determine if the function in the first column is an eigenfunction of the operator in the second column. 5y5 y2d2/dy2 yx7−xy−7 x3(∂3/∂x3) y3(∂3/∂y3) sinθcos3ϕ ∂2/∂θ2 ∂2/∂

In proportion the complete table is ,

r      1      2       4          [tex]1\frac{1}{2}[/tex]

V    4     32     256      [tex]13\frac{1}{2}[/tex]

What is proportion?

A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.

Here the given is V∝[tex]r^3[/tex] .

To remove proportion we need to include constant then,

=> V = k[tex]r^3[/tex]

Now put r=1 and V= 4 then

=> 4= k*1

=> k=4

Then the equation is V=4[tex]r^3[/tex].

Now put r=2 then

=> V= 4[tex]\times 2^3[/tex]

=> V= 4× 8 = 32

Now put V=256 then

=> 256 = 4[tex]r^3[/tex]

=> [tex]r^3=\frac{256}{4}[/tex]

=> [tex]r^3=64[/tex]

=> r = 4

Now r=1[tex]\frac{1}{2}[/tex] = [tex]\frac{3}{2}[/tex] = 1.5 then

=> V= 4[tex]\times 1.5^3[/tex]

=> V=[tex]\frac{27}{2}[/tex]

=> V = [tex]13\frac{1}{2}[/tex]

Hence the complete table is,

r      1      2       4          [tex]1\frac{1}{2}[/tex]

V    4     32     256      [tex]13\frac{1}{2}[/tex]

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The result when,

4.08 divided by 6.4 is  6.375

730.5 divided by 1.5 is  487

Division is a mathematical operation, in which we distribute the number in equal parts, the number on the upper side is the total quantity and the number on the bottom side is equal parts of numbers which have to be distributed.

We denote division by '÷' this symbol.

Given that,

Two statements,

08 divided by 6.4

and 730.5 divided by 1.5

⇒  4.08/6.4

4.08 & 6.4 cab be written as

⇒ 408/100 & 64/10

So, 408/100÷ 64/10

⇒  408 ÷ 640

⇒   6.375

Similarly,

730.5 ÷ 1.5

⇒   487

Hence, the results are respectively 6.375 & 487

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Answer:

m=1

Step-by-step explanation:

At 200 miles, the cost will be the same.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Mover R U rents moving trucks for an initial fee of $45 and charges $0.25 per mile.

And, Trunks to Use rents trucks for an initial fee of $35 and charges $0.30 per mile.

Now, Let in x miles the cost will be the same.

Hence, We can formulate;

For Mover R U rents moving trucks for an initial fee of $45 and charges $0.25 per mile.

⇒ $45 + $0.25x

And, For Trunks to Use rents trucks for an initial fee of $35 and charges $0.30 per mile.

⇒ $35 + $0.30x

Equate both equation, we get;

⇒ 45 + 0.25x = 35 + 0.30x

⇒ 45 - 35 = 0.30x - 0.25x

⇒ 10 = 0.05x

⇒ x = 10/0.05

⇒ x = 1000/5

⇒ x = 200

Thus, At 200 miles, the cost will be the same.

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The correct dot plot representation of the life spans of houseflies is option B, with the life spans ranging from 4 to 14 days and most life spans in the range of 5 to 9 days.

A dot plot is a simple and effective way of visualizing data, especially for small data sets. A dot plot represents each data point as a dot on a number line, with the position of the dot indicating the value of the data point.

Option B states that the life spans range from 4 to 14 days, with most life spans in the range of 5 to 9 days. This means that the dot plot will have a number line running from 4 to 14, with the majority of dots clustered in the 5 to 9 range. This is the correct representation of the dot plot of the life spans of houseflies.

The dot plot suggests that the distribution of the life spans of houseflies is not symmetrical and has a mode (the most frequent value) between 5 and 9 days. This indicates that most houseflies live between 5 and 9 days, with fewer houseflies living either shorter or longer lives.

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The value of the leading coefficient is equal to -1.

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression. In the term 5x, the coefficient of the number is 5. This coefficient is a whole number that is positive and real.

we know that

The formula to solve a quadratic equation of the form ax²+bx+c =0 is equal to

[tex]x = \frac{-b (+/-) \sqrt{b^{2}-4ac } }{2a}[/tex]

In this problem we have

[tex]f(x) = -x^{2} -8x-7[/tex]

Equate the function to zero

[tex]-x^{2} -8x-7 = 0[/tex]

So, a = -1

     b = -8

     c = -7

Hence, The value of the leading coefficient is equal to, a = -1.

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The weight of Dima in kilograms round to the nearest hundredth is: 58.51 kilograms.

A weight measuring unit: One pound equals 454 grams. One kilogram is roughly equivalent to 2.2 pounds.

One pound contains 16 ounces.

The word "poundus" means "weight" in Latin.

The £ symbol is derived from an ornate L in Libra.

We are given the weight of Dima as 129 pounds.

we know by conversion that:

1 pound= 0.453592 kilograms

Hence 129 pounds= 129×0.453592 kilograms

129 pounds=58.513368 kilograms.

Therefore, The weight of Dima in kilograms round to the nearest hundredth is: 58.51 kilograms.

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Answer:

0, 1 and 2

Step-by-step explanation:

1) Find the possible values of x

2) Find the possible values of y

3) See the numbers that are the same

Have a lovely day :)

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{a + b - 3}\\\mathsf{= 10 + 7 - 3}\\\mathsf{= 17 - 3}\\\mathsf{= 14}\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{14}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

A) The expression that represents the area of the rectangle is;

18x² + 63x + 55

B) The degree of the polynomial is 2 and the classification is a quadratic polynomial.

C) The multiplication of the polynomials (3x + 5) and (6x + 11) to obtain another polynomial demonstrated the closure property of polynomials

A) The formula for the area of a rectangle is;

Area = Length * Width

We are given length of sides as (3x + 5) and (6x + 11)

Thus;

Area = (3x + 5)(6x + 11)

Area = 18x² + 63x + 55

B) The degree of the expression is the highest power which is 2 in the first term 18x².

C) In part A we multiplied 2 polynomials (3x + 5) and (6x + 11) and obtained another polynomial. This demonstrated the closure property of polynomials

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The product of (-8) and a number at most 50 will be

50 * (-8) = -400

Mathematicians use multiplication to calculate the sum of two or more numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis.

Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54.

a mathematical operation that accepts two integers and outputs a result that is equal to the sum of a column that has one of the values repeated the same amount of times as the other number. Eight times three equals the total of eight times eight.

The product of (-8) and a number at most 50 will be

50 * (-8) = -400

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The matrix [Qr₁...Qrp] is the result of transforming each vector in R through the matrix Q.

A matrix is a collection of numbers arranged in rows and columns, with each element representing a specific value.

In this explanation, we will look at the relationship between a matrix Q and a set of vectors r₁,..., rp in Rⁿ, and how they can be combined to form a new matrix [Qr1...Qrp].

The matrix [Qr₁...Qrp] can be written as the product of two matrices: QR, where R is defined as [r₁...rp].

This means that when the matrix Q is multiplied by the matrix R, we get the matrix [Qr₁...Qrp].

The reason for this is that multiplying a matrix by another matrix is simply a way of transforming each vector in the original matrix.

In this case, Q transforms each vector r₁,..., rp in R to produce the new set of vectors [Qr₁...Qrp].

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Answer: [tex]AD=33[/tex]

Step-by-step explanation:

Using the formula for the perimeter of a rectangle,

[tex]2(2z+1+3z+3)=108\\\\2(5z+4)=108\\\\5z+4=54\\\\5z=50\\\\z=10\\\\\implies BC=33 \implies AD=33[/tex]

Answer:

[tex] - \frac{2}{9} \div 3 \frac{1}{4} \\ \\ \dashrightarrow \: - \frac{ 2}{9} \div \frac{13}{4} \\ \\ this \: can \: also \: \: be \: written \: as \: \\ \dashrightarrow \: - \frac{2}{9} \times \frac{4}{13} \\ \\ \dashrightarrow \: \boxed{ \: - \frac{8}{117} }[/tex]

hope helpful! :)

Answer:

-8/117

Step-by-step explanation:

[tex]\frac{-2}{9} /3\frac{1}{4} \\\\[/tex]

-first simplify 3 1/4

-simply multiply 4 by 3 and add 1. This is how you convert mixed fractions to whole fractions. Multipy denominator by whole number and add the numerator. The denominator stays the same so this will become

=13/4

- next because you're dividing two fractions, it is easier to take reciprocal of the denominator. You flip the fraction and change the sign. So instead of dividing by 13/4, you multiply by 4/13

- lets move the negative fraction (-2/9) to rigth hand side to make things easier to visualize. so our expressions right now will be:

=[tex]\frac{4}{13} *\frac{-2}{9}[/tex]

-now multiply like normal

= -8/117

Answer:

9 gal/day

Step-by-step explanation:

We are given 1 cup per 10 minutes. You can always change the way an expression looks without changing its value if you multiply it by 1. But here we need to change the units. So the 1 we're multiplying is:

1gal/16cups or

60min/1hr or

24hr/1day

See image. We can set it up to cancel the units we don't want and get the units we do want.

see image.

The equation of the tangent line of f(x)=(x-5)/(x+1) at x=6 in the form of y = mx + b is y = (6/49)x - 29/49 .

The function whose tangent line is to be found out is f(x)=(x-5)/(x+1) ;

to find the tangent equation , we differentiate the function ;

the function f(x) is of the form g(x)/h(x) ;

On differentiating g(x) and h(x) , we get that g'(x) = h'(x) = 1 ;

We get ; f'(x) = [1(x+1))-(1(x-5)]/(x+1)² ;

⇒ f'(x) = [x+1-x+5]/(x+1)² ;

⇒ f'(x) = 6/(x+1)² ;

Now, we x = 6 in the derivative to find slope of tangent at that point.

So , ⇒ f'(6) = 6/(6+1)²

⇒ f'(6) = 6/49

Now the slope is =  6/49 ,  the value of y in (6,y) by putting in x = 6 into the original function:

⇒ f(6) = (6 - 5)/(6 + 1)

⇒ f(6) = 1/7

We currently know a point (6,1/7) = (x₁,y₁) and slope of tangent, which is 6/49.

now using  point slope form to find equation of tangent.

⇒ y-y₁ = m(x-x₁)

⇒ y - 1/7 = (6/49)(x-6)

⇒ y = (6/49)x - 29/49

Therefore , The equation of the tangent is y = (6/49)x - 29/49 .

The given question is incomplete , the complete question is

What is the equation of the tangent line of f(x)=(x-5)/(x+1) at x=6 . Enter your answer as an equation in the y = mx + b form ?

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Answer:

11 2/3

Step-by-step explanation:

5 ÷ 3/7

When dividing with fractions, we use copy dot flip.

Copy the first number

5

Then change division to multiplication.

5 *

Then use the reciprocal of the last number.

5 * 7/3

35/3

Change the improper fraction to a mixed number.

11 2/3

The minutes does it take them to weld the railing are 50 minutes.

To find out the time it takes Nathaniel and Brenda to weld a railing together, you can follow these steps:

Find out how long it takes Brenda to weld a railing: Nathaniel takes 75 minutes, so Brenda takes 75 + 25 = 100 minutes.

Divide the time it takes to weld a railing by the number of workers: 100 minutes / 2 workers = 50 minutes.

Therefore, it takes Nathaniel and Brenda 50 minutes to weld a railing together.

This is a math problem that involves calculating the time it takes two workers, Nathaniel and Brenda, to complete a task of welding a railing. Nathaniel can weld a railing in 75 minutes, while Brenda can do it 25 minutes faster. The question asks how many minutes it takes for the two of them to weld the railing if they work together. To answer this, we need to find out how long it takes Brenda to weld a railing, then divide the total time between the two workers.

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If Candidate A received 36 votes, the number of votes that Candidate B received is 60 votes.

The correct option is (C)

Now, According to the question:

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

The first step is to determine the relationship between the number of votes of Candidate A and B. This can be determined by expressing the number of votes in its simplest form.

12 : 20 in its simplest form is 3 : 5

18 : 30  in its simplest form is 3 : 5

27 : 45  in its simplest form is 3 : 5

Now, determine the factor second factor of 36 if the first factor is 3.

36 / 3 = 12

Now multiply 12 by 5: 12 x 5 = 60

Hence, If Candidate A received 36 votes, the number of votes that Candidate B received is 60 votes.

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The function f(x) is equal to x√x.

The value of a is 25/4.

What is a function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.

Given integration is

[tex]5+\int_a^x\frac{f(t)}{t^2}dt =2\sqrt{x}[/tex]

Rewrite the equation

[tex]\int_a^x\frac{f(t)}{t^2}dt[/tex]= 2√x - 5

The differentiation of 2√x is f(t)/t² at t = x.

The differentiation of 2√x is 1/√x.

Therefore, 1/√x = f(x)/x²

x²/√x = f(x)

f(x) = x√x

Putting f(t) = t√t in the given equation:

[tex]5+\int_a^x\frac{t\sqrt{t} }{t^2}dt =2\sqrt{x}[/tex]

[tex]\int_a^x\frac{1 }{\sqrt{t}}dt =2\sqrt{x}-5[/tex]

[tex][2\sqrt{t}]_a^x[/tex] = 2√x - 5

2√x - 2√a = 2√x - 5

2√a = 5

√a = 5/2

Square both sides:

a = 25/4

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Answer:

The y-intercept is (0, 3).

The equation is not factorable.

Step-by-step explanation:

We are given the equation:

Y=4x^2-4x+3

and we are asked to graph it.

To do this, let's first find the vertex of the parabola that a quadratic equation creates.

[tex]V(-\frac{b}{2a}),f(x))[/tex]

Here, a = 4 and b = -4. So the vertex must be:

[tex]V(-\frac{-4}{2(4)},f(x))[/tex]

[tex]V(\frac{1}{2},f(\frac{1}{2}))[/tex]

[tex]V(\frac{1}{2},2)[/tex]

Next, let's find the intercepts.

[tex]x=0[/tex]

[tex]y=4(0^{2})-4(0)+3=3[/tex]

The y-intercept is (0, 3).

The equation is not factorable.

Answer:

68

Step-by-step explanation:

abdul＋mariya/2＝56

total abdul ＋ mariya ＝56*2＝112

112＋hari/3＝60

total 3 person＝60*3＝180

hari ＝180-112＝68

pls give brainliest if correct

Answer: 18x-4

Step-by-step explanation:

4x^2-2+2x= 18x-4

Jamal will have 63 vacation days after working at his new job for 2 years.

To calculate the number of vacation days Jamal will have after 2 years,

We need to determine the number of months he worked

(2 years = 2 * 12 = 24 months)

And then use that in the expression for his vacation days: 51 + 0.5m.

So, for 24 months, we have:

Vacation days = 51 + 0.5 * 24

Vacation days = 51 + 12

Vacation days = 63

In arithmetic, addition is the process of adding two or more integers together. The numbers being added are known as addends, while the outcome of the addition process, or the final response, is known as the sum.

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Answer:

5:12pm

Step-by-step explanation:

Total hours Mr. White used: 312M/60MPS=5.2hours

0.2 hour is 12 minutes.

He start at noon, 12  o'clock, so he will be there at 5:12pm

Answer:

A; Janae and Jerome must each have only 1 marble

Step-by-step explanation:

First, let's create equations for the amount of marbles each person has:

Janae: m

Jerome: m

Gwen: 4(m+2)

John: 8m+4

Next, let's create an inequality using the statement "John has more marbles than Janae, Jerome, and Gwen combined"

John > Janae + Jerome + Gwen : 8m+5 > m + m + 4(m+2)

Lastly, let's solve for what m could be equal to. To do this, we will need to solve the inequality for m:

8m + 5 > m + m + 4(m+2)   [Distribute 4 to (m+2) on the right side]

8m + 5 > m + m + 4m + 8   [Combine like terms]

8m + 5 > 6m + 8   [Subtract 6m from both sides]

2m + 5 > 8   [Subtract 5 from both sides]

2m > 3   [Divide both sides by 2]

m > 3/2

So, for John to have more marbles than Janae, Jerome, and Gwen combined, m, or the amount of marbles Janae and Jerome have, must be less than 3/2. When looking at the answers, only one option is less than 3/2, 1. So, Janae and Jerome must each have only 1 marble.

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The perimeter of the tabletop is 79 inches. To calculate the perimeter of a parallelogram, you would use the following formula:

In this case, the length is 30 inches and the width is 14.5 inches, so the perimeter would be 2(30 + 14.5) = 79 inches.

To calculate the perimeter of a parallelogram, use the following steps:

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Given - Cos^2(45) + cos ^2(60) + cos^2(y) = 1

We Know ,

Cos^2(45) = (1/[tex]\sqrt{2}[/tex])^2    ------- 1

cos^2(60)= (1/2)^2       --------2

From equation 1 &2

1/2 + 1/4 + cos^2(y) =1

cos^2(y) = 1- (1/2 + 1/4)

cos^2(y) = 4-2-1/4

cos^2(y) = 1/4

cos (y) = [tex]\sqrt{1/4}[/tex]

cos (y) = 1/2

cos (y) = cos (60)

y=60

The value of y that is being determined by the given

trigonometric equation Cos^2(45) + cos ^2(60) + cos^2(y) = 1 is y = 60

Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations in a triangle. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

Given that, Cos^2(45) + cos ^2(60) + cos^2(y) = 1

We Know that ,

cos(45) = 1/[tex]\sqrt{2}[/tex]  and cos(60) = 1/2

hence, Cos^2(45) = (1/[tex]\sqrt{2}[/tex])^2          (1)

cos^2(60)= (1/2)^2         (2)

From equation 1 &2

1/2 + 1/4 + cos^2(y) =1

cos^2(y) = 1- (1/2 + 1/4)

cos^2(y) = 4-2-1/4

cos^2(y) = 1/4

cos (y) = 1/[tex]\sqrt{4}[/tex]

cos (y) = 1/2

cos (y) = cos (60)

Therefore , y=60

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