Answer:
12
Step-by-step explanation:
Answer:
What do you have to do with the numbers
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:
52 32- cent stamps and 26 13-cent stamps
Step-by-step explanation:
Let x be the 32-cent stamps and y be the 13-cent stamps then...
x=2y
32x+13y=2002 (note that $20.02 is 2002 cents)
We can solve using substitution (substitute 2y for x)
32(2y)+13y=2002
64y+13y=2002
77y=2002
y=26
x=2(26)
x=52
She bought 52 32-cent stamps and 26 13-cent stamps.
