Please help me out with this!!​

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.

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:

[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:

∠A = 48°

Step-by-step explanation:

All angles in a triangle add up to 180°

Answer:

2500

Step-by-step explanation:

10,000/3,000=10/3

10x750=7500

7500/3=2500

For the given condition 2500 liters of carbonated water are needed to produce 750 bottles of soda.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, at a bottling plant, 10,000 liters of carbonated water are needed to produce 3,000 bottles of soda.

300 bottles of soda =  10,000 liters of carbonated water

By using the unitary method, we can determine the value of a single unit and, using that value, determine the value of the necessary number of units.

1 bottle of soda =  10,000 liters / 300

The amount of carbonated water needed to produce 750 bottles of soda is found as,

750 bottles of soda =  (10,000 liters / 300)×750

750 bottles of soda = 25,000 liters

Thus, for the given condition 2500 liters of carbonated water are needed to produce 750 bottles of soda.

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Answer:

Step-by-step explanation:

Given equations

Solving the first equation for x:

Then solving for y:

Solution set:

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

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:

answer is c mark brainliest pls

Step-by-step explanation:

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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To show that S+ is a subspace of[tex]R^n,[/tex] where S+ is the set of vectors orthogonal to every vector in S, we need to verify that S+ satisfies the three properties of a subspace: it contains the zero vector, it is closed under addition, and it is closed under scalar multiplication.

First, we know that the zero vector, denoted as 0, is orthogonal to every vector in S since the dot product of any vector in S with the zero vector is always zero. Therefore, the zero vector is an element of S+.

Next, we need to show that S+ is closed under addition. Let w₁ and w₂ be vectors in S+. For any vector v in S, we have (v · w₁) = 0 and (v · w₂) = 0. Now, consider the vector w = w₁ + w₂. We need to show that (v · w) = 0 for all v in S. Using the linearity property of the dot product, we have (v · w) = (v · w₁) + (v · w₂) = 0 + 0 = 0. Therefore, w is orthogonal to every vector in S, and thus w is an element of S+.

Lastly, we need to show that S+ is closed under scalar multiplication. Let c be a scalar and w be a vector in S+. For any vector v in S, we have (v · w) = 0. Now, consider the vector cw. Using the linearity property of the dot product, we have (v · cw) = c(v · w) = c(0) = 0. Therefore, cw is orthogonal to every vector in S, and thus cw is an element of S+.

Since S+ contains the zero vector, is closed under addition, and is closed under scalar multiplication, we can conclude that S+ is a subspace of [tex]R^n[/tex]

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The monthly payment of the loan is approximately $299.71. The monthly payment (M) of the loan can be calculated using the formula M L where L is the loan amount (in dollars), i is the monthly interest rate (in decimal form), and r is the term (in months).

Therefore, to calculate the monthly payment, we first need to find the monthly interest rate (i) and the term (r). The annual interest rate is 6%, so the monthly interest rate is 6/12 = 0.5%.

The loan term is 3 years, which is equivalent to 3 x 12 = 36 months.

Now, we can substitute the values into the formula:

M = (L*i) / (1 - (1+i)^(-r))where L = $10,000, i = 0.5%, and r = 36M = (10000*0.005) / (1 - (1+0.005)^(-36))

M ≈ $299.71

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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]

Answer:

22.472

Step-by-step explanation:

Answer:

i think 10.90

Step-by-step explanation:

Answer:

im just tryna get points  

Step-by-step explanation:

Answer:

area: 20 i think

perimeter: 18

pic below

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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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:

the 4th one

Step-by-step explanation:

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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Answer:

$31 dollars every week.

Answer:

108 in

Step-by-step explanation:

Step 1: Find conversion

1 ft = 12 in

Step 2: Convery

9 ft · 12 in/ft = 108 in

Answer:

12 ft

Step-by-step explanation:

15x2=30 6x2=12 simple

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

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:

32

Step-by-step explanation:

12 * (3 + 2²) / 2 - 10

12(3 + 4) / 2 - 10

12(7) / 2 - 10

84 / 2 - 10

42 - 10

32

Best of Luck!

Answer:

Step-by-step explanation:

[tex]12\times (3+2^2)\div 2-10\\\\Follow\:the\:PEMDAS\:order\:of\:operations\\\\\mathrm{Calculate\:within\:parentheses}\:\left(3+2^2\right)\:\\:\quad 7\\\\=12\times \:7\div \:2-10\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:12\times \:7\div \:2\:\\:\quad 42\\\\=42-10\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:42-10\:\\:\quad 32[/tex]

Answer:

1.8 = 18/10 = 9/5

0.2 = 2/10 = 1/5

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Thank You!!

Answer:

15: 5*3

30: 3*10 15*2 5*6

18: 6*3 9*2

17: none??

-30^2 : -30*(-30)=-900

12^4 : 12*12*12*12= 20736

11^3 : 11*11*11=1331

Step-by-step explanation:

you have to find every pair of numbers that when multiplied give for example number 15( so thats 15*3)

ex: 12^4: base is 12 and power is 4, we multiply base 12 4 times, so thats going to be 12*12*12*12=20736

Answer:

27.  1,3,5,15

28.  1,2,3,5,6,10,15,30

29.  1,2,3,6,9,18

30.  1,17

--------------------------------------

31.  30x30=900

32.  12x12x12x12= 20,736

33. 11x11x11= 1331

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