72/10-9/2=_____ <br> i need help with this problem

The equation shown below involves a perfect square trinomial. 4x2 + 20x + 25 = 7 Which of the following is a step in solving thi

fomenos

4 x^2 + 20 x + 25 = 7
Divide both sides by 4:
x^2 + 5 x + 25/4 = 7/4
Write the left-hand side as a square:
(x + 5/2)^2 = 7/4
Take the square root of both sides:
x + 5/2 = sqrt(7)/2 or x + 5/2 = -sqrt(7)/2
Subtract 5/2 from both sides:
x = sqrt(7)/2 - 5/2 or x + 5/2 = -sqrt(7)/2
Subtract 5/2 from both sides:
Answer: x = sqrt(7)/2 - 5/2 or x = -5/2 - sqrt(7)/2

3 0

3 years ago

How do I determine the range.

Nikitich [7]

Answer:

y: (5, -5)

Step-by-step explanation:

5 0

2 years ago

A sample of 5 strings of thread is randomly selected and the following thicknesses are measured in millimeters. Give a point est

liq [111]

Answer:

$s^2 = \frac{(1.48-1.502)^2 +(1.45-1.502)^2 +(1.54-1.502)^2 +(1.52-1.502)^2 +(1.52-1.502)^2}{5-1} =0.00132$

And for the deviation we have:

$s= \sqrt{0.00132}=0.0363$

And that value represent the best estimator for the population deviation since:

$E(s) =\sigma$

Step-by-step explanation:

For this case we have the following data:

1.48,1.45,1.54,1.52,1.52

The first step for this cae is find the sample mean with the following formula:

$\bar X =\frac{\sum_{i=1}^n X_}{n}$

And replacing we got:

$\bar X= \frac{1.48+1.45+1.54+1.52+1.52}{5} = 1.502$

And now we can calculate the sample variance with the following formula:

$s^2 =\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}$

And replacing we got:

$s^2 = \frac{(1.48-1.502)^2 +(1.45-1.502)^2 +(1.54-1.502)^2 +(1.52-1.502)^2 +(1.52-1.502)^2}{5-1} =0.00132$

And for the deviation we have:

$s= \sqrt{0.00132}=0.0363$

And that value represent the best estimator for the population deviation since:

$E(s) =\sigma$

4 0

3 years ago

Read 2 more answers

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

5/8 of the 64 musicians in a music contest are guitarists. Some of the guitarists play jazz solos, and the rest play classical s

motikmotik

The first thing we must do for this case is find the number of total guitarists.

We have then:

$(\frac{5}{8}) * (64) = 40$

We now look for the relationship between the number of guitarists playing jazz alone to the total number of guitarists.

We have then:

$\frac{x}{40} = \frac{1}{4}$

Where,

x: number of guitarists playing jazz alone

From here, we clear the value of x.

$x = (\frac{1}{4}) * (40)\\x = 10$

Then, the number of guitarists who play classical solo is:

$40 - 10 = 30$

Answer:

30 guitarists play classical solos in the contest

5 0

3 years ago

Read 2 more answers

72/10-9/2=_____ i need help with this problem