A diameter is 20 feet. identify the length of the radius.
2 answers:
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Answer: For the system given, there is no solution.
The slopes are the same for both equations, so the lines are parallel. With no intersection, there is no solution.
It may be easier to graph the system if you change the equations to slope intercept form y = mx + b
That locates the y-intercept, <em><u>b</u></em> and you can use the slope, <em><u>m</u></em> to plot additional points to draw the lines.
The attachment shows the graph of this system of equations.
Step-by-step explanation: Isolate y on the left
<u>First equation:</u>
4x + 6y = -12 Subtract 4x from both sides
6y = -4x -12 Divide both sides by 6
y = -4x/6 -12/6 Simplify
y = -2x/3 - 2 The y-intercept is -2, <u>the slope is -2/3</u>
<u>Second equation:</u>
2x + 3y = 6 Subtract 2x from both sides
3y = –2x + 6 . Divide both sides by 3
y = –2x/3 + 6/3 Simplify
y = –2x/3 +2 The y-intercept is -2, <u>the slope is -2/3 </u>
At this point we see that the slopes are the same, so the lines are parallel.
Answer:
Account B earns more interest.
After 20 years, account B will have earned $171.89 more.
Step-by-step explanation:
Let's calculate the total for each account.
Account A:
Account A earns simple interest. We know that the principal value is $2000 and the interest rate is 2% or 0.02. We can use the simple interest formula:
Where A is the future value, P is the principal, r is the rate, and t is the time in years.
So, let's substitute 2000 for P, 0.02 for r, and 20 for t. This yields:
Multiply and add:
Multiply. So, the total amount of money in Account A after 20 years is:
Since we initially deposited $2000 and our total is now $2800, this means that we earned an interest of
Account B:
Account B earns compound interest. Like Account A, Account B has a principal value of $2000 and the interest rate is 2% or 0.02. We also know that it's compounded annually, so once per year. We can use the compound interest formula:
Where B is the future value, P is the principal, r is the rate, n is the times compounded per year, and t is the time in years.
So, let's substitute 2000 for P, 0.02 for r, n for 1 (since it's compounded annually), and t for 20. This yields:
Simplify this to acquire:
Evaluate. Use a calculator. So, after 20 years, the amount of money in Account B is:
Since our principal was $2000, this means that we earned an interest of approximately .
So, Account A earned an interest of $800 and Account B earned an approximate interest of $971.89.
So, Account B earned more interest.
And it earned more than Account A.
And we're done!