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The solution to the differential equation y'' + y = sin2x is y = -2sin2x + (Acos2x + Bsin2x).

This differential equation can be solved by the method of variation of parameters. This method involves finding two arbitrary functions, U and V, such that U' = V and V' = -U + sin2x, so that the general solution of the differential equation is y = U + V. Solving the two equations yields U = Acos2x + Bsin2x and V = -2sin2x, where A and B are arbitrary constants. Substituting U and V into the general solution of the differential equation yields the final solution y = -2sin2x + (Acos2x + Bsin2x).

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The two (2) possible locations of point F include the following: F. [7, 9.5].

In this scenario, line ratio would be used to determine the coordinates of the point on the directed line segment that partitions the segment into a ratio of 5 to 3.

Mathematically, line ratio can be used to determine the coordinates of F and this is modeled by this mathematical expression:

F(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

Given the following parameters:

Point (x, y)= (4, 11)

Point (x, y) = (8, 9)

m:n = 3:1

Substituting the given parameters into the line ratio formula, we have;

F(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

F(x, y) = [(3(8) + 1(4))/(3 + 1)],  [(3(9) + 1(11))/(3 + 1)]

F(x, y) = [(24 + 4)/(3 + 1)],  [(27 + 11)/(3 + 1)]

F(x, y) = [(28)/(4)],  [(38)/(4)]

F(x, y) = [7, 9.5]

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Answer:legs

Step-by-step explanation: I cannot give a explanation since it is simply math, anything adjacent to a right angle is called a leg.

Answer: the legs? or opposite and hypotenuse.

Step-by-step explanation:

The height of the mt. Everest in miles exists 5.499 miles.

By changing the unit of measurement, a quality can be expressed differently. In contrast to distance, which can be stated in miles, kilometers, feet, or any other unit of length, time can also be expressed in minutes rather than hours.

By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. The right conversion factor to an equal value must be used when a conversion is required. The correct conversion factor, for instance, is 12 inches to 1 foot when converting between inches and feet.

The height of the mt. Everest is : 29035 feet.

The unit conversion is given as :

5280 feet = 1 mile

1 feet = 1/5280 mile

So, 29035 feet =29035 × 1/5280 miles

29035 feet = 29035/5280 miles

29035 feet = 5.499 miles

So, the height of the mt. Everest in miles is 5.499 miles.

The complete question is:

In the Himalaya mountains along the border of Tibet and Nepal, mount Everest reaches a record height of 29,035 feet. how high is mt. Everest in miles? use the conversion equivalency of 1 mile = 5280 feet.

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Answer:  The height of the Mount Everest in miles is 5.499 miles

Step-by-step explanation:

1 miles = 5,280 feet

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Answer:

1.5 ft

Step-by-step explanation:

The area of a parallelogram is base times height.

So to find the height, you will need to use area/base

Small: 16.25/6.5=2.5 ft

Large: 34/8.5=4ft

4-2.5=1.5ft

The equation y^ = -2.5x + 222.5 models the amount of cholesterol, LDL, for a person in mg/dl, where x is the time spent exercising per day in minutes.

What in mathematics is a quadratic equation?

Definitions: x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

To find the amount of cholesterol for a person exercising 20 minutes a day, we need to substitute x = 20 into the equation:

y^ = -2.5(20) + 222.5

Solving this equation, we get:

y^ = -50 + 222.5

y^ = 172.5

So, the amount of cholesterol for a person exercising 20 minutes a day is 172.5 mg/dl.

Therefore, the answer is 172.5 mg/dl

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18x - 9 = 72 and x = 4.5 represents the same value as 3/5(30x - 15) =72.

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.

Here,

2x – 5 and 13 are expressions

The sign that connects these two expressions is “=”.

Given

x = 4.5

And equation

3/5(30x - 15) =72

Simplifying

90x/5 - 45/5 = 72

18x - 9 = 72     -----------(a)

18x = 81

x = 81/18

x = 4.5             ------------(b)

Equation (a) and (b) are among the equations given in the options.

Hence, from the above calculation equations 18x - 9 = 72 and x = 4.5 express the same value of x as 3/5(30x - 15) =72 .

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The wheel will travel 131.8cm in 3 rotations.

The radius of the wheel, r = 7cm

Number of rotations, n= 3

distance covered in 1 rotation= circumference of circle=2πr

distance covered in 3 rotation= 2πr x 3

where π=3.14(fixed)

=2 x 3.14 x 7 x 3

Distance=131.88cm

Therefore, the distance covered in 3 rotations is 131.88cm

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Answer:

132cm

Step-by-step explanation:

use formula 22/7 *diameter which is 7*2 getting the answer as 44.For three rotations multiply the answer by three

Answer:

simply do 70 divided by 12, then that divided by 3, in total it should take 1, 2, or 3 hours to read 3 books a month

Step-by-step explanation:

Answer:

well, you didnt give me any numbers or variables, so ill do it like  this. if the container is the size of a pint, and there are 8 runners, and a pint equals 16 fluid ounces, in turn it should end as that each runner gets 2 fluid ounces of energy drink

Step-by-step explanation:

a and d are non-zero and ad = bc for the system to be consistent for all possible values of f and g.

By definition, a system is consistent if there exists a set of solutions that satisfy the equations. In this system, the constants a, b, c, and d are the coefficients of the two equations. Since the system is consistent for all possible values of f and g, then the coefficients must satisfy certain conditions. For example, a and d must both be non-zero in order for the equations to be solvable. Additionally, the coefficients of both equations must be in proportion to each other, meaning that ad must equal bc. This is necessary for the equations to have the same slope, which is necessary for them to be solvable. Thus, we can conclude that a and d are non-zero and ad = bc for the system to be consistent for all possible values of f and g.

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A reflection in the line y = -2 and then translation of 2 units right will create the same area so option (C) will be correct.

f we shift the triangle anywhere then there will be no change in the area but if we apply the scale factor then since the dimension changes so its area will also change.

In all options, there is a scale factor so it will change area but in option C

A reflection in the line y = -2 reflection gives a mirror image about y = -2 but no changes in area then translation of 2 units right will shift triangle 2 units right but no effect in the area.

Hence "A reflection in the line y = -2 and then translation of 2 units right will create the same area".

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The predicted elevation of hikers at 145 minutes, based on the trend line equation, y = 8.77x + 686 is 1,958.

A trend line equation is the equation of a linear relationship, represented as y = mx + b.

In this linear equation, y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept.

y = 8.77x + 686, where x = 145 minutes

Therefore,

y = 8.77(145) + 686

y = 1,271.65 + 686

y = 1,957.65

y = 1,958

Thus, after 145 minutes of hiking, hikers' elevation will be 1,958 units.

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The correct answer is that we cannot conclude that being able to read is beneficial for them as there can be various cause and effect relation.

A research is conducted to collect information about a specific topic for the purpose of study. A group of population is asked to fill a survey form or answer questions based on the research topic.

This data is collected and analyzed to get the required result.

Here, in this question kindergarten students are the population from whom data is collected . Here, the conclusion is that having the ability to read and write from before only doesn't means they will have academic intelligence later.

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Answer:

C

Step-by-step explanation:

The angles at point A have to be congruent so that you have two congruent angles. and one congruent side, which give SAA.

From the image, we can see than angle B and angle D are congruent. We also know that line AC is congruent to itself since it shared between the two triangles. Since we need one more angle, that angle has to be angle A.

For triangle ACE, if BD ∥AE , then BA/CB = DE/CD is proved.

For given triangle ACE,

BD || AE                             ...............(Given)

∠4 ≅ ∠1 and ∠3 ≅ ∠2      ..............(Corresponding Angles Postulates)

ΔACE ~ ΔBCD                  .............(Angle-Angle Similarity Postulate)

CA/CB = CE/CD                ............(Definition of similar triangles)

CA = CB + BA, CE = CD + DE           ..........(Segment Addition Postulate)

(CB + BA)/CB = (CD + DE)/CD   ..........(Substitution Property of Equality)

CB/CB + BA/CB = CD/CD + DE/CD  .........(Addition of Fractions)

1 + BA/CB = 1 + DE/CD                  .............(Siplification of fractions)

BA/CB = DE/CD                   ...............(Subtraction Property of equality)

Hence proved.

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The general integral is provided by y = C1e-t + C2te-t + (1/2)(t2)e-t.

(m + 1)2 =0 is the characteristic polynomial for the differential equation y" +2y' + y = e-t.

Roots -1, -1. yh = C1e-t + C2te-t is the answer to the homogeneous equation at that point.

Use the method of variation of parameters, taking into account the independent integrals y1 = e-t, y2 = te-t, and Wronskian

W(t) = e-2t, to derive the specific integral related to f(t) = e-t.

Then, use the conventional formula yp = - y1(t)(Integral of Y2(t)f(t)dt/W(t)) +y

Obtain yp = (1/2)(t2)e-t for the given situation.

As a result, the general integral is provided by

y = C1e-t + C2te-t + (1/2)(t2)e-t.

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Answer:

$720

Step-by-step explanation:

The formula is:

A = P(1 + rt)

We know

P = $6000

r = 3% = 0.03

t = 4 years

A = 6000( 1 + 0.03 x 4) = $6720

Now we have to find the interest by taking

$6720 - $6000 = $720

So, he earns $720 in interest in 4 years.

The Binomial Expression is defined as the type of algebraic expression that consists of exactly two terms .

What is Binomial Expression ?

The algebraic expression which contains exactly only two terms is termed as  binomial expression . It is called a two term polynomial.

the binomial is also called a sum or a difference between two or more monomials. Binomial is the simplest form of a polynomial.

Some Examples of Binomial Expression are ⇒ [tex]4x^{2} +6y^{2}[/tex] , [tex]xy^{3} +xy[/tex] ;

Various Mathematical Operations can be performed on Binomial Expression such as Addition , Subtraction , Multiplication and Division .

and The  Equation that contains one or more binomial expression is called as a Binomial Equation.

The given question is incomplete , the complete question is

What is a Binomial Expression ?

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x2 - 3x - 5 = 0 has a unique solution of type -11, which is what the equation entails.

The "discriminant" is the value that aids in identifying the many types of solutions when using the quadratic formula to solve a problem. It is a unique function of a co-efficient in a mathematical equation (a quadratic equation), and the value it yields provides details about the roots of the equation. Calculating the discriminant involves square rooting the "b" term and subtracting four times the "a" term from the "c" term. Alongside "D," there is a (delta) that represents discrimination. A quadratic equation with two distinct real number solutions is said to have a positive discriminant. A quadratic equation with a discriminant of zero has repeated real number solutions. Both of the solutions are not real numbers, as indicated by a negative discriminant.

given

x2 - 3x - 5 = 0

D=b2−4ac

D= −32−4×1×5

D=92−20

D= −11

x2 - 3x - 5 = 0 has a unique solution of type -11, which is what the equation entails.

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Therefore, the inequality 1.85 < 15 can be used to find h.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance. For instance, let's say you have 225 and want to purchase a new bicycle that costs $250.

When the expression's variables and constants are given values, the calculation it describes yields the expression's value. In an algebraic expression, numbers can be represented by letters.

The inequality 1.85 < 15 can be used to find h, the number of mini-hamburgers Betsy and her sister bought. This inequality represents the constraint that the total cost of the mini-hamburgers (1.85h) must be less than the amount of money they have to spend (15). To solve for h, you would divide both sides of the inequality by 1.85, giving you h < 8.1, so h can be any number less than 8.1.

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By counting the numbers of figures after the decimal points before you locate the product and shifting the decimal point from the rear to the front in the order you previously counted it after you find the product, an estimation can help you place the decimal point in a product correctly.

A high number of a certain number is estimated to be the closest whole number or significant number.

When estimating, the use of decimal points aids in separating the fractional portion from the entire figure.

For instance, we have a total of three integers after the decimal point if we want to calculate the product of 4.23 and 2.1.

     4.23

×         2.1

  4  2  3

________

8  4  6    

8  8  8  3  

Therefore, we shall move the decimal point three places, working our way from the back to the front.

The result of 4.23 and 2.1 is 8.883 then.

We can therefore say that we completely understand how estimating helps you accurately set the decimal point in a product.

Therefore, by counting the numbers of figures after the decimal points before you locate the product and shifting the decimal point from the rear to the front in the order you previously counted it after you find the product, an estimation can help you place the decimal point in a product correctly.

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Correct question:

How does estimation help you place the decimal Point in a product correctly?

if a²+b²>c², the triangle is acute, if a²+b2²=c², the triangle is a right triangle,  and if a²+b²<c², the triangle is obtuse.

where a and b are the lengths of the two shorter sides of the triangle and c is the length of the longest side.

A right-angled triangle is a triangle with one of the angles at 90 degrees. A 90-degree angle is called a right angle, and hence the triangle with a right angle is called a right triangle.

An acute triangle has three angles that each measure less than 90°. In an acute-angled triangle, all three internal angles of the triangle are acute, that is, they measure less than 90°.

An obtuse triangle is a triangle with one angle that is greater than 90° degrees, it is not possible for a triangle to have more than one obtuse angle.

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Answer:

Step-by-step explanation:

a. we konw triangle have 180°

b. A straight line have 180°， so

∠abc=180-5x-12=168-5x,

∠bca=180-10x+37=217-10x

∠cab=180-9x-1=179-9x

then  add them all 564 - 24x = 180

c.384=24x, x=16

d.so ∠bca=217-10·16=57.

Answer:

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

Sum of exterior angles is 360°:

The exterior angle at vertex C is:

The ∠BCA is the linear pair with 123°:

The correct expression to represent the similarity of these two triangles is,

21/35 = x/30.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know two triangles are similar if the ratio of their corresponding sides is equal.

Therefore, The correct way to represent the similarity is,

21/35 = x/30.

We can solve for x here,

35x = 21×30.

5x = 3×30.

x = 3×6.

x = 18.

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Answer:

Step-by-step explanation:

we know the 30% off the marked price.

so the sale price is 60-60*30%=42

Answer:$42.00

Step-by-step explanation:

The ratio tells us how often one number is contained in another. In the class, there are six girls for every five boys. D is the right answer.

A ratio is an ordered pair of numbers a and b, expressed as a / b, where b is not equal to 0. A percentage is an equation in which two ratios are made equal to one another. For instance, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) One-fourth are boys and three-fourths are girls.

The ratio tells us how often one number is contained in another.

Considering that 96 of the 176 junior students are female. Consequently, the class's gender distribution is,

96 girls are present.

80 boys out of 176, or 96 boys.

Currently, the junior class's gender distribution is as follows:

Girls to Boys in Ratio

96 girls and 80 boys.

Divide the numerator and denominator by 16 to simplify.

Boys/Girls: 6 to 5.

Therefore, the answer is option d) 6:5.

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Step-by-step explanation:

i. AD = BC= 6cm (each two opposite sides are equal in length in parallelogram)

ii.DC=AB=9cm (each two opposite sides are equal in length in parallelogram)

iii.DCB=60 ,, bec DC and AB are parallel so their interior angles are supplementary their sum equals 180°

so DCB = 180-120=60°

iv.ADC=ABC = 120° because each two opposite angles are equal in measure in parallelogram

v. DAB=DCB =60° because each two opposite angles are equal in measure in parallelogram

vi. OC=AO =7cm because the diagonals of parallelogram bisect each other

vii. OB=DO=5cm because the diagonals of parallelogram bisect each other

viii . DAB=60° ,, CDA= 120 °

DAB+CDA =180°

or you could simply say that because DC and AB are parallel their interior angles are supplementary their sum is 180°

The example of a proportion, is An alarm on a clock beeped 7 times in 6 seconds and beeped 14 times in 12 seconds.​

The term proportionality describes any relationship that is always in the same ratio.

Given are some statements,

a) A car used 3 gallons of gas to drive 72 miles on a highway and used 4 gallons of gas to drive 72 miles in a town.

Solution:- In this case, we see, a car is using 3 and 4 gallons of gas for driving in a highway and in a town for 72 miles respectively.

Since, the distance is same and quantity of gases is different therefore, this can not be represented as a proportion.

b) A store charged $20 for 2 shirts and charged $25 for 3 shirts.

Solution:- In this, let's first find the unit prices for each,

for $20 there are 2 shirts, therefore, for 1 shirt it will be $10, and for 3 shirts it costs $25, therefore, for 1 shirt it will cost $8.3

Since, unit price for both is not equal, therefore, this can not be represented as a proportion.

c) A signal light flashed yellow 7 times in 28 seconds and flashed red 5 times in 35 seconds.

Solution:- As in 2nd option, will here also find unit rate, since, yellow light is flashing 7 times in 28 seconds, therefore, in 4 seconds it will be flashed for 1 time, similarly, red  light is flashing 5 times in 35 seconds, therefore, in 7 seconds it will be flashed for 1 time,

Since, both unit rates are not equal, therefore, this can not be represented as a proportion.

d) An alarm on a clock beeped 7 times in 6 seconds and beeped 14 times in 12 seconds.​

Solution:- Again we will find unit rate, since, the alarm is beeping 7 times in 6 seconds, therefore, it will beep for 1 time in 6/7 seconds, similarly, it is beeping 14 times in 12 seconds, so for 1 time it will beep in 12/14 = 6/7 seconds.

Here, we see that, both the unit rates are equal, therefore, this is an example of a proportion.

Hence, the last option is the correct example.

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