Find the positive value of x that makes the equation true,
x2 + 4x = 4(x + 16)

You will need to make payments for approximately 432 months (or 36 years) before you can retire and afford to buy your dream boat.

To determine the number of months required to reach the retirement goal, we can use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r

Where:

FV is the future value (in this case, the retirement goal)

P is the monthly payment

r is the monthly interest rate

n is the number of periods (months)

In this case, the future value (FV) is $388,000, the monthly payment (P) is $160, and the monthly interest rate (r) is 4.75% (or 0.0475).

Plugging these values into the formula, we have:

$388,000 = $160 * ((1 + 0.0475)^n - 1) / 0.0475

To solve for n, we need to isolate it in the equation. Let's rearrange the equation:

((1 + 0.0475)^n - 1) / 0.0475 = $388,000 / $160

Simplifying further:

((1.0475)^n - 1) / 0.0475 = 2425

Now, we can solve for n by taking the logarithm of both sides. Let's use the natural logarithm (ln) for this calculation:

ln((1.0475)^n - 1) / 0.0475 = ln(2425)

n * ln(1.0475) = 0.0475 * ln(2425)

n = (0.0475 * ln(2425)) / ln(1.0475)

Using a calculator, we can find the value of n:

n ≈ 431.76

Rounding to the nearest month, we get:

n ≈ 432 months

Therefore, you will need to make payments for approximately 432 months (or 36 years) before you can retire and afford to buy your dream boat.

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Answer:

D

Step-by-step explanation:

Here, we want to select which of the options explains the scenario in the question.

Firstly, 1,000 shares were purchased at $10 per share.

Mathematically the total amount of shares bought will be 10 * 1000 = $10,000

Also, we have the growth rate as 12.5% = 12.5/100 = 0.125

Thus, representing the scenario with a function, we have;

A(t) = 10,000 e0.125t

Answer:

D

Step-by-step explanation:

Edg2020

Answer:

9

Step-by-step explanation:

8/12=2/3

6/9=2/3

Answer:

I would honestly choose 9

Step-by-step explanation:

Because it is using cross products and you want them to equal the same, so you take 6 x 12= 72 so you take 8 and multiply by each number Each time you know 72 x 8 wont work and the 576 wont work and that .75 is going to be way too little therefore its 9 and you can check by multiplying 8 x 9= 72

To get this answer, multiply each coordinate by the scale factor

(1/3)*9 = 9/3 = 3

(1/3)*12 = 12/3 = 4

The rule is [tex](x,y) \to (kx, ky)[/tex] where k is the scale factor. This rule only works if the center of dilation is the origin.

Answer:

8 ft.

Step-by-step explanation:

The formula for area of a square is:

[tex]A=s^2[/tex]

We are given the area of 64 square feet.

[tex]64=s^2\\\\\sqrt{64}=\sqrt{s^2}\\\\ \boxed{8=s}[/tex]

Each side should be 8 ft.

Hope this helps.

Answer:

This question is impossible! For two different variables, we need two different equations. Without that, there is no hope! :)

Answer:

c= -z-2

Step-by-step explanation:

[tex]7-5c=17+5z\\\\\mathrm{Subtract\:}7\mathrm{\:from\:both\:sides}\\\\7-5c-7=17+5z-7\\\\Simplify\\\\-5c=5z+10\\\\\mathrm{Divide\:both\:sides\:by\:}-5\\\\\frac{-5c}{-5}=\frac{5z}{-5}+\frac{10}{-5}\\\\Simplify\\\\c=-z-2[/tex]

The correct option for the above equation  is b. -√5/5.

The given function is f(x)=3x^5−4x^3−3x.Therefore, we have to find out where the relative maximum of the function

occurs. So, let's begin by finding the derivative of the given function. f(x)=3x^5−4x^3−3xDifferentiating both sides w.r.t.

x, we get: f'(x)= 15x^4 - 12x^2 - 3Now, to find the relative maxima and minima, we must solve for f'(x)=0 and f''(x) !=

0.Therefore, we have: f'(x)= 15x^4 - 12x^2 - 3= 3(5x^4 - 4x^2 - 1)We have to solve for the above equation: f'(x) = 0Or

3(5x^4 - 4x^2 - 1) = 0Or 5x^4 - 4x^2 - 1 = 0. We can solve the above equation by substituting t=x^2. Hence we get:5t^2 -

4t - 1 = 0Now, using the quadratic formula, we get: t = (4 ± √36)/10So, t = (2 ± √5)/5Now, we know that f''(x) = 60x^3 -

24x.We can substitute the value of x in f''(x) to check whether the given value of x is a relative maximum or not. When

we substitute x = -√5/5, we get f''(-√5/5) = -24(√5)/5 < 0Hence, x = -√5/5 is a relative maximum. Therefore, the correct

option is b. -√5/5.

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[tex]\tt Step-by-step~explanation:[/tex]

The two red ticks indicate that those lines are the same length (Isosceles triangle).

Since the two lines are the same length, then that means that both of the angles are the same measure, too. One angle is measured at 71, so that means x = 71.

[tex]\Large\boxed{\tt Our~final~answer:~x=71^o}[/tex]

Answer:

answer is c mark brainliest pls

Step-by-step explanation:

Answer:

12 ft

Step-by-step explanation:

15x2=30 6x2=12 simple

The maximum mass of the water bug to avoid sinking is approximately 0.079 grams.

To determine the maximum mass of the water bug that avoids sinking, we need to consider the buoyant force acting on it. The buoyant force is equal to the weight of the water displaced by the bug.

Calculate the volume of water displaced:

The bug's weight is balanced by the buoyant force, so the volume of water displaced is equal to the volume of the bug.

Each leg has a length of 5 mm, which means the total height of the bug is 5 mm. Assuming the cross-sectional area of the bug is constant along its height, we can use the formula for the volume of a cylinder to calculate the volume:

Volume = π * radius^2 * height

Since each leg is cylindrical, the radius would be half the leg's diameter, which is 5 mm (or 0.005 m).

Therefore, the volume of water displaced by the bug is:

Volume = π * (0.005 m)^2 * 0.005 m

Calculate the weight of the water displaced:

The weight of the water displaced is equal to the buoyant force acting on the bug.

Weight of water displaced = density of water * volume of water displaced * acceleration due to gravity

The density of water is approximately 1000 kg/m³, and the acceleration due to gravity is approximately 9.8 m/s².

So, the weight of the water displaced is:

Weight of water displaced = 1000 kg/m³ * Volume * 9.8 m/s²

Calculate the maximum mass of the bug:

The maximum mass of the bug is the mass at which its weight equals the weight of the water displaced:

Maximum mass = Weight of water displaced / acceleration due to gravity

Maximum mass = (1000 kg/m³ * Volume * 9.8 m/s²) / 9.8 m/s²

Now, let's plug in the values and calculate the maximum mass of the bug:

python

import math

radius = 0.005  # in meters (5 mm)

height = 0.005  # in meters (5 mm)

density_water = 1000  # in kg/m³

acceleration_due_to_gravity = 9.8  # in m/s²

volume = math.pi * radius**2 * height

weight_of_water_displaced = density_water * volume * acceleration_due_to_gravity

maximum_mass = weight_of_water_displaced / acceleration_due_to_gravity

maximum_mass_grams = maximum_mass * 1000  # converting to grams

print("Maximum mass of the bug to avoid sinking:", maximum_mass_grams, "grams")

Using the above calculations, the maximum mass of the water bug to avoid sinking is approximately 0.079 grams.

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Answer:

25

Step-by-step explanation:

15 divided by 3 is 5. Meaning, each bracelet cost $5. 2 bracelets cost 10 more dollars since 5x2 is equal to $10. 15+10=25

Step-by-step explanation:

using the quadratic formula......

Hi there!

How are you?

Answer:

[tex]\boxed{x = + \sqrt{5} |Or| x = 1 - \sqrt{5} }[/tex]

Step-by-step explanation:

First you have to use quadratic formula with [tex]a=1, b=-2, c=-4.[/tex]

[tex]x = \frac{-b \± \sqrt{b^2 -4ac} }{2a}[/tex]

[tex]x = \frac{-(-2) \± \sqrt{(-2)^2 - 4(1)(-4)} }{2(1)}[/tex]

[tex]x = \frac{\sqrt{^2\± \sqrt{20} } }{2}[/tex]

[tex]x = + \sqrt{5}[/tex] or [tex]x = 1 - \sqrt{5}[/tex]

Hvae a good day/night!

Answer:

what am I supposed to do I dont understand

We have proved that 1*1! + 2*2! + ... + n*n! = (n + 1)! -1 is true for all positive integers n.

Given expression is: 1*1! + 2*2! + ... + n*n! = (n + 1)! -1

We need to prove this equation for n positive integers.

Let's prove this by induction, Base Case:

For n=1,

1*1! = (1+1)! - 1

=> 1 = 2 - 1

=> 1 = 1

The base case is true.

Inductive Step:

Let's assume that the given expression holds for some k, that is:

1*1! + 2*2! + ... + k*k! = (k + 1)! - 1

Now we will prove that the same equation holds for k+1, that is:

1*1! + 2*2! + ... + (k+1)*(k+1)! = (k + 2)! - 1

By using the inductive hypothesis, we can replace the sum up to k with (k+1)! - 1, that is:

(k+1)! - 1 + (k+1)*(k+1)! = (k+1)! - 1 + (k+1)!

We can take (k+1)! common from the above equation. That is:

(k+1)![(k+1) - 1 + 1] = (k+1)! * (k+2) => (k+2)! - (k+1)!

= (k+1)! * (k+2) - (k+1)!

= (k+1)!(k+2-1)

= (k+1)!*k+1

That is: 1*1! + 2*2! + ... + (k+1)*(k+1)! = (k + 2)! - 1

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Answer:

[tex]\huge\boxed{\sf Isosceles \ triangle}[/tex]

Step-by-step explanation:

Here, the triangle has two equal sides and two equal angles. So, the type of triangle shown is an isosceles triangle.

[tex]\rule[225]{225}{2}[/tex]

The length of LM in terms of x and y can be determined using the properties of similar triangles. It is equal to x^2/(x + y).

The length of LM in terms of x and y is (x^2*y)/(x^2 + y^2).

In a trapezoid ABCD with right angles at B and D, the diagonals AC and BD intersect at point X. To find the length of LM, we can consider the similar triangles formed. Since LM is parallel to AB, we have similar triangles LXB and AXD. Similarly, we have similar triangles MXC and CXA.

Let's denote the length of LM as l. Using the similarity ratio of the triangles, we can write:

l/(x - l) = y/x    and    l/(y - l) = x/y\

Cross-multiplying these equations and simplifying, we get:

l^2 = xy(x + y) / (x^2 + y^2)

Taking the square root of both sides, we have:

l = sqrt(xy(x + y) / (x^2 + y^2))

Simplifying further, we get:

l = (x^2 * y) / (x^2 + y^2)

Therefore, the length of LM in terms of x and y is given by (x^2 * y) / (x^2 + y^2).

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Answer:

[tex] \huge{ \bold{ \boxed{ \sf{ \frac{11}{36} }}}}[/tex]

Step-by-step explanation:

[tex] \sf{ \: \frac{11}{12} \div 3}[/tex]

If any number or fraction is divided by a fraction , we multiply the dividend by the reciprocal of the divisor. Reciprocal of any number or fraction can be obtained by interchanging the position of numerator and denominator .

[tex] \mapsto{ \sf{ \frac{11}{12} \times \frac{1}{3} }}[/tex]

To multiply one fraction by another , multiply the numerators for the numerator and multiply the denominators for its denominator

[tex] \mapsto{ \sf{ \frac{11 \times 1}{12 \times 3} }}[/tex]

[tex] \mapsto{ { \sf{ \frac{11}{36} }}}[/tex]

[tex] \mapsto{ \boxed{ \sf{ \frac{11}{36} }}}[/tex]

Hope I helped!

Best regards! :D

~[tex] \sf{TheAnimeGirl}[/tex]

The division of the fraction gives the result as 11/36.

To calculate 11/12 divided by 3, express it as a fraction and then perform the division:

11/12 ÷ 3

To divide a fraction by a whole number, multiply the numerator by the reciprocal of the divisor (in this case, 3).

= 11/12 * (1/3)

Now, let's multiply the numerators and the denominators:

= (11 * 1) / (12 * 3)

= 11/36

Therefore, 11/12 divided by 3 is equal to 11/36.

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The solution to the given integral is:

-1/3 ln|x - 1| + 4/3 ln|x + 2| + (1/3) x^2 + 4/9 (1/(x - 1)) + C

Partial fraction decomposition can be used to simplify an integrand and make integration easier.

The following steps should be followed to solve the given integrals:

1. Integral 1/x^2 - 16 dx:

Let f(x) = 1/x^2 - 16. Then, we can represent f(x) as:

f(x) = A/(x - 4) - B/(x + 4)

Now, A(x + 4) - B(x - 4) = 1

By substituting x = 4, we get A = - 1/8

Similarly, by substituting x = - 4, we get B = 1/8

Thus, the partial fraction decomposition of f(x) is:

f(x) = - 1/8 (1/(x - 4)) + 1/8 (1/(x + 4))

Hence, the integral of f(x) is given by: ∫f(x) dx = - 1/8 ln|x - 4| + 1/8 ln|x + 4| + C

Therefore, the solution to the given integral is: -1/4arctanh(x/4) + C2.

Integral x^2 + 132x + 132/x^3 - 4x dx: Let f(x) = x^2 + 132x + 132/x^3 - 4x. Then, we can represent f(x) as:

f(x) = Ax + B/x + C/x^2 + D/(x + 2) + E/(x - 2)

Now, A(x^2 - 4) + B(x^2 + 2x - 8) + C(x + 4) + D(x - 2) + E(x + 2) = x^2 + 132x + 132 By equating the coefficients, we get A = 34, B = 4, C = 94, D = - 13, and E = 13 Thus, the partial fraction decomposition of f(x) is:

f(x) = 34x/3 - 4/3 (1/x) + 47/2 (1/x^2) - 13/2 (1/(x + 2)) + 13/2 (1/(x - 2)) Therefore, the integral of f(x) is given by:  ∫f(x) dx = 17x^2 - 4 ln|x| - 47/2 (1/x) - 13 ln|x + 2| + 13 ln|x - 2| + C

Thus, the solution to the given integral is: 17x^2 - 4 ln|x| - 47/2 (1/x) - 13 ln|x + 2| + 13 ln|x - 2| + C3.

Integral x^2 - x + 3/x^2 + x - 2 dx

Let f(x) = x^2 - x + 3/x^2 + x - 2.

Then, we can represent f(x) as f(x) = A/(x - 1) + B/(x + 2) + Cx + D/(x - 1)^2 Now, A(x + 2)(x - 1) + B(x - 1)^2 + Cx(x - 1)(x + 2) + D(x + 2) = x^2 - x + 3 By equating the coefficients, we get A = - 1/3, B = 4/3, C = 2/3, and D = 4/9 Thus, the partial fraction decomposition of f(x) is

f(x) = - 1/3 (1/(x - 1)) + 4/3 (1/(x + 2)) + 2/3 x + 4/9 (1/(x - 1)^2)

Therefore, the integral of f(x) is given by

∫f(x) dx = - 1/3 ln|x - 1| + 4/3 ln|x + 2| + (1/3) x^2 + 4/9 (1/(x - 1)) + C

Thus, the solution to the given integral is: -1/3 ln|x - 1| + 4/3 ln|x + 2| + (1/3) x^2 + 4/9 (1/(x - 1)) + C

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Answer:

your answer

hope this is right

Answer:

5

Step-by-step explanation:

[tex]( {4}^{x) {}^{3} } = {4}^{15} \\ {4}^{3x} = {4}^{15} \\ 3x = 15 \\ x = 5[/tex]

Answer:

26

Step-by-step explanation:

the function is f(x), and we need to find f(-2). the only difference between the two terms i gave is the -2 replacing the x. this means that you must replace every x in the first equation with -2. this makes the new function f(-2)=-9(-2)+8. after multiplying the -9 and -2 and adding that product to 8, you come up with your answer: 26.

The value of the function f(x) = - 9x + 8 at x = -2, and will be 26.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function is given below.

f(x) = - 9x + 8

The value of the function at x = -2, and will be

f(-2) = - 9(-2) + 8

f(-2) = 18 + 8

f(-2) = 26

The value of the function f(x) = - 9x + 8 at x = -2, and will be 26.

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Answer:

4 - 6x - 2 = -2(3x - 1)

This is

2 - 6x = -6x + 2

So, 0 = 0

Infinite solutions! :)

To forecast using data that has seasonality, one commonly used method is seasonal decomposition of time series (STL). This method separates the time series data into three components: trend, seasonality, and residuals. By isolating the seasonal component, you can forecast future values by extrapolating the pattern observed in previous seasons.

Another approach is the use of seasonal autoregressive integrated moving average (SARIMA) models. SARIMA models are an extension of ARIMA models that incorporate seasonal patterns. These models capture both the trend and seasonality in the data and can be used to make forecasts.

To control volatility in various time series models, a common technique is to use a volatility model, such as the generalized autoregressive conditional heteroskedasticity (GARCH) model. This model estimates the volatility of the time series by incorporating past volatility and squared residuals. By modeling and forecasting the volatility, you can better understand and manage the potential fluctuations in the time series data.

A simple moving average method is a technique used to smooth out fluctuations and identify trends in time series data. It involves calculating the average of a fixed number of data points, often referred to as the window size or period. As new data becomes available, the oldest data point in the window is dropped, and the newest data point is included in the calculation. This process is repeated for each subsequent data point. The resulting moving average values can provide insights into the overall trend of the data, helping to identify patterns or changes over time.

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Answer:

[tex]\large\boxed{\textsf{Acute Angle.}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked what type of angle is an 11}^{\circ} \textsf{angle.}[/tex]

[tex]\textsf{There are a few types of angles. Let's review them.}[/tex]

[tex]\large\underline{\textsf{Types of Angles:}}[/tex]

[tex]\textsf{Acute Angles are angles less than 90}^{\circ}.[/tex]

[tex]\textsf{Right Angles are angles equal to 90}^{\circ}.[/tex]

[tex]\textsf{Obtuse Angles are angles less than 180}^{\circ}, \ \textsf{but greater than 90}^{\circ}.[/tex]

[tex]\textsf{Straight Angles are angles equal to 180}^{\circ}.[/tex]

[tex]\textsf{Reflex Angles are angles greater than 180}^{\circ}, \ \textsf{but less than 360}^{\circ}.[/tex]

[tex]\textsf{Because our angle is less than 90}^{\circ}, \ \textsf{this angle is Acute.}[/tex]

Answer:

-18 > 17

Step-by-step explanation:

-2(12.8) + 6 > 17 (don't have the equal greater than sign) Simplify

-24 + 6 > 17

-18 > 17