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kicyunya [14]
3 years ago
15

What are the values of x and y?

Mathematics
1 answer:
scZoUnD [109]3 years ago
3 0

Answer:

x is equal to 24 and y is equal to 66.

Step-by-step explanation:

In order to find the value of y, we first have to note that the unlabeled angle in the larger triangle, y and the 78 degree angle create a straight line. The unlabeled angle is equal to 36 since it and the other two angles equal 180. So we take that 36, 78 and y and can set that equal to 180.

36 + 78 + y = 180

114 + y = 180

y = 66

Now that we have that value, we can use y and the 90 degree angle to find x.

x + y + 90 = 180

x + 66 + 90 = 180

x + 156 = 180

x = 24

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The hour hand of a clock is 3 feet long. How many feet does
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2π feet

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3 years ago
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

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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}

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

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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
IF NR = 8 ft, what is the length of arc NMP. Round to the nearest tenth.
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Check the picture below.

since chords NQ and MP cross the center of the circle at R, that means that those two chords are diametrical chords and the angles made by both are vertical angles and thus twin angles, namely both are 18° as you see in the picture, so the angle NMP in magenta is really 162° + 18° + 18° = 198°, and we know the radius NR is 8.

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