Suppose you invest in an annuity that pays 5% annual interest, compounded quarterly. If you contribute $400 every quarter for 20 years, how much interest would you earn during the 20 years? Enter your answer, rounded to the nearest cent, without the dollar sign or comma ($23,678.1235 should be entered as 23678.12.)

Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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this is the answer of the equation as a graph

The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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Answer:

To solve 5(98) =___(100-2) using the distributive property, we can distribute the 5 to both the 100 and the -2:

5(98) = 5(100 - 2)

Now, we can use the distributive property to simplify the right side:

5(98) = 5(100) - 5(2)

Multiplying, we get:

490 = 500 - 10

Simplifying further, we get:

490 = 490

Therefore, the equation is true, and we have verified the distributive property.

Answer: 2.4

Step-by-step explanation: Given the angles below, the length of EF will be 2.4

Answer:

B) 3.8.

EF = 3.8

Use the law of sines to find the unknown length EF

Answer: x = 2

Step-by-step explanation:

Let x represent the unknown number:

2x + 5 = 9

Subtract 5 from both sides

2x = 4

Divide both sides by 2

x = 2

Answer: hmmm simple it’s 15

Step-by-step explanation: your welcome

Answer:

C. ab

Explanation:

If a is a nonzero interger and b is not an integer, a + b, a - b or 2a - b will be not an integer. For example, if a = 2 and b = 0.5, then:

a + b = 2 + 0.5 = 2.5

a - b = 2 - 0.5 = 1.5

2a - b = 2(2) - 0.5 = 4 - 0.5 = 3.5

Where 2.5, 1.5 and 3.5 are not integers.

However, ab could be an integer. In this example, we get:

ab = 2(0.5) = 1

And 1 is an integer.

Therefore, the answer is ab

We will add the like terms like

w with w and 4 with 6

The answer is

Answer: 7.5

Step-by-step explanation:

the tank is 15 gallons and you can get 13 percent ethanol or 69 percent ethanol, so you simply just get 7.5gallons of 69 percent and then 7.5 gallons of 13 percent

.69 divided by 15 is .046

.13 divided by 15 is .008

The amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is equivalent to 4.35 gallons.

Given is that a car has a 15 gallon tank and can run on fuel with added

ethanol. The fuel contains either 13 percent ethanol or 69 percent

ethanol.

The amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is given by -

{x} = 69% of 15 - {40% of 15}

{x} = (69/100 x 15) - (40/100 x 15)

{x} = 10.35 - 6

{x} = 4.35

Therefore, the amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is equivalent to 4.35 gallons.

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Answer:

I pretty sure the answer is 171,000 . but if i'm wrong someone can correct me

Step-by-step explanation:

The value of 3x₁ + x₂ is 7/2

A quadratic equation is an equation of the form ax² + bx + c = 0, where x is the variable and a, b, and c are constants.

5/x - 2/x² = 2

The LCM of x and x² is x². So we have:

(5x - 2)/x² = 2

Cross multiply:

5x - 2 = 2x²

2x² - 5x + 2 = 0

Factorize:

(2x - 1)(x - 2) = 0

2x - 1 = 0 or x - 2 = 0

2x  = 1 or x = 2

x  = 1/2 or x = 2

Thus, x₁ = 1/2 and x₂ = 2

Therefore, the value of 3x₁ + x₂ will be:

3x₁ + x₂ = 3×(1/2) + 2 = 3/2 + 2 = 7/2

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Answer:

this js the answer blablabla

Answer:

See the steps below:)

Step-by-step explanation:

I could not show all the steps, But I used the app photo math which shows you all the steps.

Answer:

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

functions can only have domains that are different numbers, (first number) the rest repeat the domain and that makes it not a function

Answer:

C

Step-by-step explanation:

A set of pairs is a function if and only if there is only one y-value for each x-coordinate. In other words, the x-coordinate cannot repeat. If it does, then it must equal the same thing.

Let's go through each of the choices.

For A, -5 repeats twice. It simultaneously equals both 4 and -2. This cannot be true if this is a function, so A is not correct.

For B, 2 repeats twice. It equals both 6 and -6. So, this is also not a function.

For C, no digits are repeating. Thus, this is a function.

To make sure, in D ,-3 is repeating. It is both -4 and 8, so this is not a function.

So, our answer is C.

And we're done!

Answer:

32 mins\

beacuase taht was the amont of time that passed

9514 1404 393

Answer:

  (f-g)(x) = 4x^3 +7x^2 -6x +1

Step-by-step explanation:

(f -g)(x) = f(x) -g(x)

  = (4x^3 +7x^2 -2x -1) -(4x -2)

  = 4x^3 +7x^2 +(-2-4)x +(-1+2)

(f -g)(x) = 4x^3 +7x^2 -6x +1

Answer:

Below

Step-by-step explanation:

A cube has SIX sides of equal area

  each side has area = L x W       and L and W are the same = 4.5 m

      so:   Area =   six   X   ( 4.5  X 4.5)  =   6 * 4.5 * 4.5 = 121.5 m^2

Answer:

Hope the picture will help you...

Answer:

1. b_ 2. a_ 3. c_ 4. d

Step-by-step explanation:

1 is b mainly because it is marked that way. Your picture doesn't show all of d so not really sure about it, but I used the process of elimination. Picture c is side angle side b/c of the vertical angles.

Answer:

(2/3)^8

Step-by-step explanation:

Note that 2^8 = 256, and that 3^8 = 6561.

Then 256/6561 = (2/3)^8

In order to earn $75 interest in 7 months at 2.4% invest 53.571.

What is simple interest?

Generally, simple interest paid or received over a certain period is a fixed percentage of the principal amount that was borrowed or lent.

Simple interest is calculated using the following formula:

 Simple Interest = P×R×T where:

P=Principal amount

R=Annual interest rate

T=Term of loan, in years

​

According to the given question

Given that

Simple interest= 75

Time= 7/12= 0.583

Rate of interest= 2.4

Principle amount=?

S.I= PTR

75 = P x 0.583 x 2.4

75 = P x 1.4

P = 75 / 1.4

P= 53.571

Therefore, principle is 53.571

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Step-by-step explanation:

Just multiply the two dimensions to get m^2  area

7.2 m * 11 m = 79.2 m^2

Answer:

2. or 3 one ejei2iieieieo2ow9w

Answer:

1

Step-by-step explanation:

cause she works 2 hours then her hour pay plus the $4 tip and you get 32

Answer:

Step-by-step explanation:

-15-9 = -24

I would think about it as adding 15 and 9, but just make the answer negative.

Step-by-step explanation:

the numbers : x, y

x - y = 8

2y = x + 4

2y - 4 = x

we use the last equation in the first :

2y - 4 - y = 8

y - 4 = 8

y = 12

x = 2y - 4 = 2×12 - 4 = 24 - 4 = 20

the smaller number is 12.

The value of the smaller number will be 12.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The difference between two whole numbers is 8.

And, Twice the smaller number is 4 more than the larger number.

Now,

Let two numbers are x and y.

Where, x is larger number and y is smaller number.

Since, The difference between two whole numbers is 8.

Hence, We get;

⇒ x - y = 8

⇒ x = 8 + y  ..(i)

And, Twice the smaller number is 4 more than the larger number.

So, We get;

⇒ 2y = 4 + x  ..(ii)

Substitute the value of x from (i) in above equation, we get;

⇒ 2y = 4 + 8 + y

Solve for y as;

⇒ 2y - y = 12

⇒ y = 12

Thus, The value of the smaller number will be 12.

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\((\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-7}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{1}}} \implies \cfrac{ -13 }{ -6 } \implies \cfrac{13 }{ 6 }\)