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3 years ago

Write an equation of a line in slope intercept form that is perpendicular to y = -4x -2 and passes through the point (-16, -11).

1 answer:

4 0

Y = -4x - 2
P (-16, -11)
a = -4, b = 0, c = -2
m = -a/b
m = -(-4)/(-2)
m = 4/(-2)
m = -2

y-yo = m(x-xo)
y-(-11) = -2[x-(-16)]
y+11 = -2(x+16)
y+11 = -2x-32
2x+y+11+32 = 0
2x+y+43 = 0

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The population of a city has increased by 27% since it was last measured. If the current population is 38,100, what was the prev

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Answer:

the previous population was 62,000.

Step-by-step explanation:

The current population of a city = 83,700

The population of a city has increased by 35% since it was last measured.

We have to calculate the previous population before increasing 35%.

Let the previous population be p

p +(35% × p) = 83,700

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1.35p = 83,700

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Step-by-step explanation:

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Imagine that you would like to purchase a $275,000 home. Using 20% as

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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;

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

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

$M = \dfrac{P \cdot \left(\dfrac{r}{12} \right) \cdot \left(1+\dfrac{r}{12} \right)^n }{\left(1+\dfrac{r}{12} \right)^n - 1}$

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)

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

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

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

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

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

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

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3 years ago

Unit 5. 17) Please help. Which solids could have a cross section in the shape shown above?

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Answer:

I think the correct answers are options 2 and 4.

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3 years ago

Ramon earns $1,735 each month and pays $53.10 on electricity. To the nearest tenth of a percent, what perfect of ramons earnings

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Answer:

$\boxed{3.1 \, \%}$

Step-by-step explanation:

The formula for calculating percentage is

$\text{Percentage} = \dfrac{\text{Part}}{\text{Whole}} \times 100 \, \%$

The "part" is the electricity payment.

The "whole" is Ramon's earnings.

$\begin{array}{rcl}\text{\% of earnings} & = & \dfrac{53.10}{1735} \times 100 \, \% \\\\& = & \mathbf{3.1 \, \%}\\\end{array}\\\boxed{\mathbf{3.1 \, \%}} \text{ of Ramon's earnings are on electricity}$

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3 years ago