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oksano4ka [1.4K]
4 years ago
12

Solve 3y^{2} - (y + 2) (y - 2)

Mathematics
2 answers:
hram777 [196]4 years ago
8 0

Answer:

3y^2 - (y + 2) (y - 2) = 0

<=> 3y^2 - (y^2 - 4) = 0

<=> 2y^2 + 4 =0

<=>y^2 + 2 = 0

=> Because y^2 is always equal or larger than 0, there is no real solution.

Hope this helps!

:)

Paladinen [302]4 years ago
8 0

Answer:

2 {y}^{2}  + 4

Step-by-step explanation:

3 {y}^{2}  - (y + 2)(y - 2) \\ 3 {y}^{2}  - ( {y}^{2}  - 4) \\ 3 {y}^{2}  -  {y}^{2}  + 4 \\  = 2 {y}^{2}  + 4 \\  = 2( {y}^{2}  + 2)

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On 1st January 2020, Laurie invests P dollars in an account that pays a nominal annual interest rate of 5.5%, compounded quarter
andrezito [222]

Answer:

1) The common ratio =  1.055

2) The year in which the amount of money in Laurie's account will become double is the year 2032

Step-by-step explanation:

1) The given information are;

The date Laurie made the investment = 1st, January, 2020

The annual interest rate of the investment = 5.5%

Type of interest rate = Compound interest

Therefore, we have;

The value, amount, of the investment after a given number of year, given as follows;

Amount in her account = a, a × (1 + i), a × (1 + i)², a × (1 + i)³, a × (1 + i)ⁿ

Which is in the form of the sum of a geometric progression, Sₙ given as follows;

Sₙ = a + a × r + a × r² + a × r³ + ... + a × rⁿ

Where;

n = The number of years

Therefore, the common ratio = 1 + i = r = 1 + 0.055 = 1.055

The common ratio =  1.055

2) When the money doubles, we have;

2·a = a × rⁿ = a × 1.055ⁿ

2·a = a × 1.055ⁿ

2·a/a = 2 = 1.055ⁿ

2 = 1.055ⁿ

Taking log of both sides gives;

㏒2 = ㏒(1.055ⁿ) = n × ㏒(1.055)

㏒2 = n × ㏒(1.055)

n = ㏒2/(㏒(1.055)) ≈ 12.95

The number of years it will take for the amount of money in Laurie's account to double = n = 12.95 years

Therefore, the year in which the amount of money in Laurie's account will become double = 2020 + 12..95 = 2032.95 which is the year 2032

The year in which the amount of money in Laurie's account will become double = year 2032.

3 0
3 years ago
-27 - x = -51<br> ................
Katarina [22]

Answer:

24

Step-by-step explanation:

-27 - x = -51

+27     +27

-x = -24

x = 24

6 0
3 years ago
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