First, incorporate the 5 into the 2/3 fraction by multiplying the 5 by the 3 and then adding that quantity by the 2, which now makes the fraction:
17/3
Now set it up with the equation:
r/6 = 17/3
r/6×3 = 17/3×3
r/3 = 17
r/3×3 = 17×3
r = 51
Answer:
4.5 gallons.
Step-by-step explanation:
Multiply the volume value by 4.
In this case, you multiple 4.5 by 4 which equals 18.
4.5 gallons = 18 quarts
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.
The work has one step: divide the expression by 3.
.. -4 > x
Because the symbol is "greater than", the circle at x=-4 is an open circle.
