Express y in terms of x

Answer:

The mortgage chosen is option A;

15-year mortgage term with a 3% interest rate because it has the lowest total amount paid over the loan term of $270,470

Step-by-step explanation:

The details of the home purchase are;

The price of the home = $275,000

The mode of purchase of the home = Mortgage

The percentage of the loan amount payed as down payment = 20%

The amount used as down payment for the loan = $55,000

The principal of the mortgage borrowed, P = The price of the house - The down payment

∴ P = $275,000 - 20/100 × $275,000 = $275,000 - $55,000 = $220,000

The principal of the mortgage, P = $220,000

The formula for the total amount paid which is the cost of the loan is given as follows;

[tex]Outstanding \ Loan \ Balance = \dfrac{P \cdot \left[\left(1+\dfrac{r}{12} \right)^n - \left(1+\dfrac{r}{12} \right)^m \right] }{1 - \left(1+\dfrac{r}{12} \right)^n }[/tex]

The formula for monthly payment on a mortgage, 'M', is given as follows;

[tex]M = \dfrac{P \cdot \left(\dfrac{r}{12} \right) \cdot \left(1+\dfrac{r}{12} \right)^n }{\left(1+\dfrac{r}{12} \right)^n - 1}[/tex]

A. When the mortgage term, t = 15-years,

The interest rate, r = 3%

The number of months over which the loan is payed, n = 12·t

∴ n = 12 months/year × 15 years = 180 months

n = 180 months

The monthly payment, 'M', is given as follows;

M =

The total amount paid over the loan term = Cost of the mortgage

Therefore, we have;

220,000*0.05/12*((1 + 0.05/12)^360/( (1 + 0.05/12)^(360) - 1)

[tex]M = \dfrac{220,000 \cdot \left(\dfrac{0.03}{12} \right) \cdot \left(1+\dfrac{0.03}{12} \right)^{180} }{\left(1+\dfrac{0.03}{12} \right)^{180} - 1} \approx 1,519.28[/tex]

The minimum monthly payment for the loan, M ≈ $1,519.28

The total amount paid over loan term, A = n × M

∴ A ≈ 180 × $1,519.28 = $273,470

The total amount paid over loan term, A ≈ $270,470

B. When t = 20 year and r = 6%, we have;

n = 12 × 20 = 240

[tex]\therefore M = \dfrac{220,000 \cdot \left(\dfrac{0.06}{12} \right) \cdot \left(1+\dfrac{0.06}{12} \right)^{240} }{\left(1+\dfrac{0.06}{12} \right)^{240} - 1} \approx 1,576.15[/tex]

The total amount paid over loan term, A = 240 × $1,576.15 ≈ $378.276

The monthly payment, M = $1,576.15

C. When t = 30 year and r = 5%, we have;

n = 12 × 30 = 360

[tex]\therefore M = \dfrac{220,000 \cdot \left(\dfrac{0.05}{12} \right) \cdot \left(1+\dfrac{0.05}{12} \right)^{360} }{\left(1+\dfrac{0.05}{12} \right)^{360} - 1} \approx 1,181.01[/tex]

The total amount paid over loan term, A = 360 × $1,181.01 ≈ $425,163

The monthly payment, M ≈ $1,181.01

The mortgage to be chosen is the mortgage with the least total amount paid over the loan term so as to reduce the liability

Therefore;

The mortgage chosen is option A which is a 15-year mortgage term with a 3% interest rate;

The total amount paid over the loan term = $270,470

Answer:

A.

Step-by-step explanation:

Answer:

it should be 628.32 I'm not sure if I'm correct

Answer:

2/3

Step-by-step explanation:

Answer:

D) b

Step-by-step explanation:

Rise Over Run = Rate of change.

Answer:

A 0.4kg object rolling at 2 m/s that's d right answer

Answer:

A 0.4 kg object moving at 4 m.

Step-by-step explanation:

The heavier the object is, the faster it goes. Also the faster is goes and the heavier it is, the more momentum it has.

Answer:

$5.10

Step-by-step explanation:

Ratios:

[tex]\frac{6}{1.8} =\frac{17}{x} \\\\6x=30.6\\x=5.1[/tex]

Answer:

Step-by-step explanation:

Given:

To find:

Solution:

Answer:

A Jenna

Step-by-step explanation:

Because if Jenna received 22% votes and Jordan, Kelsey, Nathan received less 20 percentage that means Jenna won for school president.

Answer:

slopes is 1/4

y intercept is 3 i think the inequality would be y=mx+b so it would be y=1/4x+3

Step-by-step explanation:

Answer:

Un sistema de ecuaciones es un conjunto de ecuaciones con las mismas incógnitas. Un

sistema de ecuaciones lineales es un sistema de ecuaciones en el que cada ecuación es lineal. Una solución de un sistema es una asignación de valores para las incógnitas que hace

verdadera cada una de las ecuaciones. Resolver un sistema signifi ca hallar todas las soluciones del sistema.

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

In a triangle, a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

Given this formula, we knoe c^2 is the product of 21^2 + 20^2.

This gives you 841. Now you just find the square root of 841 which is 29.

Hope this helps :)

Answer:Cost of goods sold =Php125,000

Step-by-step explanation:

Profit = Cost Price-Selling Price

Also we know that

Gross Profit = Net Sales– Cost of Goods Sold

Php275,000=Php400,000– Cost of Goods Sold

Cost of Goods Sold=Php400,000-Php275,000=Php125,000

Answer:

8.38

Step-by-step explanation:

The underlined number is in the hundredths place, so that means that we're going to round there. That means that you look at the number to its right and if it's lower than 5, it stays the same. However, if it's 5 or higher, you round it up. For example, if the number was 8.386, we would round it to 8.39.

Answer:5.83

Step-by-step explanation:

s= p+3

(number of sports drinks= s)

(pizza slices= p)

Answer:

3/5

Step-by-step explanation:

35.

Step-by-step explanation:

The simplest form of 610 is 35.

Chocolate = 18%

Vanilla = 25%

Strawberry = 12%

Mint Chip = 10%

Other = 35%

The explanation for me getting these exact percentages is because of the formulas given for calculating the percentages from specific numbers and real world problems like this. When you are trying to find the calculation precentages of these types of questions, you divide the number by the total surveyed and multiple by 100.

Example:

125 / 500 = 0.25

0.25 x 100 = 25%

So, this is also how I got the other numbers, just change the "125" to the other numbers.

The experimental probability of each outcome in the sample space are:

P(chocolate) = 18%, P(strawberry) = 12%, P(vanilla ) = 25%, P(mint chip) = 10% and P(other) = 35%

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Flavor               Number of people

chocolate                  90

strawberry                 60

vanilla                        125

mint chip                    50

other                          175

So, the Experimental probability are:

P(chocolate)= 90/ 500 x 100 = 18%

P(strawberry) = 60/ 500 x 100 = 12%

P(vanilla ) = 125/ 500 x 100 = 25%

P(mint chip) = 50/ 500 x 100 = 10%

P(other) = 175/ 500 x 100 = 35%

Learn more about Probability here:

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9514 1404 393

Answer:

  5 seconds

Step-by-step explanation:

Suppose the front parts of the trains meet at point A. Since both are the same length and traveling the same speed, each will pass point A in time ...

  time = distance/speed

  time = (1/18 mi)/(40 mi/h) = (1/720 h) × (3600 s)/(1 h) = 5 s

That is, the rear part of each train will be at point A 5 seconds after the front part.

The rear parts will pass each other 5 seconds after the front parts meet.

Answer:

Step-by-step explanation:

Area is the product of two dimensions.

If the scale factor is 1/4, the ratio of the areas will be:

The smaller prism has a surface are of 45 cm².

The larger prism has a surface area:

Answer:

A is the correct answer.

Hope this helps [tex]\mathtt{: )}[/tex]

Answer:

A . $46

Step-by-step explanation:

because 575 - 8% = 529

529 + 49 = 575

Answer:

60 Gallons in 1/2 hour. So we can convert that to 240 quarts. it says 2 so we divide that by two. 240/2=120

Step-by-step explanation:

Hope this helps!

Answer:

(x + 5)² = 2 ==> x² + 10x + 27 = 0

Completing the square of the given quadratic equation leads to the equivalent equation (x + 5)² = -2.

Quadratic equations are polynomial equations of second degree.

The general form of a quadratic equation is ax² + b x + c = 0.

Given quadratic equation is,

x² + 10x + 27 = 0

We have the algebraic identity that,

(a + b)² = a² + 2ab + b²

The given quadratic equation is in the form of a² + 2ab + b², where a = x.

So, 2xb = 10x

⇒ b = 5

Now, b² = 25.

So, the given can be written as,

(x² + 10x + 25) + 2 = 0

(x + 5)² = -2

Hence the equivalent form is (x + 5)² = -2.

Learn more about Quadratic Equations here :

https://brainly.com/question/12014272

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Answer:

its 4,000

Step-by-step explanation:

Answer:

1001.35

Step-by-step explanation:

Assuming  

n

=

5

for which sum to be found.

We know sum of geometric series up to  

n

th term is

S

n

=

a

1

⋅

r

n

−

1

r

−

1

Here  

a

1

=

0.11

,

r

=

9.5

,

n

=

5

∴

S

5

=

a

1

⋅

r

5

−

1

r

−

1

=

0.11

⋅

9.5

5

−

1

9.5

−

1

≈

1001.35

[Ans]

Answer:

A≈153.94mi²

Step-by-step explanation:

A = πr2 = π · 72 ≈ 153.93804mi²

Answer:

I read the title wrong, please remove my answer

Step-by-step explanation: