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ss7ja [257]
3 years ago
10

Consider the function represented by 9x+3y=12 with x as the independent variable. How can this function be written using

Mathematics
1 answer:
Phoenix [80]3 years ago
3 0

Answer:

f(x) = - 3x + 4

Step-by-step explanation:

Given

9x + 3y = 12 ← rearrange making y the subject

Subtract 9x from both sides

3y = - 9x + 12 ( divide all terms by 3 )

y = - 3x + 4, or in functional notation as

f(x) = - 3x + 4

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You have $36,948.61 in a brokerage account, and you plan to deposit an additional $3,000 at the end of every future year until y
Luba_88 [7]
Current amount in account
P=36948.61

Future value of this amount after n years at i=11% annual interest
F1=P(1+i)^n
=36948.61(1.11)^n

Future value of $3000 annual deposits after n years at i=11%
F2=A((1+i)^n-1)/i
=3000(1.11^n-1)/0.11

We'd like to have F1+F2=280000, so forming following equation:
F1+F2=280000
=>
36948.61(1.11)^n+3000(1.11^n-1)/0.11=280000

We can solve this by trial and error.


The rule of 72 tells us that money at 11% deposited will double in 72/11=6.5 years, approximately.
The initial amount of 36948.61 will become 4 times as much in 13 years, equal to approximately 147800 by then.
Meanwhile the 3000 a year for 13 years has a total of 39000.  It will only grow about half as fast, namely doubling in about 13 years, or worth 78000.
Future value at 13 years = 147800+78000=225800.
That will take approximately 2 more years, or 225800*1.11^2=278000.

So our first guess is 15 years, and calculate the target amount
=36948.61(1.11)^15+3000(1.11^15-1)/0.11
=280000.01, right on.

So it takes 15.00 years to reach the goal of 280000 years.
8 0
3 years ago
Solve similar triangles (basic)
fiasKO [112]

Answer:

<em>T </em><em>=</em><em> </em><em>1</em><em>6</em>

Step-by-step explanation:

As triangles are similar

AB/DE = BC/EF = AC/DF

13.5/18 = 6/4 = 12/T

3/4 = 3/4 = 12/T

3/4 = 12/T

T = 12×4/3

T = 16

4 0
2 years ago
Simplify: 0.9(2b-1)-0.5b+1
Nutka1998 [239]

Answer:

Step-by-step explanation:

0.9*2b = 1.8b

0.9*-1 = -0.9

So far we have 1.8b-0.9. It can't be simplified further.

Then, we add the 2nd part, -0.5b+1.

We have:

1.8b-0.9-0.5b+1. Next we combine like terms.

1.8b-0.5b = 1.3b.

-0.9+1 = 0.1

Then we put it together.

1.3b+0.1 is our answer.

Hope this helped! Have a nice day :D

5 0
3 years ago
Read 2 more answers
Factor the polynomial. x2 - 6x + 9 A) (x - 9)(x - 1) B) (x - 3)(x + 3) C) (x + 9)(x + 1) D) (x - 3)(x - 3)
mihalych1998 [28]
X² - 6x +9
x          -3
x          -3

D)   (x - 3) (x -3) is your answer

To check, do your FOIL
x(x) = x^2
x(-3) = -3x
-3(x) = -3x
-3(-3) = 9
x^2 -6x +9  True

hope this helps


6 0
4 years ago
Read 2 more answers
Simplify the expression. (20 points)
goldenfox [79]
- 9/ ((-x^2 + 9)^1/2(x+ 3))(x-3)
7 0
3 years ago
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