simply the following
a) 2(y-1)/3-3(y-2)/4=1
b) 3x=44/5=2x+6

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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An expression to represent the sum of their ages is as follows.

g = 14 + L

If the ratio of the ages of X and Y is p:q and their sum is X, then the following formula can be used to calculate Y's age: Age of Y = Y/Total Ages x Total Ratios. Age of Y = (p+q) q x A.

Assume that L is Louannel's sister's age, m is Mark's age, and g is Gregory's age.

Gregory's age difference with his cousin Mark, who is 20 years older (m).

∴ g = 20 + m            .............(1)

Also given that Mark is 6 years younger than his sister Louanne(L)

∴ m = L - 6                ............(2)

Now, substituting m = L - 6 from (2) in (1),

∴ g = 20 + L - 6

∴ g = 14 + L

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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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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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Answer:

1st, 4th and 5th are correct.

Step-by-step explanation:

Answer:

[tex]\dfrac{3}{a-6}\quad \textsf{if}\;\;a \neq -6,a \neq 6[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{a^2}{36-a^2}[/tex]

Rewrite the third fraction:

[tex]\implies \dfrac{a^2}{36-a^2}=\dfrac{-a^2}{-(36-a^2)}=\dfrac{-a^2}{a^2-36}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Difference of two squares }\\\\$x^2-y^2=(x-y)(x+y)$\\\end{minipage}}[/tex]

Apply the difference of two squares to the denominator of the third fraction:

[tex]\implies a^2-36=a^2-6^2=(a-6)(a+6)[/tex]

Therefore the expression can be written as:

[tex]\implies \dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{-a^2}{(a-6)(a+6)}[/tex]

[tex]\implies \dfrac{a}{a-6}-\dfrac{3}{a+6}-\dfrac{a^2}{(a-6)(a+6)}[/tex]

The least common multiplier (LCM) of the denominator is (a - 6)(a + 6).

Adjust the fractions based on the LCM:

[tex]\implies \dfrac{a(a+6)}{(a-6)(a+6)}-\dfrac{3(a-6)}{(a-6)(a+6)}-\dfrac{a^2}{(a-6)(a+6)}[/tex]

Simplify:

[tex]\implies \dfrac{a^2+6a}{(a-6)(a+6)}-\dfrac{3a-18}{(a-6)(a+6)}-\dfrac{a^2}{(a-6)(a+6)}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}-\dfrac{d}{c}=\dfrac{a-b-d}{c}:[/tex]

[tex]\implies \dfrac{a^2+6a-(3a-18)-a^2}{(a-6)(a+6)}[/tex]

Simplify:

[tex]\implies \dfrac{3a+18}{(a-6)(a+6)}[/tex]

Factor out 3 from the numerator:

[tex]\implies \dfrac{3(a+6)}{(a-6)(a+6)}[/tex]

Cancel the common factor (a + 6):

[tex]\implies \dfrac{3}{a-6}[/tex]

Therefore:

[tex]\dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{a^2}{36-a^2}=\dfrac{3}{a-6}\quad \textsf{if}\;\;a \neq -6,a \neq 6[/tex]

Mama bear only ate (1/4) of the pie, leaving Goldilocks with the remaining (1/8) fraction.

The fraction is expressed in the form a/b, where an is referred to as the numerator and b is referred to as the denominator. The fraction is a rational number that only divides two integers.

Let the pie's largest portion be a.

Half of the pie was consumed by Papa Bear.

Papa Bear then consumed = (1/2)a.

Rest of the pie is equal to a- (1/2).

a= (1/2)a

Mama bear consumed (half) of the remaining pie.

Mother bear consumed (1/2)(1/2).

pie portion a= (1/4) pie portion after mom bear has eaten = (1/2)

a- (1/4)a= (1/4)a

Baby bear afterwards consumed (half) of the remaining pie.

Baby bear ate (1/2)(1/4), thus. After the young bear has finished eating, the remaining pie is equal to (1/4) a- (1/8)a= (1/8)

The remainder of the component was given to GoldLiocks.

As a result, mom bear only ate (1/4) of the pie, leaving Goldilocks with the remaining (1/8) portion.

The complete question is Papa Bear ate 1/2 of a pie. Mama Benr ate 1/2 of what was left Baby Bear ate 1/2 of what

was left after Mama Bear finished.

3) What fractional part of the pie did Mama Bear eat?

4) What fractional part of the pie was left for Goldilocks?

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x = 5

AB = 6

BC = 13

A line can be defined as a straight set of points that extend in opposite directions, It has no ends in both directions(infinite). It has no thickness. It is one-dimensional.

Given,

AB = 2x - 4

BC = 3x - 2

AC = 19

By the figure

AB + BC = AC

2x - 4 + 3x - 2 = 19

5x - 6 = 19

5x = 25

x = 5

AB = 2 × 5 - 4 = 10 - 4 = 6

BC = 3 × 5 - 2 = 15 - 2 = 13

Hence the value of x, AB and BC is 5, 6, 13 respectively.

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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.

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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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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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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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 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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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 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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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 sum of two functions, f and g: (f + g)(x) = f (x) + g(x) and The difference of two functions f and g: (f - g)(x) = f (x) - g(x).

What is operation function ?

The operations function refers to all the activities that focus on producing goods and services for the customers. It includes the production process of converting raw material into final products. It helps to reduce costs and make process improvements.

Have given ,

Two function f and g then ,

There is one more way that functions can be combined. The fifth operation is called the composition of two functions. The composition of the functions f (x) and g(x) is symbolized this way: (fog)(x). It is equivalent to f (g(x)). It is read "f of g of x." The concept is simple. First, the value of g at x is taken, and then the value of f at that value is taken. Let's try an example to clear things up.

So , The sum of two functions, f and g: (f + g)(x) = f (x) + g(x) and The difference of two functions f and g: (f - g)(x) = f (x) - g(x).

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Answer:√17

              √81

                √27

This 3 numbers are irrational number

Answer:

17 and 27 are irrational

Step-by-step explanation:

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

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: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:

On solving the provided question, we can say that - The provided arithmetic sequence's 66th term is -950.

An arithmetic sequence is a set of integers that are ordered and have a common difference between each following word.An ordered group of integers with a shared difference between each word is known as an arithmetic sequence.

The given arithmetic sequence is,

25, 10, -5, .....

The sequence's initial word, a, equals 25, while the common difference, d, equals -15.

Use the formula nth term of arithmetic series = a+ (n-1)d to determine the 66th term of the sequence.

66th term =

[tex]25 + (66-1)(-15)\\ = 25 + 65× (-15)\\ = 25 - 975\\ = -950\\[/tex]

The 66th term of the arithmetic sequence is -950.

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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:

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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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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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:

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:

$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 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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