verify by substitution that the function y(x) = x cx−2is a solution of the differential equation xy′ 2y = 3x. in addition, find the value of c ∈rso that we have y(1) = 5.

A graph cannot intersect its vertical asymptote. A graph can intersect is horizontal asymptote. A graph that intersect its vertical asymptote is not a valid function.

Asymptote is a line that touches the graph of a function only at infinity but it never touches its vertical asymptotes but it can touch its horizontal asymptote and that too at +∞ , -∞. The older definition of asymptotes implies it cannot intersect the graph but recent discoveries shows it is not the case. For example vertical asymptotes,

The graph of [tex]x^{2}[/tex]  / [tex]x^{2} +1[/tex] has x- axis as its horizontal asymptotes and it intersects at origin. Also [tex]\frac{sin(x)}{x}[/tex] is asymptotic to y=0 as x→∞

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The average change of the function is given by 3.5 over the interval [4,8]

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here : The corresponding values of the functions to input x

now F(4)=-4 & F(8)=11

Thus the average rate of change of the function of the interval is given by

A= F(4)+F(8) / 2

  =-4+11 /2

  = 3.5

Hence,  The average change of the function is given by 3.5 over the interval [4,8]

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The distance between any two raisins will not change when the bread doubles its size.

This is because the proportion of the raisins to the size of the dough remains constant. Mathematically, this can be expressed as:

Let d = the original distance between any two raisins

Let n = the new (doubled) size of the bread

d/n = constant

This means that when the size of the bread (n) doubles, the distance between the two raisins (d) remains unchanged. For example, if the original size of the bread was 10cm, and the distance between two raisins was 2cm, then when the bread is doubled to 20cm, the distance between the two raisins will still be 2cm.

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The parabola f(x) = -x² - 6x - 13 is open downward.

Write the equation in vertex form f(x) = a(x-h)² + k

So, f(x) = -x² - 6x - 13

           = -(x² + 6x + 13)

           = -(x² + 6x + 9 + 4)

           = -((x + 3)² + 4)

           = -(x + 3)² - 4

Here, a = -1, h = -3 and k = -4

If a > 0, the parabola is open upward and if a < 0, the parabola is open downward.

In f(x) = -(x + 3)² - 4, a= -1 < 0. Therefore, the parabola is open downward.

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Answer: $13.65 per ticket

Step-by-step explanation:

54.6/4

The simplified form of the expression (3x + 8y)/(x² + 8xy + 16y²) × (x + 4y)/4

is  [(3x² + 20xy + 32y²)/(4x² + 32xy + 64y²)].

A polynomial is an algebraic expression.

A polynomial of degree n in variable x can be written as,

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

Given, (3x + 8y)/(x² + 8xy + 16y²) × (x + 4y)/4.

= [(3x + 8y)×(x + 4y)/(x² + 8xy + 16y²)×4].

= [3x² + 8xy + 12xy + 32y²/4x² + 32xy + 64y²].

= [(3x² + 20xy + 32y²)/(4x² + 32xy + 64y²)].

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Answer:

straight angles

Step-by-step explanation:

Angles that are 180 degrees (θ = 180°) are known as straight angles.

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each sitcom is 33 minutes long

each drama is 19 minutes long.

Let x be the length in minutes of a sitcom and y be the length in minutes of a drama.

We can write the following system of equations to represent the situation:

6x + y = 179

6x + 4y = 302

To solve the system using elimination, we can multiply the first equation by 4 to make the coefficients of y equal, and then subtract the second equation from the first:

24x + 4y = 716

6x - 4y = -123

18x = 593

Finally, we can divide both sides of the equation by 18 to find x:

x = 33

So, each sitcom is 33 minutes long. To find the length of each drama, we can substitute the value of x into either of the original equations:

6x + y = 179

6 * 33 + y = 179

198 + y = 179

y = 19

So, each drama is 19 minutes long.

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Using the Normal Z-distribution and the values from the Z-table, We can calculate that 12.5% can be expected to score between 70 and 90 according to the value of the mean and standard deviation provided.

A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution or z-distribution. By transforming the values of any normal distribution into z scores, it is possible to standardize it.

mean =100

standard deviation =60

70≤ x ≤ 90

70 - 100 ≤ x - 100 ≤ 90 -100

-0.5 ≤  Z ≤ -0.167

P = 0.125(From Z-Table)

Required percentage  = 12.5%

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The correct question is:

certain standardized math exams have a mean of 100 and a standard deviation of 60. of a sample of 36 students who take this exam, what percent could you expect to score between 70 and 90?

After 11 years, Mrs. Smith was hired when she was most likely to have a salary of $45,378.

Now, According to the question:

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

"Information available from the question"

The equation is given as:

y = 305x + 41,987

and, the value of y is $45,378

45,378=305x+41,987

305x=45,378-41,987

305x=3391

x=11.11 years

Hence, After 11 years, Mrs. Smith was hired when she was most likely to have a salary of $45,378.

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the 6th term of the geometric sequence will be 3888.

What is geometric sequence?

A geometric progression or geometric sequence is the order in which each word is different from the next by a common ratio. The next term in the series is produced by adding a constant (that is not zero) to the term that came before it. A, ar, ar2, ar3, ar4, etc. are used as substitutes.

Mathematicians use the term "Geometric Progression" (GP) to describe a type of sequence in which each word is formed by multiplying the previous term by a predetermined number, or "common ratio". An integer geometric series gets that follows a pattern is another name for this development.

The terms are given, 16,48,144

a = 16

r = 48/16 =3

The 6th term will be= a(r)[tex])^{5}[/tex]

= 16(3)[tex])^{5}[/tex]

= 16* 243

=3888

Hence, the 6th term of the geometric sequence will be 3888.

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Answer:

1/5

Step-by-step explanation:

1/7 * x = 1/35    multiply both sides by 7

x = 7/35 = 1/5

The amount of total distance walked (in miles) has walked by Eric in a man made circular lake is 62.8 miles.

A circle's circumference is the length of its perimeter. The circumference of a circle can be calculated using length units such as centimeters, meters, or kilometers by opening a circle and measuring the boundary in the same way that we would measure a straight line.

Let's now discover the components of circumference. The three most crucial components of a circle are those three.

Circumference = D*π

Total distance walked two times = 2.C

=2* D* π

=2x10x3.14

=62.8 miles

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Answer:

what is this? ahdhdjxkdjjshsysusiiaiajsjjdyxc

If a translation maps H onto J, the option from the following statements which is true is:  ∠I ≅ ∠K (Option 1)

A translation is a sort of transformation that involves sliding each point in a figure the same distance in the same direction. The four fundamental translations or transformations in geometry are:

With regard to the above answer, note that, because both triangles have the same vertex, angle HGI is equivalent to angle JGK. Angle H is parallel to angle J.

As a result, by converting angle I to angle K, their measurements will be equivalent. As a result, the angle I is congruent with angle K.

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Full Question:

If a translation maps H onto J, which of the following statements is true?

1. ∠I ≅ ∠K

2. GH = 2GJ

3. ∠G ≅ ∠K

4. HI = 2JK

The discontinuity as x is  -3 is removable by defining f(-3) is -1/8.

Factoring the function's denominator and numerator first is the recommended approach.When a number has zeros in both the numerator and denominator, a point of discontinuity is reached.

There is a point of discontinuity there since the denominator and numerator are both zeros.If x is between 0 and 1, we say that the function is discontinuous.

This function has 3 asymptotes, which are lines that the curve approaches but doesn't cross.The vertical line x=1 is one of them, along with the x-axis, y-axis, and (denoted by a dashed line in the graph above).

Maybe you have

f ( x) = x+ 3/x²- 2x -15

= x+3/(x+3)(x-5)

= 1/x- 5

x infinite  -3

This will have discontinuities (points where the function is undefined) at .

   x = -3

   x = 5

The discontinuity as x = -3 is removable by defining f(-3) = -1/8.

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If your car gets 29 miles per gallon, then it cost to drive 410 when gasoline costs $3.30 per gallon is $46.662.

Your car gets 29 miles per gallon.

It drive 410 miles.

Now determining how much gallon you used to drive 410 miles.

Total Gallon = Total Distance that you covered/Miles per gallon

Total Gallon = 410/29

Total Gallon = 14.14

The costs of per gallon = $3.30

Now we finding the total cost by multiplying the total gallon by the cost of per gallon. After multiplying we get how much it cost to drive 410 when gasoline costs $3.30 per gallon.

So, the cost of 14.14 gallon = 14.14 × $3.30

The cost of 14.14 gallon = $46.662

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Answer:

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

Area of circle with radius r is:

We have r = 8.5 m and using 3.14 for π to find the area:

The larger radius of Cylinder P, which produces a lower the height per unit volume, compared to the smaller radius of Cylinder Q, indicates;

Graph a, matches the graph of Cylinder Q

Graph b, matches the graph of Cylinder P

The volume of water in a cylinder can be found using the formula;

V = π·r²·h

The volume of water is therefore, directly proportional to the volume, therefore, we get;

V ∝ h

V = k·h

Where; k = The constant of proportionality = The slope of the graph of the proportional relation

The equation, V = π·r²·h, indicates that we get;

k = π·r²

The value of the radius for P, r₁ is larger than the value of the radius for Q, r₂

Therefore, k₁ = π·r₁² > k₂ = π·r₂²

h = V/(π·r²)

Therefore, for a specified volume, V, V/π·r₁² < V/π·r₂², h₁ < h₂, and as the water is added, the height of the water in Cylinder Q increases more than the height of the water in Cylinder P, which indicates that we get;

Graph a corresponds to the graph of Cylinder Q, and graph b corresponds to the graph of Cylinder P.

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The bucket will be 30% full at 772 seconds

It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).

The formula and procedure we will use to solve this problem is:

v= x/t

Where:

Information about the problem:

Calculating how many ounces the bucket will be when it has 30% full:

Volume = 220.5 * 30%

Volume = 66.15oz

The bucket will lose:

x = 220.5oz - 66.15oz

x = 154.35 oz

The time that the bucket will have 66.15 oz (30%) is:

t = x/v

t = 154.35 oz / 0.2 oz/s

t = 771.75 s = 772 s

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Correctly written question:

A pail holds 220.5 ounces (oz.) of water when full. The bucket loses 0.2oz of water per second. In how many seconds will the bucket be 30% full? Round your answer to the nearest second.

Matching the transactions to their relevant posting in the ledger are;

Business purchases furniture: furniture account debited

Business sells furniture: furniture account credited

Business takes a loan from the bank: loan account debited

Business pays off the loan: loan account credited

The ledger transactions are simply defined as a summary of transactions made as journal entries to sub-ledger accounts.

Now, the three main types of ledgers are;

1) General ledger: This  contains accounts that correspond to the income statement and balance sheet for which they are destined.

2) Sales ledger or debtor's ledger: This shows  at any given time how much your customers owe you and your company.

3) Purchase ledger or creditor's ledger: This shows a record of a company's purchases of goods and services showing the amounts that have been paid and remain to be paid.

From the above, we can classify the transactions as;

Business purchases furniture: furniture account debited

Business sells furniture: furniture account credited

Business takes a loan from the bank: loan account debited

Business pays off the loan: loan account credited

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The option that describes the viable solution for the system is all real number values, with y ≥ 0 which is denoted as option C.

This is referred to as a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

all real number values, with x >=0 and y>=0​

The following system of inequalities is given below:

-y ≤ 3x + 4

-3x - 3y ≤ 9 which can be rewritten as:

-3y ≤ 9 + 3x

-3y/3 ≤ 9/3 + 3x/3

-y ≤  3 + x

The system of inequalities is therefore:

-y ≤  3 + x

-y ≤ 3x + 4

Since x and y are both positive or 0, the system is true and we can conclude that the correct choice is option C which is all real number values, with y ≥ 0

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y(t) = 3u(t) is a constant function that is equal to 3 for t >= 0 and equal to 0 for t < 0.

The function x(t) = 3tu(t) is a product of a scalar 3 and a unit step function u(t). Here, u(t) is defined as:

u(t) = 0 for t < 0

u(t) = 1 for t >= 0

So, x(t) is equal to 3t for t >= 0 and equal to 0 for t < 0.

The function y(t) is the derivative of x(t) with respect to t. To find the derivative of x(t), we use the power rule for differentiation, which states that the derivative of tx(t) is x(t) + t × dx(t)/dt.

So, we have:

y(t) = dx(t)/dt = d(3tu(t))/dt = 3u(t) + 3tu'(t) = 3u(t)

Here, u'(t) is the derivative of u(t) with respect to t, which is equal to the Dirac delta function δ(t).

So, we have:

y(t) = 3u(t) = 3 for t >= 0

y(t) = 0 for t < 0

Hence, y(t) = 3u(t) is a constant function that is equal to 3 for t >= 0 and equal to 0 for t < 0.

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It is not possible to determine the probability that an individual student likes between 5.5 and 8.5 songs from Eminem without any additional information. Probability is a measure of the likelihood of an event occurring, and it requires data or information about the event in question. In this case, without knowing the number of songs from Eminem the student has heard, the student's taste in music, or any other relevant information, it is impossible to determine the probability that the student likes between 5.5 and 8.5 songs from Eminem.

The number of lunches were sold on friday this week with a relative frequency of 0.22 is 297.

The word "relative" is used to describe how something is being viewed in connection to or in comparison to another event. How frequently an event occurs can be determined by looking at its frequency. On the other hand, relative frequency is a means to compare the frequency of a specific event to all other occurrences.

Let's learn about the relative frequency formula,

Relative frequency = f/n

So 0.22 = f / 1350

so f= 1350 x 0.22

f = 297

So  number of lunches were sold on friday this week were 297.

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Answer:

9058 Bagels

Step-by-step explanation:

14x657 I hope this helped!

The original amount of water is  15 cups.

The change in David's water intake is  3 cups.

The percent change is 20 %. This is a percent  decrease.

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

Given that, David is tracking the amount of water he drinks each day.

On Thursday, he drinks 15 cups of water.

On Friday, he drinks 12 cups of water.

The percent change in his water intake = (12 - 15) / 15 × 100 = -20%

Where minus sign is showing a decrease in the water intake,

The original amount of water is 15 cups.

The change in David's water intake is (15-12) = 13 cups.

Hence, the answers are;

The original amount of water is  15 cups.

The change in David's water intake is  3 cups.

The percent change is 20 %. This is a percent  decrease.

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I need the answer...

Answer:

67%

Step-by-step explanation:

Percent change is the change divided by the original value.  The change for the flower is (70" - 42") = 28"

The original value was 42".

Percent change is (28"/42")*(100%) = 67%

Equations with exponents, coefficients, and variables are called polynomial equations.

Polynomial equations are equations that contain variables, exponents, and coefficients. The greater exponent is referred to as the degree of the equation and it can have many exponents.

A polynomial is an expression in mathematics made up of coefficients and indeterminates, which are also known as variables. It can only be solved using the addition, subtraction, multiplication, and powers of positive-integer variables.

When a variable in an equation like the quadratic equation, cubic equation, etc. has only non-negative integer powers or only positive integer exponents, the function is said to be polynomial.

The absence of square roots of variables, fractional or negative powers on the variables, and the absence of variables in any fraction's denominator are specifically required for an expression to qualify as a polynomial term.

Therefore, the correct answer is option iii) -7 v² - 6v + 4.

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By rearranging the terms, the correct answer is option iii) -7 v² - 6v + 4. Equations with exponents, coefficients, and variables are called polynomial equations.

Polynomial equations are those that have exponents, coefficients, and variables. The higher exponent of the equation, which may have multiple exponents, is known as the equation's degree.

A polynomial is an equation in mathematics made composed of coefficients and indeterminates, often known as variables. The only operations that may be used to solve it are addition, subtraction, multiplication, and powers of positive-integer variables.

If a variable in an equation, such as a quadratic equation or a cubic equation, only has positive integer exponents or non-negative integer powers, the variable is said to be a polynomial.

Expressions must expressly be free of variable square roots, fractional or negative powers on the variables, and variable presence in any fraction's denominator in order to be classified as polynomial terms.

Therefore, the correct answer is option iii) -7 v² - 6v + 4.

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The correct reaction profile is it applies to both SN1 and E1 reactions.

The term reaction is defined as a process in which one or more substances, also called reactants, are converted to one or more different substances, known as products

Here we have know that in a chemical reaction and then a transition state is a state that exists between reactants and intermediates or products directly,

Here in which bonds are concurrently breaking and forming new ones.

And it is extremely unstable and highly energetic.

We know that both intermediates and transition states are the states that are present between the reactants and the reaction's end products, on the other hand they differ in that intermediates have full bonds, are more stable than the substrate and therefore have a lower energy and have a discrete lifetime,

Here we know that instead of a transition state has only partial bonds and is least unstable, thus making it the state with the highest energy at the reaction profile.

Therefore the correct option is (a).

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