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2 years ago

Prove that an equilateral triangle can be constructed on any given line segment

Mathematics

1 answer:

xz_007 [3.2K]2 years ago

8 0

Step-by-step explanation:

Answer is in the photo with diagram

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Clark and Lana take a 30-year home mortgage of $128,000 at 7.8%, compounded monthly. They make their regular monthly payments fo

svp [43]

Answer:

Step-by-step explanation:

From the given information:

The present value of the house = 128000

interest rate compounded monthly r = 7.8% = 0.078

number of months in a year n= 12

duration of time t = 30 years

To find their regular monthly payment, we have:

$PV = P \begin {bmatrix} \dfrac{1 - (1 + \dfrac{r}{n})^{-nt}}{\dfrac{r}{n}} \end {bmatrix}$

$128000 = P \begin {bmatrix} \dfrac{1 - (1 + \dfrac{0.078}{12})^{- 12*30}}{\dfrac{0.078}{12}} \end {bmatrix}$

128000 = 138.914 P

P = 128000/138.914

P = $921.433

∴ Their regular monthly payment P = $921.433

To find the unpaid balance when they begin paying the $1400.

when they begin the payment ,

t = 30 year - 5years

t= 25 years

$PV= 921.433 \begin {bmatrix} \dfrac{1 - (1 - \dfrac{0.078}{12})^{25*30}}{\dfrac{0.078}{12}} \end {bmatrix}$

PV = $121718.2714

C) In order to estimate how many payments of $1400 it will take to pay off the loan, we have:

$121718.2714 = \begin {bmatrix} \dfrac{1300 (1 - \dfrac{12.078}{12}))^{-nt}}{\dfrac{0.078}{12}} \end {bmatrix}$

$121718.2714 = 200000 \begin {bmatrix} (1 - \dfrac{12.078}{12}))^{-nt} \end {bmatrix}$

$\dfrac{121718.2714}{200000 } = \begin {bmatrix} (1 - \dfrac{12.078}{12}))^{-nt} \end {bmatrix}$

$0.60859 = \begin {bmatrix} (1 - \dfrac{12}{12.078}))^{nt} \end {bmatrix}$

$0.60859 = (0.006458)^{nt}$

$nt = \dfrac{0.60859}{0.006458}$

nt = 94.238 payments is required to pay off the loan.

How much interest will they save by paying the loan using the number of payments from part (c)?

The total amount of interest payed on $921.433 = 921.433 × 30(12) years

= 331715.88

The total amount paid using 921.433 and 1300 = (921.433 × 60 )+( 1300 + 94.238)

= 177795.38

The amount of interest saved = 331715.88 - 177795.38

The amount of interest saved = $153920.5

6 0

3 years ago

Find the length of arc XPY. Leave your answer in terms of pi.

PIT_PIT [208]

Answer:

2π m.

Step-by-step explanation:

Arc XY is 1/4 of the circumference of the circle

= 1/4 * 2π * r

= 1/2 π * 4

= 2π m.

8 0

1 year ago

[2P-3.) ^2+(2P+3)^2<br>

WINSTONCH [101]

Answer:

[2P-3.) ^2+(2P+3)^2[2P-3.) ^2+(2P+3)^2[2P-3.) ^2+(2P+3)^2

4 0

2 years ago

The measure of angle M is_degrees.

jasenka [17]

Answer:

m=37

Step-by-step explanation:

The 2 angles are complementary, or add to 90 degrees. Wee know this because of the little square in the corner that indicates a right angle, which is equal to 90 degrees.

m+53=90

Solve for m by getting m by itself. To do this, subtract 53 from both sides to "reverse" the addition being done to m.

m+53-53=90-53

The 53s on the left cancel, and we are left with:

m=37

3 0

3 years ago

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Rohan makes $86,534.25 a year. How much will he pay in Social Security and Medicare taxes this year?

matrenka [14]

Answer:

porfavor en español pls para yo poder resolverlo

4 0

2 years ago

Read 2 more answers