7y2 - 7y+ 4
-(-3y2 + 7y + 7)
(Simplify your answer.)

The dimensions of the carpet are 73 x 43. = 3139.

In mathematics, a dimension is a way to quantify the size or separation of an area, an object, or a space inside one direction. In simpler terms, It is just the measurements of an object's length, width, and height.

Geometric figures can be created using any configuration of points, lines, or planes. Depending on their dimensions, geometric figures can be categorized as either a space figure, a surface figure, a line, another line segment, a ray, or a point.

The perimeter of the carpets = is 232.

The length of the carpet = 30 in.

In a rectangle, the edge is P = 2W + 2L

In this case 232 = 2W + 2L

Also, the 2nd sentence says L = W + 30

This length variable can be changed in the perimeter formula:

232 = 2W + 2(W+30)

232 = 2W + 2W + 60

232 = 4W + 60

172 = 4W

43 = W

Then, since L = W+30

L = 43+30 = 73

So the dimensions of the carpet are 73 x 43. = 3139.

To know more about rectangle visit:

https://brainly.com/question/13658599

#SPJ4

Answer:

(C) 2x^3 - 3x^2 - 35x + 36

Step-by-step explanation:

First multiply 2x by x^2 + 3x - 4:

(2x)(x^2 + 3x - 4)

2x^3 + 6x^2 - 8x

Next multiply -9 by x^2 + 3x - 4:

(-9)(x^2 + 3x - 4)

-9x^2 - 27x +36

Now add the two polynomials by adding like terms:

(2x^3 + 6x^2 - 8x) + (-9x^2 - 27x +36)

2x^3 + 6x^2 - 9x^2 - 8x - 27x + 36

2x^3 - 3x^2 - 35x + 36

Hope this helps (●'◡'●)

The expression of ⁴√(81x³y⁴z⁸) with rational exponents is: 3x(¾)yz²

The 8 laws of exponents can be listed as follows:

Zero Exponent Law: a^(0) = 1.

Identity Exponent Law: a^(1) = a.

Product Law: a^m × a^n = a^(m+n)

Quotient Law: a^m/a^n = a^(m - n)

Negative Exponents Law: a^(-m) = 1/a^(m)

Power of a Power: (a^m)^n = a^(mn)

Power of a Product: (ab)^m = a^m*b^m

Power of a Quotient: (a/b)^m = a^m/b^m

We are given the algebra expression as:

⁴√81x³y⁴z⁸

This gives us:

81^(1/4) * x^(3/4) * y^(4/4) * z^(8/4)

= 3x^(3/4)yz²

Read more about Laws of Exponents  at: https://brainly.com/question/11761858

#SPJ1

Each time X increases, there is a perfectly predictable increase in Y  is indicated by a Pearson correlation of r= +1.00 between X and Y

A Pearson correlation coefficient of +1.00 indicates a perfect positive linear relationship between the variables X and Y. It means that as X increases, Y increases in a perfectly predictable manner. The correlation coefficient of +1.00 indicates a strong and direct relationship between the two variables, where the values of Y can be precisely determined based on the values of X.

Know more about Pearson correlation here:

https://brainly.com/question/30916205

#SPJ11

The given statement " MP=0 and M is idempotent" is proved.

To verify that MP = 0, we need to substitute the given expressions for M and P and simplify the expression:

MP = (Ix - P)P

= IxP - PP

= X(X x)(X x) - X(X x)(X x)(X x)

= X(X x)[(X x) - (X x)(X x)]

= X(X x)[Ix - (X x)]

= X(X x)Ix - X(X x)(X x)

= X(X x) - X(X x)

= 0

Therefore, MP = 0.

To show that M is idempotent, we need to prove that M^2 = M. First, we compute M^2:

M^2 = (Ix - P)(Ix - P)

= IxIx - IxP - PIx + PP

= Ix - Ix(X x)(X x) - X(X x)Ix + X(X x)P

= Ix - X(X x)(X x) - X(X x)X(X x) + X(X x)(X x)(X x)

= Ix - X(X x)(X x) - X(X x)(X x) + X(X x)(X x)(X x)

= Ix - X(X x)(X x)

= M

Therefore, M is idempotent since M^2 = M.

To know more about idempotent:

https://brainly.com/question/15297309

#SPJ4

Answer:

A = 628.32

Step-by-step explanation:

Area of a circle = 2\(\pi\)\(r^{2}\)

A = 2 x \(\pi\) x \(10^{2}\)

A = 628.32

Please mark brainliest, hope this helps!

Answer:

3

Step-by-step explanation:

Hope this helps

Pls mark brainliest

A ring with a idempotent not equal to 0 or 1 is 3 and 4.

Make (R,+) a domain that is integral.

As a commutative ring with two elements, R, ab = 0 when either an or b are equal to zero.

If a ∈ R is an idempotent element, then a ≠ 0,a ≠ 1 will result.

\(a^{2}\) = a

We can take multiple of 1 because the same number return if we multiply 1 to any number.

\(a^{2}\) = a·1

Subtract a·1 on both side, we get

\(a^{2}\) - a·1 = 0

Taking a common

a(a -1) = 0

(a -1) = 0 or a =0

R has no zero divisors.

So, a = 1 or a = 0

As a result, the only idempotent elements in the integral domain R are 0 and 1.

A ring that is not equal to 0 or 1 and is idempotent.

A ring with respect to addition and multiplication is the set R = 0 through 5.

Let 3 ∈ R,

\(3^{2}\) = 6+3 = 0+3 = 3

Let 4 ∈ R.

\(4^{2}\) = 16 = 12+4 = 2

Hence, 3 and 4 are idempotent elements other than 0 and 1

To learn more about idempotent element link is here

brainly.com/question/15297309

#SPJ4

The complete question is:

An element x in a ring is called an idempotent if \(x^2\) = x. Prove that the only idempotents in an integral domain are 0 and 1. Find a ring with an idempotent x not equal to 0 or 1.

Answer:

Try and start at the line?

Step-by-step explanation:

Probability to find a number odd or at most 16,

P(odd or at most 16) = 7/18

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Given sample

Number 1 - 72

There are 36 odd numbers in between 1 to 72

Probability to find odd numbers P(odd) = 36/72 = 1/2

There are 16 numbers at most 16

Probability to find at most 16 P(at most 16)= 16/72 = 2/9

P(odd or at most 16) = P(odd) + P(at most 16) - P(odd and at most 16)

                                 = 1/2 + 2/9 - (1/2 × 2/9)

                                 = 1/2 + 2/9 - 2/18

                                 = (9 + 4 - 2)/18

                                 = 7/18

Hence, 7/18 is probability to find a number odd or at most 16.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ1

The coordinates of the recycle bin will be = ( -1, 2.5 )

According to the information given in the question,

The coordinates of the vertices of the park are,

( 1, 1 ), ( 1, 4 ), and ( -3, 4 )

We have to find the coordinates of the recycle bin.

Let us consider the equation of the circle,

\(x^{2} +y^{2}+Dx + Ey+ F =0\)

So putting the values of the coordinates into the equation,

First Equation,

\(1^{2}+1^{2} + D + E + F = 0\)

Second Equation,

\(1^{2} +4^{2} +D + 4E + F=0\)

Third Equation,

\((-3)^{2} + 4^{2} - 3D+4E+F=0\)

Subtracting the first equation from the second,

\(1^{2} +4^{2} +D + 4E -E=0\)

15 + 3E = 0

3E = -15

E = -5

Subtracting the third equation from the second,

1 + 16 - 9 - 16 + D + 3D = 0

4D = 8

D = 2

Putting the values of E and D in the first equation,

1 + 1 + D + E + F = 0

F = -2 - D - E

F = 1

So now the equation of the circle becomes,

\(x^{2} +y^{2}+2x - 5y+ 1 =0\)

By expanding the above equation we can find the standard equation,

\(x+2x+1^{2} +y^{2} -5y+ 2.5^{2}- 1^{2} -2.5^{2} +1 =0\)

\((x+1)^{2} + (y - 2.5)^{2} = 1^{2} + 2.5^{2} -1\)

\((x+1)^{2} + (y - 2.5)^{2} = 2.5^{2}\)

So the required circumcenter will be = ( -1, 2.5 )

Therefore, the coordinates of the recycle bin will be = ( -1, 2.5 )

To know more about Circular Coordinates,

https://brainly.com/question/24974036

#SPJ4

A city planner is mapping out some new features for a triangular park. She sketches the park on grid paper. The coordinates of the vertices of the park are (1, 1), (1,4), and (-3,4). The city planner wants to put recycling bins at the circumcenter of the park. What are the coordinates of the recycling bins?

The required volume of the given composite space figure is 1512 \(cm^3\).

Given that, the rectangular pyramid fits exactly on top of a rectangular prism. The length of the prism is 18 cm, width is 6 cm and height is 9 cm. The length of the pyramid is 18 cm, width is 6 cm and height is 15 cm.

To find the volume of the composite figure formed by the rectangular pyramid on top of the prism, find the volume of prism and pyramid and then add it .

The volume of the prism is given by V1 = length × width × height.

The volume of the pyramid is given by V2 = length × width × height.

The volume of the composite figure is V = V1 +V2.

By using the given data and formula, find the volume of the prism,

Volume of prism V1 = length × width × height.

Volume of prism V1 = 18 × 6 × 9.

Thus, Volume of prism V1 = 972 \(cm^3\) .

By using the given data and formula, find the volume of the pyramid,

Volume of pyramid V2 = (length × width × height)/3.

Volume of pyramid V2 = (18 × 6 × 15)/3.

Thus, Volume of pyramid V2 =  1620/3= 540 \(cm^3\) .

By using above volumes, find the volume of the composite figure.

V = V1 +V2.

V = 972 + 540.

V = 1512 \(cm^3\) .

Hence, the required volume of the given composite space figure is

1512 \(cm^3\)

Learn more about volume click here:
https://brainly.com/question/29753475

#SPJ1

EXPLANATION.

The whole numbers are the same natural numbers that start from zero to infinity, they are positive and negative, for example in the number line we can see them from zero to positive infinity, and from zero to negative infinity.

Whole numbers express a complete unit, this means that they do not have an integer part and a decimal part.

Now according to what has already been mentioned, we can see in the exercise that the integers are 9 and 1.00000, which we must enclose in a circle.

The inequality that correctly describes the number of ounces of water, w, that tom drinks each day is d. 64<w.

Amount of water that the bottle can hold = 32 ounces

Bottles of water consumed = 2

A mathematical comparison and representation of the connection between two expressions is known as an inequality. It can be regarded as a generalisation of an equation and is denoted by signs such as <, > and =.

Tom consumes more than two complete bottles of water every day. Since each bottle can carry up to 32 ounces of water, we can describe Tom's daily water consumption as -

= w > 2 × 32

Therefore,

Simplifying the right side of the inequality:

w > 64

Complete Question:

Toms water bottle can hold up to 32 ounces of water. each day he drinks more than 2 full bottles of water. which inequality correctly describes the number of ounces of water, w, that tom drinks each day?

a. w>2

b. 32<w

c. w = 64

d. 64<w

Read more about inequality on:

https://brainly.com/question/24372553

#SPJ4

Answer:

use the formula( I=PTR/100)

The initial value solution of the given ODE is y = -2secx + 5/2, where y(π/2) = 3. To find the general solution of the ordinary differential equation (ODE), we'll begin by separating the variables and integrating both sides.

Given the ODE: (tanx)dy = (2y - 5)dx

We can rewrite it as: dy/(2y - 5) = dx/tanx

Integrating both sides, we have:

∫(1/(2y - 5))dy = ∫(1/tanx)dx

Applying the integral on each side, we get:

(1/2)ln|2y - 5| = ln|secx| + C

where C is the constant of integration.

Now, we can simplify the equation further by exponentiating both sides:

e^((1/2)ln|2y - 5|) = e^(ln|secx| + C)

Simplifying the right-hand side using properties of logarithms, we have:

2y - 5 = e^(ln|secx|) * e^C

Since e^C is just a constant, we can rewrite it as a new constant, let's say A:

2y - 5 = A * secx

Now, we can solve for y:

2y = A * secx + 5

y = (A/2) * secx + 5/2

This is the general solution to the given ODE. However, we are also given the initial condition y(π/2) = 3. We can use this condition to find the specific solution.

Plugging in x = π/2 and y = 3 into the equation, we get:

3 = (A/2) * sec(π/2) + 5/2

3 = (A/2) * 1 + 5/2

3 = A/2 + 5/2

A/2 = -2

A = -4

Substituting A = -4 back into the general solution, we have:

y = (-4/2) * secx + 5/2

y = -2secx + 5/2

Therefore, the initial value solution of the given ODE is y = -2secx + 5/2, where y(π/2) = 3.

Learn more about logarithm here:

https://brainly.com/question/30226560

#SPJ11

The division of the numbers 273.23÷36 yields the value 7.589.

Long division in mathematics is a strategy for breaking down complicated division problems into a series of simpler steps. It is the approach that division-based issues are often solved with. Much like the usual division questions, the dividend is divided by the divisor which yields a result known as the quotient, and occasionally it gives a remainder too.

The given expression is:

273.23÷36

Divide the number 273.23 with 36 and write the remainder at the bottom.

Again, divide the remainder with 36, until further reduction is not possible.

Hence, the division of the numbers 273.23÷36 yields the value 7.589.

Learn more about division here:

https://brainly.com/question/28824872

#SPJ1

As the number of sides approaches infinity, the approximation becomes more and more accurate, and approaches the exact value of πr².The relationship between a circle and a right triangle is a fundamental concept in mathematics and geometry, and has numerous applications in fields such as physics, engineering, and architecture.

The formula for calculating the area of a circle is πr², where r is the radius of the circle and π (pi) is a mathematical constant that equals approximately 3.14159. Archimedes' insight regarding the relationship between a circle and a right triangle can be used to prove this formula mathematically.

According to Archimedes, the area of any circle is equal to the area of a right triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference of the circle. This can be proven through a process known as exhaustion, in which the area of the circle is approximated by a series of polygons with an increasing number of sides. As the number of sides of the polygon approaches infinity, the approximation becomes more and more accurate. In order to calculate the area of a circle using the right triangle method, a right triangle is constructed with one leg equal to the radius and the other leg equal to the circumference of the circle.

The area of this right triangle can be calculated using the formula 1/2bh, where b is the length of the base (which is equal to the circumference of the circle) and h is the length of the height (which is equal to the radius).The area of the circle can then be approximated by calculating the area of a series of right triangles with increasing numbers of sides, using the same method.

Learn more about area:

https://brainly.com/question/30307509

#SPJ11

Complete Question:
According to Archimedes, the area of any circle is equal to the area of a right triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference of the circle. Verify this formula for yourself using the formula for the circumference of a circle.

Answer:

idfk divided by idfk = 378

Step-by-step explanation:

The expression for the total cost of their trip is 7 + 2x + 3y.

As per the question, assuming the number of bottles to be x and number of bags to be y. The equation will have one time fee of admission, product of cost of bottles and number of bottles and product of cost of bags and number of chips bags.

The one time fee and two products will be added to form the expression. Forming the equation now -

Expression = 7 + 2x + 3y

Therefore, the expression of trip when x bottles of water were bought during the visit is 7 + 2x + 3y.

Learn more about expression -

https://brainly.com/question/723406

#SPJ9

Answer:

Step-by-step explanation:

volume of a cylinder=πr^2h

=3.14*2^2*4

=3.14*4*4

=50.24 m^3

Answer:

(0, -10)

If you graph the points and follow where the line would go, then it would hit these coordinates.

Answer:

(0,-10)

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

To find the slope of a graph, use rise/run or change of y over change of x.

Just from looking at the graph, the slope has to be positive as the line is going up!

Start from the point that intersects with the line and graph. Then find another point that also intersects with the line and graph as well.

So for this graph, I am using the two points to the left.

I start from the bottom point and go up 1. Then I go to the right 4 times until I get to the second point.

Thus, the slope is 1/4!

Hope this helps :D

The natural values of n for which the difference (2-2n) - (5n-27) is positive are 1, 2, 3, and 4.

To find the natural values of n for which the difference (2-2n) - (5n-27) is positive, we need to simplify the expression and then solve for n.

(2-2n) - (5n-27) = 2 - 2n - 5n + 27

= -7n + 29

So, we need to find the natural numbers n for which -7n + 29 > 0.

To do this, we can solve for n as follows

-7n + 29 > 0

-7n > -29

n < 29/7

Since n is a natural number, it must be an integer greater than or equal to 1. Therefore, the natural values of n for which the difference (2-2n) - (5n-27) is positive are 1, 2, 3, and 4.

To know more about natural values here

https://brainly.com/question/15155149

#SPJ1

The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.

The sample variance is a measure of how much the individual data points in a sample vary from the mean.

It is calculated by finding the average of the squared differences between each data point and the mean.

To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:

Calculate the mean (average) of the data set:

Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90

Subtract the mean from each data point and square the result:

(93 - 90)^2 = 9

(89 - 90)^2 = 1

(91 - 90)^2 = 1

(87 - 90)^2 = 9

(91 - 90)^2 = 1

(89 - 90)^2 = 1

Calculate the sum of the squared differences:

9 + 1 + 1 + 9 + 1 + 1 = 22

Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):

Variance = 22 / 5 = 4.4

It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.

For more such questions on sample variance

https://brainly.com/question/28542390

#SPJ8

All data sets can be modeled by linear regression. This statement is False.

Linear regression is a method in statistics and machine learning used to investigate the relationship between variables. In simple linear regression, the relationship between two variables is modeled using a straight line. The purpose of this method is to find the best-fit line or curve that explains the relationship between two variables. The equation for a straight line is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. In multiple linear regression, more than two variables are used to predict the value of the dependent variable.

Linear regression is a technique used to model the relationship between two variables, such as height and weight.

It is used in statistics and machine learning to identify patterns and predict future outcomes.

Although many data sets can be modeled using linear regression, not all data sets are suitable for this method.

For example, data sets that have a nonlinear relationship cannot be modeled by a straight line.

Nonlinear relationships can be modeled using other techniques such as polynomial regression or exponential regression.

Additionally, data sets that have outliers or missing values may not be appropriate for linear regression.

Overall, linear regression is a powerful tool for analyzing data and making predictions, but it is not suitable for all data sets.

To know more about linear regression visit:

brainly.com/question/32505018

#SPJ11

A function representing the line that includes the points (3,3) and (-6,15) is 3y=-4x+21.

The given coordinate points are (3,3) and (-6,15).

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.

The standard form of the slope intercept form is y=mx+c.

Now, slope=(y2-y1)/(x2-x1)

= (15-3)/(-6-3)

= 12/(-9)

= -4/3

Substitute m=-4/3 and (x, y)=(3, 3) in y=mx+c, we get

3=-4/3 (3) +c

c=7

Put, m=-4/3 and c=7 in y=mx+c, we get

y=-4/3 x+7

3y=-4x+21

Therefore, a function representing the line that includes the points (3,3) and (-6,15) is 3y=-4x+21.

To learn more about the slope intercept form visit:

brainly.com/question/9682526.

#SPJ5

Answer:

81000000

Step-by-step explanation:

bracket one

3^2 = 9

9^2 = 81

bracket two

10^3 = 1000

1000^2 = 1000000

81 × 1000000 = 81,000,000

im not very good at explaining but ive tried to break it into parts just to make it a bit simpler to understand :)