Solve the proportion 8/x equals 14/28

rusak2 [61]

Here i how I would do it:f(x)=−x2+8x+15
set f(x) = 0 to find the points at which the graph crosses the x-axis. So−x2+8x+15=0
multiply through by -1x2−8x−15=0 (x−4)2−31=0 x=4±31−−√
So these are the points at which the graph crosses the x-axis. To find the point where it crosses the y-axis, set x=0 in your original equation to get 15. Now because of the negative on the x^2, your graph will be an upside down parabola, going through(0,15),(4−31−−√,0)and(4+31−−√,0)
To find the coordinates of the maximum (it is maximum) of the graph, you take a look at the completed square method above. Since we multiplied through by -1, we need to multiply through by it again to get:f(x)=31−(x−4)2
Now this is maximal when x=4, because x=4 causes -(x-4)^2 to vanish. So the coordinates of the maximum are (4,y). To find the y, simply substitute x=4 into the equation f(x) to give y = 31. So it agrees with the mighty Satellite: (4,31) is the vertex.

8 0

3 years ago

(Please show step by step workings)

matrenka [14]

Answer:

a. They will need $90,000.00 for the down payment

b. The mortgage amount (principal) will be $360,000.00

c. The monthly principal payment will be $1,500,00

The monthly interest payment will be $634.40

d. The total interest they will pay: $152,256.00

Step-by-step explanation:

house price= $450,000

down payment = 20%

20-year mortgage

Interest rate= 3.75%

a. How much they will need for the down payment?

The down payment (DoP) is 20% of the house price

DoP= 20% de $450,000

DoP= 0.20*450,000

DoP= $90,000

b. What will be the mortagage amount (the principal)?

The mortgage amount (MoA) (principal) is the difference between the house price and the down payment.

MoA= $450,000 - $90,000

MoA= $360,000

c. How much will their monthly payment be for the principal and interest?

This equation represents the monthly payment (M):

$M=P \frac{r(1+r)^{n} }{(1+r)^{n}-1}$

where

P= the principal = $360,000

r= monthly interest rate = 3,75% divided by 12 = 0,31%

n= number of payments = 20 years multiplied by 12 months = 240

Let´s input these data into the equation:

$M= 360,000\frac{0.0031(1+0.0031)^{240} }{(1+0.0031)^{240} -1}$

$M= 360,000\frac{0.0031(1.0031)^{240} }{(1.0031)^{240} -1}$

Solving the equation:

M= $2,134.40

the principal component of this M would be

$360,000 divided by the 240 months

So, the principal component of M = $1,500.00

And the interest component of M is the difference

$2,134.40 - $1,500.00

So, the interest component of M = $634.40

d. How much total interest will they pay if they take the full 20 years to pay off the mortgage?

With every payment, they will be paying:

$634.40 per month, multiplied by 240 months

The total interest will be $152,256.00

5 0

3 years ago

The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had los

Gnesinka [82]

The bones at the time they were discovered when the radioactive element carbon-14 has a half-life of total 5750 years are 10062.5-year-old.

<h3>What is half-lives?</h3>

Half lives is the time interval which is need to decay the atomic nuclei of a radioactive sample.

There is a scientist who determined that the bones from a mastodon had lost 70.3% of their carbon-14. Thus, the fraction remaining is,

f=1-(70.3/100)=1-0.703

f=1-(70.3/100)=0.297

Now the fraction remaining can be given as,

f=(1/2)ⁿ

Here, n is the half life elapsed. Put the value of fraction remaining.

0.297=(1/2)ⁿ

n=1.75

The radioactive element carbon-14 has a half-life of total 5750 years. Thus,

Years=1.75*5750

Years=10062.5

Thus, the bones at the time they were discovered when the radioactive element carbon-14 has a half-life of total 5750 years are 10062.5-year-old.

Learn more about the half lives here;

brainly.com/question/2320811

#SPJ1

6 0

2 years ago

Please help !! Will mark brainliest - NO links and files please. 5 is 1/2 of what number?

Arisa [49]

Answer:

10

Step-by-step explanation:

10/2=5

7 0

3 years ago

Read 2 more answers

At the beginning of the season, MacDonald had to remove 5 orange trees from his farm. Each of the remaining trees produced 210 o

Rainbow [258]

he initial number of trees was 204.

<h3>How to find the initial number of trees?</h3>

The first step to finding the initial number of trees is to write an equation that represents the situation.

T is equal to the initial number of trees.
5 trees were removed = t - 5
Each tree produces 210 oranges = (t-5) (210)
The total of oranges is 41,780 = (t-5) (210)= 41,780

Solve the equation:

(t-5) (210)= 41,780
t-5= 41,780 / 210
t-5 = 198.95
t = 198.95 + 5
t = 203.9

This number can be rounded as 204.

Note: This question is incomplete; here is the missing section:

Find the initial number of trees.

Learn more about equation in: brainly.com/question/2263981

6 0

2 years ago