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3 years ago

For which values of k does have no solution "kx + y = 1" "x + ky = 1"

1 answer:

8 0

When they are paralell

hum

kx+y=1
x+ky=1

if k=0 then they intersect at (1,1)
if k=1, they are the same equation
they have to be paralell, so same slope

solve for y to get y=mx+b

y=-kx+1 and
y=-x/k+1/k

the slopes are -k and -1/k
slopes must be the same
-k=-1/k
times -1 both sides
k=1/k
times k both sides
k^2=1
k=1 or -1

1 doesn't work so k=-1

answer is k=-1

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Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate

sertanlavr [38]

The monthly payment for option 1 is $1755.144 and option 2 is $2088.97, total amount for option 1 is $631851.84 and option 2 is $376014.6, and on comparing option 2 will be better option.

Given that for $200,000 loan Option 1 is a 30-year loan at an APR of 10% Option 2 is a 15-year loan at an APR of 9.5%.

A concept that implies that the future value of money will be lower than its present value due to several factors such as inflation is known as TVM(time of value money).

Monthly Payments

Option 1

Loan Amount = $200,000

Number of payments = 30×12 = 360

Monthly interest rate = 10%/12 = 0.008333333

Monthly payment = Loan amount (1+ monthly interest rate)ⁿ×monthly interest rate/[(1+monthly interest rate)ⁿ- 1]

Monthly payment=200,000×(1+0.008333333)³⁶⁰×(0.008333333)/[(1+0.008333333)³⁶⁰-1]

Monthly payment=33062.328/18.83739

Monthly payment=$1755.144

Option 2

Loan Amount = $200,000

Number of payments = 15 x 12=180

Monthly interest rate = 9.5%/12=0.00792

Monthly payment = 200,000(1+0.00792)¹⁸⁰(0.00792)/[(1+0.00792)¹⁸⁰-1]

Monthly payment=6553.096/3.137

Monthly payment=$2088.97

Total Payments

Option 1

As we've found out the monthly payments, we now need to multiply it by the number of months.

$1755.144×360 = $631851.84

Option 2

$2088.97×180 = $376014.6

Conclusion

Option 2 will always be the better option economically as it saves $255837.24 ($631851.84 - $376014.6) in total payments.

Hence, For $200,000 loan Option 1 a 30-year loan at an APR of 10% Option 2 a 15-year loan at an APR of 9.5% is the monthly payment for option 1 is $1755.144 and option 2 is $2088.97, total amount for option 1 is $631851.84 and option 2 is $376014.6, and on comparing option 2 will be the better option.

Learn more about monthly cost from here brainly.com/question/1476828.

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5 0

2 years ago

If the discriminant of a quadratic equation is equal to -8, which statement describes the roots?

Dovator [93]

Keywords

quadratic equation, discriminant, complex roots, real roots

we know that

The formula to calculate the roots of the quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}}{2a}$

where

The discriminant of the quadratic equation is equal to

$b^{2}-4ac$

if $(b^{2}-4ac)> 0$ ----> the quadratic equation has two real roots

if $(b^{2}-4ac)=0$ ----> the quadratic equation has one real root

if $(b^{2}-4ac)< 0$ ----> the quadratic equation has two complex roots

in this problem we have that

the discriminant is equal to $-8$

the quadratic equation has two complex roots

therefore

the answer is the option A

There are two complex roots

5 0

3 years ago

Read 2 more answers

Which function is represented by the table?

choli [55]

Answer:

Choice A

Step-by-step explanation:

You take the x value and plug it into the formula to see if the answer lines up with the table

5 0

3 years ago

◕ A dealer sold a photocopy machine at Rs 4200 with 13% VAT to a retailer. The retailer added transportation cost of Rs 250 , pr

satela [25.4K]

Given :-

A dealer sold a photocopy machine at Rs 4200 with 13% VAT to a retailer.
The retailer added transportation cost of Rs 250 , profit Rs 300 and local tax Rs 150 and sold to consumer .
Customer has to pay 13% VAT .

To Find :-

Amount to be paid by the customer .

Solution :-

Here , according to the question ,

$\sf\dashrightarrow Cost\ of \ machine \ = \ Rs 4200$

$\sf\dashrightarrow VAT = 13\%$

Therefore cost after adding VAT ,

$\sf\dashrightarrow Cost = Cost_{initial}+13\% of Cost_{initial}\\$

$\sf\dashrightarrow Cost = Rs4200 + Rs 4200 \times \dfrac{13}{100}\\$

$\sf\dashrightarrow Cost = Rs4200 + Rs546\\$

$\sf\dashrightarrow \bf{ Cost = Rs 4746}$

Again the values added by the retailer before selling to customer ,

Transport = Rs 250
Profit = Rs 300
Tax = Rs 150

Therefore total cost after adding these ,

$\sf\dashrightarrow Cost = Rs( 4746+ 250+ 300 + 150 )\\$

$\sf\dashrightarrow\bf { Cost = Rs 5446}$

Again Selling price after addition of 13% VAT ,

$\sf\dashrightarrow SP = Rs 5446 + 13\% \ of \ Rs 5446\\$

$\sf\dashrightarrow SP = Rs 5446 + \dfrac{13}{100}\times 5446 \\$

$\sf\dashrightarrow SP = Rs (5446 + 707.98) = Rs ( 5446 + 708)\\$

$\sf\dashrightarrow \underline{\underline{\bf SP_{to\ the \ customer} = Rs 6154}}$

Hence the amount to be paid by the customer is Rs 6154 .

3 0

2 years ago

Read 2 more answers

2..52 X 10 to the fifth???? PLS HELPP!

love history [14]

Answer:

252000

Step-by-step explanation:

we take 2.52 and move the decimal back 5 places. when we run out of numbers we add zeros. so if we moved 3 places back it would be 2520 but since we move 5 it is 252000. 10 by any power you just move the decimal place if it is negtive move it forward if positive move backward.

7 0

2 years ago