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3 years ago

Rectangle DEFG with vertices D(-4, 3), E(0, 2), F(-2, 6), and G(-6, -5): (x + 4, y + 1)

Mathematics

1 answer:

Maru [420]3 years ago

6 0

Answer:

D'(0,4)

E'(4,3)

F'(2,7)

G'(-2, -4)

Step-by-step explanation:

It's simple. Just add the x and y values by the rule.

For example, say I had (0,0) as a point.

To change it, It'd be simple!

(0+4,0+1) = (4,1)

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Victor earns a gross annual income of $64,570 and is buying a home for $125,340. He is making a 15% down payment and financing t

Oliga [24]

Part A:

Given that Victor is buying a home for $125,340 and that he is making a 15% down payment.

The amount of down payment is given by 15% of $125,340 = 0.15 x $125,340 = $18,801.

Therefore, the amount of mortgage he needs to borrow is given by $125,340 - $18,801 = $106,539

Part B

Given that he earns a gross annual income of $64,570 and that the loan of $106,539 will be spread for 20 years at 3.75% interest.

$106,539 / 20 = $5,326.95

Roughly he will be paying about $5,000 every year which is way below his annual gross income.

Therefore, he can afford the mortgage.

Part C

The monthly mortgage payment can be calculated using the present value of annuity formula given by

 $PV=P\left( \frac{1-\left(1+\left( \frac{r}{t} \right)\right)^{-nt}}{ \frac{r}{t} } \right)$

where: PV is the current value of the loan, P is the periodic (monthly) payment, r is the annual interest rate, t is the number of payment in one year and n is the number of years.

Here, PV = $106,539; r = 3.75% = 0.0375; t is 12 payments in one year (since payment is to be made monthly); n = 20 years.

Thus, we have:

$106,539=P\left( \frac{1-\left(1+\left( \frac{0.0375}{12} \right)\right)^{-20\times12}}{ \frac{0.0375}{12} } \right) \\ \\ =P\left( \frac{1-\left(1+0.003125\right)^{-240}}{0.003125} \right)=P\left( \frac{1-\left(1.003125\right)^{-240}}{0.003125} \right) \\ \\ =P\left( \frac{1-0.472919}{0.003125} \right)=P\left( \frac{0.527081}{0.003125} \right)=168.666P \\ \\ \Rightarrow P= \frac{106,539}{168.666} =631.66$

Therefore, the monthly mortgage payment is $631.66

Part D

Since he will make a monthly payment of $631.66 for 20 years, thus he will make a total of $631.66 x 12 x 20 = $151,598.40

Therefore, his total payment for the house will be $151,598.40

Part E

Since he will make a total payment of $151,598.40 for a mortgage loan of $106,539.

Therefore, the amount of interest he will pay is given by $151,598.40 - $106,539 = $45,059.40

7 0

3 years ago

If the angles of a triangle are in the ratio 3:4:2 find the value of all triangle

Nata [24]

Answer:

Step-by-step explanation:

If the ratio of triangle = 3:4:2

Total ratio = 3+4+2 = 9

The sum of angle in a triangle is 180°

1st angle= 3/9 × 180 = 2 × 20 = 60°

2nd angle= 4/9 × 180 = 4 × 20 = 80°

3rd angle= 2/9 × 180 = 2 × 20 = 40°

6 0

3 years ago

In the expression 710 , which number is the exponent?

DiKsa [7]

Answer:

A.10

Step-by-step explanation:

An exponent is a number or letter written above and to the right of a mathematical expression called the base.

x is the base and n is the exponent or power. Definition: If x is a positive number and n is its exponent, then xn means x is multiplied by itself n times.

6 0

2 years ago

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Bob would like to get his debt-to-income (DTI) ratio down to 36%. His current monthly expenses are outlined in the chart below.

a_sh-v [17]

Answer:

from my understanding the answer is 175.80

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

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