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2 years ago

Which equation represents a line perpendicular to the line whose equation is 2x+3y=12?

Mathematics

1 answer:

Gnoma [55]2 years ago

5 0

Answer:

use socratic i think they have the answer!! im not good at math sorry love!

Step-by-step explanation:

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Samantha divides $16,000 into three investments: a savings account 3 points paying 7% annual interest, a bond paying 9%, and a m

kipiarov [429]

Answer:

2000 was the amount of the investment in the savings account

6000 was the amount of the investment in the payment of bonds

8000 was the amount of the investment in the money market

Step-by-step explanation:

In this case, a system of equations must be generated with the information given in the statement.

Let x be the amount of the investment in the savings account

Let y be the amount of the investment in the payment of bonds

Let z be the amount of investment in the money market

Now, the first equation would be that of total investment:

x + y + z = 16000

The second equation is that of interest:

0.07 * x + 0.09 * y + 0.12 * z = 1640

Last, her equation has invested three times more in the bond payment than in the savings account:

3 * x = y

So we have 3 equation with 3 unknowns. Therefore there is a solution.

x + y + z = 16000

0.07 * x + 0.09 * y + 0.12 * z = 1640

3 * x = y

In order not to make the answer too extensive, we will solve the system of equations with the help of symbolab, here is the step-by-step of everything they do in a very detailed and precise way.

https://es.symbolab.com/solver/step-by-step/x%20%2B%20y%20%2B%20z%20%3D%2016000%3B%200.07%20%5Ccdot%20x%20%2B%200.09%20%5Ccdot%20y%20%2B%200.12%20%5Ccdot%20z%20%3D%201640%3B%203%20%5Ccdot%20x%20%3D%20y

From this, the results are as follows:

x = 2000

y = 6000

z = 8000

Thus

2000 was the amount of the investment in the savings account

6000 was the amount of the investment in the payment of bonds

8000 was the amount of the investment in the money market

7 0

2 years ago

Suppose you want to have $300,000 for retirement in 25 years. Your account earns 8% interest. How much would you need to deposit

Rus_ich [418]

Using the future value formula, it is found that you would need to deposit $272.95 in the account each month.

<h3>What is the future value formula?</h3>

It is given by:

$V(n) = P\left[\frac{(1 + r)^{n-1}}{r}\right]$

In which:

P is the payment.

n is the number of payments.

r is the interest rate.

For this problem, considering that there are monthly compoundings, the parameters are:

r = 0.08/12 = 0.0067, V(n) = 300000, n = 25 x 12 = 300.

Hence we solve for P to find the monthly payment.

$V(n) = P\left[\frac{(1 + r)^{n-1}}{r}\right]$

$300000 = P\left[\frac{(1.0067)^{299}}{0.0067}\right]$

1099.12P = 300000

P = 300000/1099.12

P = $272.95.

You would need to deposit $272.95 in the account each month.

More can be learned about the future value formula at brainly.com/question/24703884

#SPJ1

4 0

1 year ago

The first term of an arithmetic sequence is 5. if the25th term is 101 find the common difference?

d1i1m1o1n [39]

An arithmetic sequence is one where each term is a constant difference, called the common difference, from the preceding term. The arithmetic sequence can always be expressed as:

a(n)=a+d(n-1), a=first term, d=common difference, n=term number.

We are given two terms and term numbers, so we can solve for the common difference...

101=5+d(25-1)

101=5+25d-d

101=5+24d

96=24d

d=4

So the common difference is 4.

8 0

2 years ago

Read 2 more answers

The length of a rectangular poster is 7 inches more than twice its width. Find the length of the poster if its perimeter is 110

Scilla [17]

Total perimeter:
2u+7 inches+2u+7 inches+1u+1u
7 inches x 2 = 14 inches
*As there are 2 lengths, there are two sets of "extra" 7 inches.*
(2ux2)+1u+1u=6u
6u=110 inches - 14 inches = 96 inches
1u = 96 inches ÷ 6=16 inches (width)
(2x16 inches)+7 inches=32 inches+7 inches=39 inches

Ans: 39 inches

6 0

2 years ago

Use distributive property for 3.2= 4/5(b - 5)

tigry1 [53]

I hope this helps :)

5 0

2 years ago