What's the numerator for the following rational expression? 8/y+3/y=?/y
2 answers:
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Answer:
- Part A: $12,220
- Part B: $12,134.08
- Part C: First option
- Parte C: Second option.
Explanation:
Part A: 7.4% simple interest
- r = 7.4% = 0.074
- P = $10,000
- t = 3 years
Formula:
Calculations:
<u>Part B: 6.5% compounded quaterly</u>
- r = 6.5% = 0.065
- n = 4
- P = $10,000
- t = 3 years
Formula:
Substitute and compute:
<u>Part C: Which investement is better</u>
Over the first three years the first option, 7.4% per year simple interest, is a better investment, because the value of its value is $12,220 - $12,134.0 = $85.94 greater than the second option.
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<u>Part D: Recomendation</u>
If George is unsure how long he will keep the money in the account, I would recommend to use the second option, because the compounded interest will overcome the simple interest, since the year 5. You can show that with a table:
Value of A in $:
Year Simplet intertest Compound interest
1 10,000 + 10,000(0.074)(1) 10,000(1 + 0.0650/4)¹
10,740 10,666
2 10,000 + 10,000(0.074)(2) 10,000(1 + 0.065/4)²
11,480 11,376
3 10,000 + 10,000(0.074)(3) 10,000(1 + 0.0650/4)³
12,220 12,314
4 10,000 + 10,000(0.074)(4) 10,000(1 + 0.065/4)⁴
12,960 12,942
5 10,000 + 10,000(0.074)(5) 10,000(1 + 0.065/4)⁵
13,700 13,804
<h3>Answer: (x,y) = (-2, 5)</h3>
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Explanation:
4x-3y = -23 is the same as 12x-9y = -69 when we multiply both sides by 3
-3x-2y = -4 is the same as -12x-8y = -16 when we multiply both sides by 4
Our updated system looks like this
Notice how we have 12x and -12x. They combine to 0x allowing the x terms to go away.
The y terms combine to -9y+(-8y) = -17y and the right hand sides combine to -69+(-16) = -85
After doing those three sets of additions, we get the new equation -17y = -101 which solves to y = -85/(-17) = 5
The last step is to use this y value to find x
4x-3y = -23
4x-3(5) = -23
4x-15 = -23
4x = -23+15
4x = -8
x = -8/4
x = -2
So the solution is (x,y) = (-2, 5)
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Check:
Let's plug the solution into the first equation
4x-3y = -23
4(-2)-3(5) = -23
-8-15 = -23
-23 = -23
We get a true result. Let's do the same for the second equation
-3x-2y = -4
-3(-2) - 2(5) = -4
6 - 10 = -4
-4 = -4
This result is true as well. So we've confirmed both equations to fully confirm the solution of this system.