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3 years ago

Give triangle TRY, find TY. Round your answer to the nearest hundredth.

Mathematics

1 answer:

3241004551 [841]3 years ago

8 0

The length of TY is 2.26.

Solution:

In ΔTRY, θ = 37°, Adjacent side = 3.

To find the length of TY.

Using trigonometry identity,

$$\tan\theta=\frac{{opposite}}{{Adjacent}}$

$$\tan37^\circ=\frac{{TY}}{3}$

$$3\tan37^\circ=TY$

$$3\times 0.75355=TY$

$$TY=2.26065$

TY = 2.26

Hence the length of TY is 2.26.

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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

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3 years ago

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Answer:

the answer is x + 3

Step-by-step explanation:

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Solve. 54 ÷ (4 – 1)3

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54 divide 3*3=54 is the answer

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Answer:

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A car salesman makes 2% commission on all cars, x, that he sells. How much commission does he make?

HACTEHA [7]

Answer: 0.02x

Step-by-step explanation:

The value of the cars the salesman makes is x in this instance.

The salesman makes a 2% commission on every sale so this can be represented by multiplying 2% by the value of the cars which in this case is x.

= 2% * x

= 0.02 * x

= 0.02x

If for instance he sells $40,000 worth of cars, his commission would be:

= 0.02 * x

= 0.02 * 40,000

= $800

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3 years ago