Use the factor theorem to determine whether the first polynomial is a factor of the second polynomial x-3;2x^2-4x+30
x−3,2x^2−4x+30
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:
A
Step-by-step explanation:
Sales tax is a certain percent of a bill that is taken and sent to the state. Example: Florida sales tax is 7% of the total.
Simple problem:
When simplifying 3(x-6) they subtracted 3 instead of multiplied by 3.
3(x-6) should be 3x-18.
Now when you simplify:
3x-18+4x+12-6x
Which is x -6 =0
Or x =6
