Calculate the geometric center of the graph the function

The general solution to the differential equation y'' + 2y = −18x^2e^(2x) by undetermined coefficients is y = (-9x^2)e^(2x).

The given differential equation is y'' + 2y = −18x^2e^(2x)

To solve this equation by undetermined coefficients, we first find the characteristic equation of the homogeneous equation, which is r^2 + 2 = 0.

The solutions to this equation are r = i and r = -i. Therefore the general solution to the homogeneous equation is yh(x) = c1 cos(x) + c2 sin(x)

Now, we use the method of undetermined coefficients to guess the form of the particular solution. Since the non-homogeneous term is −18x^2e^(2x), we guess that the particular solution is of the form

yp = (Ax^3 + Bx^2)e^(2x) + Cx^2e^(2x).

Substituting this into the differential equation, we get

y'' + 2y = (6Ax + 2B)e^(2x) + 2Cxe^(2x) = −18x^2e^(2x)

Equating the coefficients of the like terms, we get:

6A = 0, 2B = −18, and 2C = 0

Solving for A, B and C, we get A = 0, B = −9 and C = 0

Therefore, the general solution to the differential equation y'' + 2y = −18x^2e^(2x) by undetermined coefficients is y = (Ax^3 + Bx^2)e^(2x) + Cx^2e^(2x) = (-9x^2)e^(2x)

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If Colah Company purchased $2,000,000 of Jackson, Inc., 6% bonds at par on July 1, 2021. The journal entries for the purchase of the Jackson bonds on July 1 is: Debit Available-for-sale securities $2,000,000

Credit Cash $2,000,000.

Journal entry is used by companies to record their day to day business transaction.

July 1 2021

Debit Available-for-sale securities $2,000,000

Credit Cash $2,000,000

December 31 2021

Debit Cash $60,000

Credit Interest income  $60,000

(6% ×$2,000,000 / 2)

December 31 2021

Debit Available-for-sale securities $300,000

Unrealized Gain - Other comprehensive income $300,000

($2,000,000 - $2,300,000)

June 30 2022

Debit Cash $60,000

Credit Interest income  $60,000

(6% ×$2,000,000 / 2)

The entry necessary upon sale of the Jackson bonds on July 1, 2022 is:

July 1 2022

Debit Available-for-sale securities  $2,300,000

Unrealized Gain-Other comprehensive income account $300,000

Credit Cash $1,800,000

Credit Realized Loss on the sale of Available-for-sale securities $200,000  

[$1,800,000 - $2,000,000= $200,000 (Realized Loss)]

2. Table to show the effect of the Jackson bonds on Colah’s net income,

                             2021                   2022                       Total

Net Income       $60 ,000        ($140,000)              ($80,000)

( 60,000 - $200,000= -$140,000)

OCI                       $300,000                                         $300,000

Comprehensive Income $360,000 ($140,000) $220,000

Therefore the  journal entries for the purchase of the Jackson bonds on July 1 is: Debit Available-for-sale securities $2,000,000

Credit Cash $2,000,000.

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Pre-algebra is a primary branch of algebra designed to prepare students for a standard high school algebraic course

Real number system, linear connections, functions, linear equations, systems of equations, geometric concepts such as transformations, Pythagorean Theorem and angle relationships, and scatter plots are all studied.You will learn about and investigate subjects such as integers, order of operations, algebraic expressions, one and two-step equations, proportions, percents, probability, geometry, and linear equations in Pre-Algebra.

Pre-algebra classes are intended to prepare pupils for a typical algebraic curriculum in high school. Integers, fractions, square roots, step equations, linear equations, and decimals are introduced to students. They will also learn how to use variables to solve basic problems.

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The rocket reaches a maximum height of 1045.6 feet.

The height of the rocket under free fall is described by a parabola and parabolas are explained by second order polynomials, whose form are:

y = a · x² + b · x + c

Where:

The maximum height can be found by means of discriminant of the quadratic formula associated with following variant:

a · x² + b · x + (c - y) = 0

Discriminant

b² - 4 · a · (c - y) = 0

b² = 4 · a · (c - y)

b² / (4 · a) = c - y

y = c - b² / (4 · a)

If we know that a = - 16, b = 246 and c = 100, then the maximum height reached by the rocket is:

y = 100 - 246² / [4 · (- 16)]

y = 1045.563 ft

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Answer:

are the capital letter formed by three line segments.

$0.14 is the selling price of each egg.

percentage, a relative value indicating hundredth parts of any quantity.

Given that shopkeeper buys 1800 eggs  $1.20 per dozen.

1 dozen = 12 eggs

So 1.20 ÷ 12 = $0.1 cost of one egg

Total cost (C) 1800×0.1 = $180

1800×0.95 = 1710 eggs to be sold

Profit % = 100×(SP - C)/C

33 = 100×(SP - 180/180

SP = $239.4

239.4 ÷ 1710 = $0.14 is the selling price of each egg.

Hence, $0.14 is the selling price of each egg.

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Answer:

I beleive 4

Step-by-step explanation:

let me know if im wrong

Answer:

We can set up an equation using the information provided. Let x be the cost to clean a pair of pants.

The cost to clean 4 shirts is 4*2.95 = $11.80

The cost to clean 5 pants is 5x

The total cost is $11.80 + 5x = $29.05

So, we can represent the cost to clean a pair of pants as:

x = $29.05 - $11.80 / 5

This number sentence shows the cost to clean a pair of pants is x = $4.81

Answer:

D) y = 5/3x - 7

A) 5/3

Step-by-step explanation:

5x - 3y = 21   Subtract 5x from both sides

5x - 5x - 3y = -5x + 21

-3y = -5x + 21  Divide all the way through by -3

[tex]\frac{-3y}{-3}[/tex] = [tex]\frac{-5}{-3}[/tex] x + [tex]\frac{21}{-3}[/tex]

y = [tex]\frac{5}{3}[/tex] x = 7

The slope is the number before the x 5/3

One solution of the following system is:

A. (–6, 0)

The above mathematical expression requires that we use the substitution formula to obtain the correct value.

2y - 2x = 12     ... 1

x² + y² = 36     ... 2

For equation 1

2y = 12 + 2x

          2

y = 6 + x           ... 3

Now we substitute equation 3 in equation 2

x² + (6 + x)² = 36

= x² + 36 + 12x + x² = 36

2x² + 12x = 36 -36

2x² + 12x = 0

2x (x + 6) = 0

x = 0, -6

When we substitute x for 0 in the third equation, we will have

y = 6 + 0 = 6

If we substitute x to be -6 in the third equation, we will arrive at

y = 0.

Therefore, the two solutions that can be obtained are (0,6) and (-6,0) as seen in the first option.

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The volume of this cone is equal to: A. 2,411.5 cm³.

Mathematically, the volume of a cone can be calculated by using this formula:

V = 1/3 × πr²√(l² - r²)

Radius = diameter/2 = 24/2 = 12 cm.

Substituting the given parameters into the volume of a cone formula, we have;

Volume of a cone, V = 1/3 × 3.142(12)²√(20² - 12²)

Volume of a cone, V = 1/3 × 3.142(144)×√(400 - 144)

Volume of a cone, V =  2,411.5 cubic cm.

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When w=12 and x=1/2, the value of the given equation 13-0.75w +8x is 8.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The product of 8 and 3 equals 11. 8 + 3 is an expression.

Here,

given expression,

=13-0.75w +8x

x=1/2

w=12

=13-0.75*12 +8*1/2

=8

The value of given expression 13-0.75w +8x when w=12 and x=1/2 is 8.

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The statement that is true about the ratios comparing the width and length of each painting is:

The paintings' width to length ratios are equal because the ratio 4 to 6 is equal to the ratio 2 to 3.

A ratio is a fraction which compares the values of two numbers. Such that they can be expressed as a ratio of one to the other. Example is the ratio of a to b which can be expressed as; a:b or a/ b.

From the first dimension of the canvas size, we have;

length = 6 feet

width = 4 feet

So that,

the ratio comparing the width and length = 4/ 6

                                                       = 0.6667

From the second dimensions of the canvas size, we have;

length = 3 feet

width = 2 feet

the ratio comparing the width and length = 2/ 3

                                                        = 0.6667

Therefore, the statement that is true about the ratios comparing the width and length of each panting is; The paintings' width to length ratios are equal because the ratio 4 to 6 is equal to the ratio 2 to 3.

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The area of the given triangle is 45 square units.

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

In the given triangle, measure of the side base is 10 units and height is 9 units.

Here, area of a triangle = 1/2 ×10×9

= 45 square units

Therefore, the area of a triangle is 45 square units.

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Answer:

The lateral surface of an object is all of the sides of the object, excluding its base and top (when they exist). The lateral surface area is the area of the lateral surface. This is to be distinguished from the total surface area, which is the lateral surface area together with the areas of the base and top.

Answer:

To find out how many paddle balls will be in each hopper, you can divide the total number of paddle balls by the number of hoppers.

paddle balls ÷ hoppers = paddle balls per hopper

2798 ÷ 40 = 69.95

So there will be approximately 69.95 paddle balls in each hopper. Since it's not possible to put 0.95 of a paddleball in a hopper, you can round it to the nearest whole number. This means each hopper will have 70 paddleballs.

Step-by-step explanation:

Answer: We can use the concept of conditional probability to find the probability that a student who passed the first test also passed the second. Conditional probability is the probability of an event occurring given that another event has already occurred.

The probability that a student who passed the first test also passed the second is the probability of both events occurring (passing both tests) divided by the probability of the first event occurring (passing the first test).

We can use the information provided to calculate this probability:

Probability of passing both tests = 0.45 (45%)

Probability of passing the first test = 0.60 (60%)

Probability of passing both tests given that the student passed the first test = (Probability of passing both tests) / (Probability of passing the first test) = 0.45 / 0.60 = 0.75

So the probability that a student who passed the first test also passed the second is 0.75 or 75%.

It means, if we know that a student passed the first test, there's a 75% chance that the student also passed the second test.

Step-by-step explanation:

f(1) = -1

Quadratic equations form the shape of a parabola, which looks like a U-shape.

Graph

To find f(1) we need to find the y-value when x = 1. To do this, we can just look at the graph. Find where on the graph x = 1, then look for where the graph intersects this value. This graph has an x value of 1 when y = -1. We can see this at the coordinate point (1,-1). Thus, f(1) = -1.

Equation

We can also solve this using the equation of the function. This function is represented by f(x) = x² - 2. Now, to find f(1), plug 1 in for x.

This also shows that f(1) = -1.

Answer:  

To express the deaths per capita as a decimal, we can divide the number of new construction accidents (deaths) by the population:

4172/11300000 = 0.00037

Rounded to 6 decimal places, the deaths per capita as a decimal is 0.00037

To express the deaths per capita in scientific notation, we can use the decimal value found above and convert it to scientific notation:

3.7 x 10^-4

To express the deaths per capita as a per 100,000 value, we can multiply the decimal value by 100,000:

0.00037 * 100,000 = 37

So the deaths per capita are 37 deaths per 100,000 people.

Step-by-step explanation:

The sum of the interior angles of a decagon is 1440 degrees.

The inner angles of a normal decagon are equal. Every interior angle in a normal decagon is 144° in length because 1440°/10 = 144°. Additionally, each external angle measures 36°.

A decagon is a ten-sided polygon, or ten-gon, in geometry. A basic decagon's inner angles add up to 1440°, and its external angles add up to 360°.

A decagon is a polygon with ten sides, ten internal angles, and ten vertices, or points where the sides meet. There are 10 equal-length sides and 10 equal-sized interior angles in a normal decagon. The sum of all the angles, each of which is 144°, is 1,440°.

A decagon is a polygon having 10 sides.

The sum of interior angles of a polygon having 'n' sides is (2n- 4) × 90°.

sum of interior angles of a decagon= (204) × 90°

= 16 x 90°

= 1440°

Therefore, the sum of the interior angles of a decagon is 1440 degrees.

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Step-by-step explanation:

Let’s use the equation: 3|2x-1|-8=-14

3(|2x−1|)−8=−14

Step 1: Add 8 to both sides.

3(|2x−1|)−8+8=−14+83(|2x−1|)=−6

Step 2: Divide both sides by 3.3. (|2x−1|)3=−63|2x−1|=−2

Step 3: Solve Absolute Value. |2x−1|=−2

No solutions. (Absolute value cannot be less than 0.)

The ratio of miles to hours is 24 to 2, which can be written as 24:2 or 12:1.

What is the ratio?

A ratio is a mathematical comparison of two or more quantities. It is used to show the relationship between the sizes of different quantities or amounts. It is typically expressed as a ratio of two numbers, such as 24:2, with a colon separating the numbers.

The ratio of miles to hours is 24 to 2. This can also be written as 24:2 or 12:1. It means that for every 24 miles, 2 hours are required to travel that distance.

Hence, The ratio of miles to hours is 24 to 2, which can be written as 24:2 or 12:1.

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Example of dependent events and independent events and their probabilities are as given below.

1. a. Two independent events that I know the probability of are:

Rolling a fair die and getting a 4 (probability of 1/6)

Flipping a fair coin and getting heads (probability of 1/2)

b. I know these events are independent because the outcome of one event does not affect the outcome of the other event. The outcome of rolling a die does not affect the outcome of flipping a coin, and vice versa.

c. The probability of both events occurring is (1/6) × (1/2) = 1/12

2a. Two dependent events:

i. Drawing a red card from a deck of cards and then drawing another card (without replacement)

ii. Drawing a red ace and then drawing another red card (without replacement)

b. I know these events are dependent because the outcome of the first event affects the outcome of the second event. The probability of the second event depends on the outcome of the first event.

c. These dependent events might require a different method for calculating the probability of both events occurring, such as conditional probability.

The probability of both events occurring would be P(A and B) = P(A) × P(B|A)

where P(A) is the probability of the first event and P(B|A) is the probability of the second event given that the first event has occurred.

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Answer:

14z + 12x is not equivalent to any of the others

2 + (7z + 6x) is not equivalent to any of the others

2(7z + 6x) is equivalent to 14z + 12x

9x + 3(4z + x) + 2z is not equivalent to any of the others

Step-by-step explanation:

14z + 12x is equivalent to itself

2 + (7z + 6x) is equivalent to (7z + 6x) + 2

2(7z + 6x) is equivalent to 14z + 12x

9x + 3(4z + x) + 2z is equivalent to itself.

Answer:

=4-347-12-8-7+27

=-343

*Mark me brainliest -_- *_*

Answer: (4-347-12)-(8+7-27)= -343

40

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Answer:

Step-by-step explanation:

its 40

the bisectors of two supplementary angles are perpendicular to each other is proved along with the given diagram.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

Here, we have,

from the given diagram we get,

∠BOP=x  &   ∠AOP=180-x

and, ∠NOP=x/2   &   ∠MOP=(90-x/2)

Now,

∠MON=∠MOP+∠NOP

          =90-x/2 + x/2

          =90

Hence, it is proved that  the bisectors of two supplementary angles are perpendicular to each other.

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To the nearest percentage point, Lupita's retirement funds increased by 44% from June to July.

A percentage is a term used in mathematics to describe a value or ratio that may be expressed as a fraction of 100. If we need to calculate a percentage of a number, we should first divide it by 100 before multiplying it by the remainder. Consequently, the percentage refers to a portion per hundred.

Given that Lupita had $115 in her bank account at the beginning of June

The amount Lupita had set aside climbed to $165 in July.

We are expected to calculate the percentage growth in money.

% increase

[tex]= {(165 - 115) / 115 } × 100 = 43.48%. ≈ 44%[/tex]

To the nearest percentage point, Lupita's retirement funds increased by 44% from June to July.

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Answer: x =2

Step-by-step explanation: Since the two triangles have to shared sides then all sides must be equal so 9x-12=3x. -6x=-12 and x =2

Answer:

9x=12

so

x=12/9 = 4/3

and

The linear system could the graph represent is, x + y = 2 & 2x + 2y = 8

So, Option D is correct.

The equation of a straight line is a relationship between x and y coordinates, The equation of a straight line for given two points  is y-y₁ = y₂-y₁/x₂-x₁(x-x₁)

Given that,

The graph of  linear system

first line intersects the  x & y   axes at (2,0) & (0,2) respectively

Similarly, second line intersects the  x & y   axes at (4,0) & (0,4) respectively

By using two point form of the line we can write equation for both the lines,

x + y = 2  _____ (1)

x + y = 4  _____ (2)

by multiplying 2 in equation  (2)

2x + 2y  = 8

Hence, The linear system is  x + y = 2 & 2x + 2y = 8

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