I think there are two solutions, 63 or 147:
63 = 3² x 7, factors 1 | 3 | 7 | 9 | 21 | 63<span>
147 = 3 x 7</span>², factors 1 | 3 | 7 | 21 | 49 | 147
Answer:
Step-by-step explanation:
The exponential model for the population in t years after 2013 is given by:
In which P(0) is the population in 2013 and r is the growth rate.
In 2013, the moose population in a park was measured to be 5,100
This means that 
So
By 2018, the population was measured again to be 5,200.
2018 is 2018-2013 = 5 years after 2013.
So this means that 
.
We use this to find r.
So the equation for the moose population is:
Answer:
I'm guessing it's C because it's the only one that looks right
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:
Katie is 6 years old and Thomas is 3 years old
Step-by-step explanation:
Given that we should let K and T be the current ages of two siblings, Katie and Thomas.
If Katie is currently twice the age of Thomas then,
K = 2T
and in 6 years, Katie will be 4 times Thomas's current age then
K + 6 = 4T
Solving both equations simultaneously by substituting the value of K given in the first equation into the second
2T + 6 = 4T
Collect like terms
6 = 4T - 2T
6 = 2T
Divide both sides by 2
T = 3
Recall that K = 2T
K = 2 * 3
= 6
Hence Katie is 6 years old while Thomas is 3 years old
