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2 years ago

If x2 + y2=6 , xy = 5 , then (X + y)2?

Mathematics

1 answer:

VARVARA [1.3K]2 years ago

3 0

Answer:

(x + y)² =16

Step-by-step explanation:

hello :

(x + y)² = x²+y²+2xy and : x²+y² = 6 xy = 5

(x + y)² = 6+2(5)

(x + y)² =16

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2. Harry just deposited $1500 into a savings account giving 6% interest compounded quarterly.a) How much will be in the account

Studentka2010 [4]

The formula for compound interest is:

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{where,} \\ A=\text{ Final amount} \\ r=\text{ Interest rate} \\ n=\text{ Number of times interest applied per period} \\ t=\text{ Number of time period elapsed} \\ P=\text{ Intial principal balance} \end{gathered}$

Given data:

$\begin{gathered} P=\text{ \$1500} \\ r=6\text{ \%}=0.06 \\ n=4\text{ times (compounded quarterly)} \end{gathered}$

a. After ten years, that is t = 10 years, the amount in the account will be

$\begin{gathered} A=1500(1+\frac{0.06}{4})^{4\times10} \\ A=\text{ }1500(1+0.015)^{40} \\ A=\text{ }1500(1.015)^{40} \\ A=\text{ \$2721.03} \end{gathered}$

b. After twenty years, that is t = 20 years, the amount in the account will be:

$\begin{gathered} A=1500(1+\frac{0.06}{4})^{4\times20} \\ A=1500(1.015)^{4\times20} \\ A=1500(1.015)^{80} \\ A=\text{ \$}4935.99 \end{gathered}$

c. The time it takes for Harry's initial account value to double will be:

$\begin{gathered} A=2\text{ x initial value = 2 }\times\text{ \$1500 = \$3000} \\ 3000=1500(1.015)^{4t} \\ (1.015)^{4t}=\frac{3000}{1500} \\ (1.015)^{4t}=2 \\ \text{ Find the logarithm of both sides} \\ \ln (1.015)^{4t}=\ln 2 \\ 4t=\frac{\ln 2}{\ln 1.015} \\ 4t=46.56 \\ t=\frac{46.56}{4}=11.64 \end{gathered}$

Therefore, the time it takes Harry's initial account to double is approximately 11 years

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1 year ago

There are 20 alligators in the swamp. Each year, the number of alligators increases by 25%. There are 25 crocodiles in the swamp

Vera_Pavlovna [14]

Answer:

Step-by-step explanation:

We have given that:

There are 20 alligators in the swamp. Each year, the number of alligators increases by 25%. There are 25 crocodiles in the swamp. Each year, 10 new crocodiles join the swamp

Part A:

According to the above mentioned statement the function for representing the number of alligators and crocodiles in the swap throughout the year is:

Alligators = y=20(1.25)^x (x represents years)

crocodiles: y=10x+25

Part B:

Number of alligators after 4 years in the swap = y=20(1.25)^x

Number of alligators after 4 years in the swap = y=20(1.25)^4

Number of alligators after 4 years in the swap=48.82

This shows that about 48 to 49 alligators will be there in the swap after 4 year

Number of crocodiles after 4 years in the swap = y= 10(4)+25 = 65

Part C:

We will use the graph method to solve this part:

After approximately 7 years, the number of animals of each type will be the same, 95.

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3 years ago

Show all work. Write the equation in point slope form (5, -9); m = 6

eduard

Point slope form:
y+9=6(x-5)

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2 years ago

Yo not free braily points <br> soryy its a little

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2 years ago

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makkiz [27]

Answer:

Option A.

Step-by-step explanation:

According to this survey results :

Students : 80 like viking and 20 like patriot.

Teachers : 5 like viking and 15 like patriot.

In Option B it is given that patriot is more popular in students while viking is more popular in teachers which is not correct.

In option c patriot is equally popular in students and teachers, which is also not correct. because patriot is popular in 20% of students but 80% in teachers, which is not correct.

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In Option A it is said that viking is more popular in students but patriot is more popular in teachers. this is correct.

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3 years ago

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If x2 + y2=6 , xy = 5 , then (X + y)2? ​

If x2 + y2=6 , xy = 5 , then (X + y)2?