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.

7 0

2 years ago

Drag each tile to the correct box. Not all tiles will be used.

katrin [286]

Answer+Step-by-step explanation:

$f^{-1}\left( x\right) =\frac{1}{7} x^{2}+3 \ ,\text{where}\ x\geq 0$

7 0

1 year ago

In 1995, Orlando, Florida, was about 175,000. At the time, the population was growing at a rate of about 2000 per year. Write an

gladu [14]

Answer:

y= 2000 * x + 175000

Step-by-step explanation:

Given is Population is 175,000

Increase in rate = 2000/year

Let x be the population in 1995 which is C= 175,000

y= Population after per year

We know the formula for slope intercept form is

y= mx + C ............... (i)

Now from the suppose values and given

m= 2000

Now putting values in equation (i) gives

y= 2000 * x + 175000

Here x is the No of years

6 0

2 years ago