Let b= length and a=width
Area= a*b and the problem said b=2a+3 (the length is 3ft more than double the width)
Replace b into Area formula:
Area= a*(2a+3) and we know that Area=77ft from the problem, so:
77=2a^2+3a now order and equal to zero:
2a^2+3a=77 now solve this with quadratic formula and you will get so values for a: -7ft and 5.5ft as you know the dimensions could not be negative so the correct answer for "a" side is 5.5ft, for getting the b side you haeve to replace a=5.5 into b=2a+3 and you will get b=2*5.5+3= 14ft.
Finished.
Answer: yes is it a function
Step-by-step explanation:
A graph is a function when there is only one y value for each x value. You can also use the vertical line test. This example is a “quadratic function”.
She should invest $30000 in the 9% fund and $10000 in the 13% fund.
<u><em>Explanation</em></u>
Suppose, the amount of investment at 9% rate is
dollar.
As the total amount of investment is $40000 , so the investment at 13% rate will be: ![(40000-x) dollar](https://tex.z-dn.net/?f=%2840000-x%29%20dollar)
So, the amount of earnings per year from 9% fund
dollar
and the amount of earnings per year from 13% fund
dollar.
Given that, the <u>total earnings per year is $4000</u>. So the equation will be......
![0.09x+0.13(40000-x)=4000\\ \\ 0.09x+5200-0.13x=4000\\ \\ -0.04x=4000-5200\\ \\ -0.04x= -1200\\ \\ x= \frac{-1200}{-0.04}=30000](https://tex.z-dn.net/?f=0.09x%2B0.13%2840000-x%29%3D4000%5C%5C%20%5C%5C%200.09x%2B5200-0.13x%3D4000%5C%5C%20%5C%5C%20-0.04x%3D4000-5200%5C%5C%20%5C%5C%20-0.04x%3D%20-1200%5C%5C%20%5C%5C%20x%3D%20%5Cfrac%7B-1200%7D%7B-0.04%7D%3D30000)
So, the amount of investment at 9% fund is $30000 and the amount of investment at 13% fund = ($40000- $30000)= $10000