Simplifying
(2a + 5)(3a + -4) = 0
Reorder the terms:
(5 + 2a)(3a + -4) = 0
Reorder the terms:
(5 + 2a)(-4 + 3a) = 0
Multiply (5 + 2a) * (-4 + 3a)
(5(-4 + 3a) + 2a * (-4 + 3a)) = 0
((-4 * 5 + 3a * 5) + 2a * (-4 + 3a)) = 0
((-20 + 15a) + 2a * (-4 + 3a)) = 0
(-20 + 15a + (-4 * 2a + 3a * 2a)) = 0
(-20 + 15a + (-8a + 6a2)) = 0
Combine like terms: 15a + -8a = 7a
(-20 + 7a + 6a2) = 0
Solving
-20 + 7a + 6a2 = 0
Solving for variable 'a'.
Factor a trinomial.
(-5 + -2a)(4 + -3a) = 0
Subproblem 1
Set the factor '(-5 + -2a)' equal to zero and attempt to solve:
Simplifying
-5 + -2a = 0
Solving
-5 + -2a = 0
Move all terms containing a to the left, all other terms to the right.
Add '5' to each side of the equation.
-5 + 5 + -2a = 0 + 5
Combine like terms: -5 + 5 = 0
0 + -2a = 0 + 5
-2a = 0 + 5
Combine like terms: 0 + 5 = 5
-2a = 5
Divide each side by '-2'.
a = -2.5
Simplifying
a = -2.5
Subproblem 2
Set the factor '(4 + -3a)' equal to zero and attempt to solve:
Simplifying
4 + -3a = 0
Solving
4 + -3a = 0
Move all terms containing a to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + -3a = 0 + -4
Combine like terms: 4 + -4 = 0
0 + -3a = 0 + -4
-3a = 0 + -4
Combine like terms: 0 + -4 = -4
-3a = -4
Divide each side by '-3'.
a = 1.333333333
Simplifying
a = 1.333333333
Solution
a = {-2.5, 1.333333333}
Answer:
The total cost of operating a truck would be $18000 as calculated below.
Explanation:
The total costs of operating the truck is a combination of fixed costs of $5500 per year and variable of $0.50 per mile ,hence the total cost function is given as:
TC=5500+0.50X
Where represents the number of miles driven per year.
Since X=25000 miles
TC=$5500+($0.50*25000)
TC=$5500+$12500
TC=$18000
The understanding here is that wages paid to the two employees working with the truck is already embedded in the fixed costs of $5500 per year, otherwise that would been given as a distinct cost entirely.
Answer: $403.20
Explanation:We use a mortgage calculator to calculate the interest paid in the final payment. Since each repayment is made at the end of year, the repayments are annual payments. So, the calculator should have an annual amortization schedule to solve the problem.
I used
http://www.calculator.net/loan-calculator for the calculation because it has an annual payment schedule. Then, I went under the subtitle
Paying Back a Fixed Amount Periodically because the payments are equal. In that online calculator, I just input these data:
- Loan Amount: $12,000
- Loan Term: 4 (Loan term is number of years to pay the loan)
- Interest Rate: 11.5%
- Compound: Annually (APY)
- Pay Back: Every year
Then, I clicked the
calculate button and view amortization table. The annual amortization schedule is attached in this answer.
To determine the interest paid at the final payment, I looked at payment #4 because the final payment is at the 4th year. (The loan is paid in 4 annual payments).
As seen in the attached image, the interest paid in payment #4 is $403.20. Hence, the interest paid in the final payment is
$403.20.