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4 years ago

True or False: The following system of equations is consistent.

Mathematics

1 answer:

vampirchik [111]4 years ago

6 0

A system of equation is consistent if there is at least one solution. Since this system of equations has a single solution, it is consistent, the answer is true.

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The basketball team practices every day from 2:30 pm to 4:00 pm.todays practice ended 20 minutes early.at what time did basketba

Goshia [24]

3:40 because 4:00 minus 20 is 3:40

8 0

3 years ago

Sin^2 a/2 - sin a/2 + 1/4 = 0

zimovet [89]

Answer:

a = 60° or π/3

Step-by-step explanation:

Given :-

sin² a/2 - sin a/2 + 1/4

To find :-

Solving :-

sin² a/2 - sin a/2 + 1/4 = (sin a/2 - 1/2)² = 0

sin a/2 - 1/2 = 0

sin a/2 = 1/2

a/2 = 30°

Solution :-

a = 60° or π/3

3 0

2 years ago

Solve using zero property : (x-7)(x+10) = 0

Alla [95]

Answer:

Step-by-step explanation:

Aight

x^2+3x−70=0

x−7=0 or x+10=0

x=7 or x=−10

8 0

4 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

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

If the product of a number and negative −3 is subtracted from the number, the result is 11 more than the number. find the numbe

Ierofanga [76]

The answer would be 2.2.

This sentence as an expression would be n - (-3n) = n + 11.
Solve it and you'll get 2.2!

8 0

4 years ago