How many degrees is the angle for each part? How many degrees is the angle for 5parts?
    6·1 answer
  • Write an argumentative essay for or against using public money to maintain national landmarks, such as the Gateway Arch in St. L
    9·2 answers
  • What is the correlation coefficient for the data shown in the table?
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!