Since the graph is a linear function, we're going to use the slope formula solve this:
Note I am replacing m with k
Inserting 2 points from the graph, let's use (1,8) and (2,16).
k=8
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:
2 dimes, 1 nickel and 3 quarters.
Step-by-step explanation:
The price of 2 postcards is $1. Any combination of coins that adds to $1 will work here. Remember, a penny is worth 0.01, a nickel is worth 0.05, a dime is worth 0.10, and a quarter is worth 0.25.
Adding 2 dimes, 1 nickel, and 3 quarters would be 2(0.10)+1(0.05)+3(0.25)=1.
