Let's say:
lengh=x
width=y
"The length of a rectangle is 4 inches greater than the width."
That means: x=y+4 (in inches).
the parameter is (by definition) 2*lenght+2*width.
so we have 2*x+2y=24.
we also know that x=y+4
Substituting:
2*(y+4)+2y=24.
2*y+8+2y=24
4*y+8=24//substitute 8 from both sides
4*y=16//dividing both sides by 4.
y=4
So the width is 4!
The lenght is y+4=8!
the dimensions are 4 by 8.
(check: 2*4+2*8=24, correct!)
Using an exponential function, it is found that it's annual growth rate is of 4%.
<h3>What is an exponential function?</h3>
An increasing exponential function is modeled by:
In which:
- A(0) is the initial value.
- r is the growth rate, as a decimal.
In this problem, the card appreciates exponentially in value by 50% over 10 years, hence:
A(10) = 1.5A(0).
Thus:
![\sqrt[10]{(1 + r)^{10}} = \sqrt[10]{1.5}](https://tex.z-dn.net/?f=%5Csqrt%5B10%5D%7B%281%20%2B%20r%29%5E%7B10%7D%7D%20%3D%20%5Csqrt%5B10%5D%7B1.5%7D)
1 + r = 1.04.
r = 0.04.
0.04 x 100% = 4%.
It's annual growth rate is of 4%.
More can be learned about exponential functions at brainly.com/question/25537936
The method that results in more money after 2 years is Peggy's investment.
<h3>Which method results in more money in 2 years?</h3>
The formula for calculating the future value of an investment:
FV = P (1 + r)^nm
- FV = Future value
- P = Present value
- R = interest rate
- m = number of compounding
- N = number of years
Future value of Larry's investment: $350 x [1 + (0.04/4)]^(4 x 2) = $379
Future value of Peggy's investment: $350 x [1 + (0.06/12)]^(12 x 2) = $394.51
To learn more about future value, please check: brainly.com/question/18760477
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Answer: (C) 4
<u>Step-by-step explanation:</u>
The corresponding sides of a 30°-60°-90° triangle are: b - b√3 - 2b
The side corresponding to 90° is 8 = 2b --> b = 4
The side corresponding to 30° is y = b <em>as stated above, b = 4</em>, so y = 4
1. 4.47 x 10^3
2. 4.8 x 10^8
