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.
Answer:
hypotenuse is 34
Step-by-step explanation:
a²+b²=c²
16²+30²=c²
256+900=1156
√1156 =34
hypotenuse =34
Well for 1.4 will be 1, 2.2 will be 2, 0.7 will be 1, 3.9 will be 4, and 1.8 is 2
Answer: Option D.
Step-by-step explanation:
this is a quadratic equation of the form:
y = ax^2 + bx + c
First, things you must see.
The graph opens up, so we must have thata a is greater than zero, so we can discard the first option.
Second, we can see that the vertex is located in x ≈ 70
The vertex of a quadratic equation is: x = -b/2a
so we have:
70 = -b/2a
let's try our options and see if we can discard other:
B:
-b/2a = 69.9/2 = 34.95
we can discard this option.
C:
-b/2a = 78/2 = 39 we can discard this option.
D:
-b/2a = 69.9/2*0.5 = 69.9
This is the only one that fits, so this is the correct option.
