Do the equations 1/5 + 2= 6 and 1/5(x +2)= 6 represent the same situation? Explain

The relation 'x' and 'y' vary inversely, when x = 4, y = 5/2.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

Given, The variables x and y vary inversely.

Let, y ∝ 1/x.

y = k/x.

2 = k/5.

k = 10.

Now, x = 4.

y = k/x.

y = 10/4.

y = 5/2.

learn more about proportion here :

https://brainly.com/question/7096655

#SPJ9

The height of the cylinder is 7 inches and the the new volume of the package is 175.84 cubic inches

1. The formula for the volume of a cylinder is V = Bh, where B is the base area and h is the height. The base of the cylinder is a circle, and the formula for the area of a circle is A = πr^2.

Substituting the given values into the formula for the volume of a cylinder, we get:

87.92 = πr^2h

87.92 = 3.14(2^2)h

87.92 = 12.56h

h = 87.92/12.56

h ≈ 7

Rounding to the nearest inch, the height of the cylindrical package is 7 inches.

Part B:

If the company doubles the height while keeping the radius the same, the new height will be 2h. Therefore, the new volume will be:

V = πr^2(2h) = 2πr^2h

Substituting the given values into this formula, we get:

V = 2(3.14)(2^2)(2h)

V = 25.12h

To find the new volume, we need to substitute the value of h from Part A into this formula:

V = 25.12(7)

V ≈ 175.84

Rounding to the nearest hundredth, the new volume of the package is 175.84 cubic inches.

learn more on volume of cylinder here;

https://brainly.com/question/10390389

#SPJ1

Answer:

(-1, -5)

Equation form:

x=-1, y=-5

Step-by-step explanation:

Basically, all you have to do is solve for the first variable in one of the equations, then substitute the result into the other one. It's as simple as that.

Hope this helps

Answer:

We can use Heron's Formula to calculate the area of a triangle given its three side lengths. The formula is:

A = √(s*(s-a)*(s-b)*(s-c)),

where s = (a + b + c)/2, a, b and c are the three sides of the triangle.

In this case, a = 15, b = y and c = (y-2). Therefore, we can plug these numbers in to get:

80 > √[(y + 7.5) * (y - 7.5) * (y - 2) * (y - 15)]

We can simplify this equation to get:

y^2 - 5y - 80 > 0

This equation can be solved using the quadratic formula, where the solution for y is:

y < 14.09 or y > 10.91

Therefore, the possible values for y are any number between 10.91 and 14.09.

The matrix A  eigenvalues and eigenvectors are as follows:

Eigenvalue λ1 = 1 with eigenvector v1 = [1, -1]

Eigenvalue λ2 = 6 with eigenvector v2 = [4, 1]

Using the equation  (A - λI)v = 0, where is an eigenvalue of A, I am the 2x2 identity matrix, and v is the associated eigenvector, we can determine the eigenvalues and eigenvectors of the matrix A = [[5, 4], [1, 2]].

First, we calculate the (A - λI) matrix's determinant:

det(A - λI) = |5-λ 4| = (5-λ)(2-λ) - 4 = λ^2 - 7λ + 6

|1 2-λ|

We obtain the characteristic equation by setting the determinant to zero:

λ^2 - 7λ + 6 = 0

We obtain two eigenvalues after solving for  λ :

λ = 1 and λ = 6

Next, For each eigenvalue, we identify the appropriate eigenvectors:

For λ = 1, We solve the system of linear equations represented by the equation(A - λI)v = 0:

4v1 + 4v2 = 0

v1 + v2 = 0

The second equation is evidently as straightforward as v1 = -v2. When we enter this into the initial equation, we get:

4v2 - 4v2 = 0

Thus, the eigenvector for λ = 1 is v = [1, -1].

For λ = 6, We solve the system of linear equations represented by the equation(A - λI)v = 0:

-v1 + 4v2 = 0

-v1 + 4v2 = 0

v1 - 4v2 = 0

It is evident that the first equation is just v1 = 4v2. When we enter this into the second equation, we get:

4v2 - 4v2 = 0

Thus, the eigenvector for λ = 6 is v = [4, 1].

Therefore, The matrix A  eigenvalues and eigenvectors are as follows:

Eigenvalue λ1 = 1 with eigenvector v1 = [1, -1]

Eigenvalue λ2 = 6 with eigenvector v2 = [4, 1]

To learn more about eigenvalues,visit the link below:

https://brainly.com/question/29749542

#SPJ4

The five number summary is 77.5.

First Quartile: 7.5

Median: 15.5

Third Quartile: 23.5

Maximum: 30

1, 2, 3, 4, 5, 6, 7, 8,9,10,11, 12, 13,14, 15, 16,17, 18, 19, 20 21, 22, 23, 24, 25, 26, 27, 28, 29, 30.

Minimum = 1

First Quartile = 7 + 8

                           2

                   = 15/2

                    = 7.5

Median = 15+ 16

                    2    

                =31/2

                =15.5

Third Quartile = 15 + 16

                              2

                        =  31/2

                         =   15.5

Maximum = 30

five - number summary = Minimum number +  Lower quartile (Q₁)  + median (Q₂) + Upper quartile  (Q₃) + maximum number

five - number summary = 1 + 7.5 + 15.5 + 23.5 + 30 = 77.5

Learn more about five - number summary on

https://brainly.com/question/29297089

#SPJ1

0900 military time is 9:00 AM in the 24-hour time format used by the military, also known as the 24-hour clock.

The 24-hour clock is a timekeeping system that uses a continuous count of 24 hours, instead of two sets of 12 hours for AM and PM. In this system, each hour of the day is numbered from 0 to 23, and is referred to as "military time" or "24-hour time". So, 0900 military time is equivalent to 9:00 AM, with the "0" indicating the first hour of the day. This system is commonly used in the military, as well as in other fields where precise and standardized timekeeping is important, such as aviation and public transportation.

To learn more military time click here

brainly.com/question/30387466

#SPJ4

The perimeter of the actual field is 91.8 meters.

The area of the actual field is 437.4 square meters.

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

The perimeter of a rectangle = 2(L+W)

Where W is the width of the rectangle  and L is the length of the rectangle

The scale of a rectangular field is given in the question, as follows:

1 cm = 4.5 m

So, the dimensions of the actual field, are as:

L = 7.2 ×  4.5 = 32.4 m

W = 3 ×  4.5 = 13.5 m

The perimeter of the actual field = 2(L+W)

The perimeter of the actual field = 2(32.4 + 13.5) = 2(45.9) = 91.8 m

The area of the actual field = L × W

The area of the actual field = 32.4 × 13.5 = 437.4 m²

Learn more about the Perimeter of the rectangle here:

brainly.com/question/15287805

#SPJ9

The value is approximately equal to 12.0711°

While measuring angles, we use various units of measurements such as the degrees or the SI unit radians as per our convenience.

When we use the degree system, we can use the degree-minute-second or the degree decimal system as per our requirement of precision.

The angle in degree - minutes - seconds is 12°4'16"

We know that [tex]\frac{1}{60}[/tex] of a degree is minute and [tex]\frac{1}{60}[/tex] of a minute is a second.

Hence, [tex]\frac{1}{3600}[/tex] of a degree is a second.

Therefore the angle [tex]\theta[/tex] in degrees and decimal fractions of degrees will be:

[tex]\theta[/tex] = [tex]12+\frac{1}{60}[/tex] × 4 + [tex]\frac{1}{3600}[/tex] × 16

 = [tex](12+\frac{1}{15}+\frac{1}{225} )[/tex]°

The value is approximately equal to 12.0711°

Learn more about Angle at:

https://brainly.com/question/28451077

#SPJ4

The given question is incomplete, complete question is:

The angle 12 degrees 4'16" is given in degrees, arcminutes, and arcseconds. How do you rewrite them in degrees and decimal fractions of degrees?

nswer:

Step-by-step explanation:

6*[tex]10^{6}[/tex]------100

x-------40

x=6*10^6*4*10/100=24*10^5(social media)

6*[tex]10^{6}[/tex]------100

y-------30

y=6*10^6*3*10/100=18*10^5(music)

6*[tex]10^{6}[/tex]------100

z-------25

z=6*10^6*25/100=15*10^5(games)

6*[tex]10^{6}[/tex]------100

f-------5

f=6*10^6*5/100=3*10^5(video)

Since Xavier states that the decay rate of the value of the car is 40%, an answer option that accurately describes Xavier's statement is: A) Xavier correctly determined the decay rate of the value of the car.

In Mathematics, an exponential function can be modeled by using this mathematical expression:

f(x) = a(b)^x

Where:

In this scenario, we can logically deduce that values of a certain type of car x years after it is purchased can be modeled by the following exponential function:

f(2) = 19,400(0.40)^2

By comparison, we have:

Decay rate (r) = 0.40, which simply means Xavier correctly determined it.

Read more on exponential equation here: brainly.com/question/28939171

#SPJ1

The decimal form of 15/16 is 0.9375.

To convert a fraction to a decimal, you can divide the numerator by the denominator. In this case, 15 divided by 16 equals 0.9375.

Alternatively, you can also use long division to find the decimal form of a fraction.

1. Set up the long division problem with 15 as the dividend and 16 as the divisor.
2. Since 16 does not go into 15, add a decimal point and a zero to the dividend.
3. Divide 16 into 150, which equals 9 with a remainder of 6.
4. Add another zero to the dividend and divide 16 into 60, which equals 3 with a remainder of 12.
5. Add another zero to the dividend and divide 16 into 120, which equals 7 with a remainder of 8.
6. Add another zero to the dividend and divide 16 into 80, which equals 5 with no remainder.
7. The final answer is 0.9375.

So, 15/16 as a decimal is 0.9375.

To know more about decimal form click on below link:

https://brainly.com/question/16361602#

#SPJ11

The error is in the second part of the solution.

The definition of an expression in math is a statement composed of terms and operations. The terms may be constant (numbers), or variables with coefficients. The operations may be addition, subtraction, multiplication, or division.

Given that the difference of two expressions, (x²+x) - (2x²-3x), we need to find the error in the solution given,

= (x²+x) - (2x²-3x)

= (x²+x) + (-2²-3x) [Error here]

= (x² - 2x²) + (x²-3x)

= -2²-2x

The error is in the second step,

(x²+x) + (-2²-3x)

When we multiply - sigh with a - sign, we will get a positive sign,

So, the correct step is =

(x²+x) + (-2²+3x)

The correct solution is =

= (x²+x) - (2x²-3x)

= x²+x-2x²+3x

= -2x²+4x

= 2x(2-x)

Hence, the error is in the second part of the solution.

Learn more about expressions, click;

https://brainly.com/question/13947055

#SPJ1

The fraction of the £80 that you have left is 3/10.

Let's start by calculating how much money you spent at the bookshop.

40% of £80 = 0.4 x £80 = £32

£80 - £32 = £48

One third of £48 = £16

£48 - £16 = £32

£32 - £8 = £24

£24 is the same as 24/80 when expressed as a fraction.

24/80 = 3/10

So the fraction of the £80 that you have left is 3/10. This is the simplest form.

Learn more about The Fraction here:

https://brainly.com/question/10354322

#SPJ1

Answer:

the answer is c 95

Step-by-step explanation:

180-41-44=95

a  triangle has 180 degrees

Answer: I think A. 75

Step-by-step explanation: why not pick A……

Hope this helps^^

to tiny submit closer picture

Answer:

= 6.25 hours.

Step-by-step explanation:

If 5 hours = 12 loaves of bread

than ? = 15 loaves of bread.

therefore 15/12 × 5 hours

= 75/12

= 6. 25 hours.

Answer:

He rented the bike for 5 hours.

Step-by-step explanation:

Fixed rate for renting a bike is $8 and rate per hour for renting is $5.

Amount paid by Jermaine is $33.

To find the hourly rent amount that he paid, subtract the fixed rate ($8) from total amount $33.

Rent amount for the bike = 33 - 8

                                          = $ 25

Number of hours rented = 25 ÷ 5

                                        = 5 hours

128 pounds is equal to 58.059 kilograms.

To convert pounds (lbs) to kilograms (kg), you can use the conversion factor that 1 pound is equal to 0.45359237 kilograms.

To convert 128 pounds to kilograms, you can multiply 128 by the conversion factor:

= 128 lbs x 0.45359237 kg/lb

≈ 58.059 kilograms

Therefore, 128 pounds is equal to 58.059 kilograms.

Learn more about Unit Conversion here:

brainly.com/question/5567854

#SPJ6

Answer:

most likely next spring

Step-by-step explanation:

Step-by-step explanation:

Answer:1/12

Step-by-step explanation:

Answer: 1/12

just a find a common denominator, and subtract, hope this helped =)

Answer:

7/10

Step-by-step explanation:

all number converted to decimals are X/1. X is any number.

0.7 is equal to 0.7/1

now fractions cannot contain a decimal number so we can times is by 10 to get 7/10.

Answer: 0.7, I think you multiply, algebraic answer ig

Step-by-step explanation:

Answer:

1/15 chance

Step-by-step explanation:

BASKETBALL = 10 letters

taking out a B = 2/10 or 1/5

Then picking a vowel = 3/9 or 1/3

1/5 x 1/3 = 1/15 chance

if I'm Wrong Sorry And Have a Nice Day .

In MATLAB, you can convert a string to an integer using the str2double() or str2num() function. Both functions convert a string to a double-precision floating-point number, but str2num() also supports the conversion of strings to other numeric data types.

Here's an example of how to convert a string to an integer using str2double():

str = '123';  % string to convert to integer

num = str2double(str);  % convert the string to a double-precision number

int = int32(num);  % convert the double-precision number to a 32-bit integer

In this example, the str variable contains the string '123', which we want to convert to an integer. We first use the str2double() function to convert the string to a double-precision number, which we then convert to a 32-bit integer using the int32() function.

Alternatively, you can use the str2num() function to convert the string directly to an integer:

str = '123';  % string to convert to integer

int = int32(str2num(str));  % convert the string to a 32-bit integer

In this example, we use the str2num() function to convert the string directly to a 32-bit integer, and then assign the result to the int variable.

It is important to note that if the string cannot be converted to a number, both functions will return NaN (Not a Number). Additionally, if the string represents a number that is too large to be represented by an integer, the result will be rounded or truncated.

To know more about string to an integer click here:

brainly.com/question/28670026

#SPJ4

The spring compressed in stopping the ore car is  4.4719 m.

For answer this we will apply the rule of the conservation of energy,

The conservation of energy principle states that in a closed system, the energy of interacting objects or particles remains constant. Kinetic energy, sometimes known as the energy of motion, was the first type of energy to be identified. The total of the kinetic energy of the particles before collision and the sum of the kinetic energy of the particles after collision are identical in some particle collisions, known as elastic collisions.

where:

[tex]E_i=E_f[/tex]

First, we will call:

[tex]E_i[/tex]:the automobile is parked

[tex]E_f[/tex]:when the spring is shortened

so:

[tex]E_i=E_f[/tex]

[tex]mgh=\frac{1}{2}kx^2[/tex]

where M is the vehicle's mass, g is gravity, h is height, K is the spring's constant, and X is the compressed spring used to halt the ore car. By substituting values, we obtain:

4800×9.8×13.8=[tex]\frac{1}{2}\times 410000\times x^2[/tex]

calculating x:

x = 4.4719 m

Learn more about spring

brainly.com/question/14159361

#SPJ4

Answer:

Choice B

Step-by-step explanation:

(7/4)^11 = 471.431...

(7^11)/(4^11) =  471.431...

The complete table is,

⇒ B = 41°

⇒ a = 9.525

⇒ b = 8.25

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle is shown in figure.

Now, We have;

Two angles of triangle are,

⇒ A = 49°

⇒ C = 90°

Hence, We can formulate;

⇒ B = 180 - (49 + 90)

⇒ B = 180 - 139

⇒ B = 41°

And, By using Sine rule as;

⇒ sin A / a = sin B / b = sin C / c

Takin two identity as;

⇒ sin A / a = sin C / c

⇒ sin 49° / a = sin 90° / 12.7

⇒ 0.75 / a = 1/12.7

⇒ 0.75 × 12.7 = a

⇒ a = 9.525

⇒ sin B / b = sin C / c

⇒ sin 41° / b = sin 90 / 12.7

⇒ 0.65/b = 1/12.7

⇒ 0.65 × 12.7 = b

⇒ b = 8.25

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ1

Answer: its A

Step-by-step explanation: you welcome