2. Consider divided by . (a) Write a real-world problem for the division. (b) Create a model or write an equation for the division. (c) Find the quotient for the real-world problem in part (a). Show your work or explain your reasoning.

The dimension which this rug should have is 23 feet × 13 feet.

Mathematically, the area of a rectangle can be calculated by using this formula;

A = LW

Where:

Let x represent the width of this rug.

Also, the dimension of this rug is given by:

299 = (29 - 2x) × (19 - 2x)

299 = (29 - 2x)(19 - 2x)

Evaluating the equation, we have:

299 = 551 - 58x - 38x + 4x²

4x² - 58x - 38x + 551 - 299 = 0

4x² - 96x + 252 = 0

Dividing all through by 4, we have:

x² - 24x + 63 = 0

x² - 21x - 3x + 63 = 0

x(x - 21) - 3(x - 21) = 0

(x - 3)(x - 21) = 0

x = 3 or 21 feet.

Note: The plausible solution is x = 3.

Therefore, the width and length of this rug is given by:

Length = 29 - 2(3)

Length = 29 - 6

Length = 23 feet.

Width = 19 - 2(3)

Width = 19 - 6

Width = 13 feet.

In conclusion, the dimension of this rug is 23 feet × 13 feet.

Read more on area of rectangle here: https://brainly.com/question/27404871

#SPJ4

Answer: x = 50°

Step-by-step explanation:

As you can see in the triangle, the two sides are congruent. One of the angles next to the congruent side is 50 degrees. Therefore the other angle also has to be 50 degrees.

Answer:

X=50°

Step-by-step explanation:

This is because the triangle is an isocele triangle and as we all know an isocele triangle is a triangle with 2 sides equal.

Answer:

hey thank you it's I don't know lol thanks

A parabola has an axis of symmetry y =3 and passes through the point (2, 1), another point that lies on the graph of the parabola is (2,5).

Axis of symmetry:

Axis of symmetry is a line that divides an object into two equal halves, thereby creating a mirror-like reflection of either side of the object.

Given,

Axis of Symmetry y = 3.

One point = (2,1)

Here we need to find the another point that lies on the graph of the parabola.

Use the axis of symmetry.

Point given (2,1) is 2 units away from that axis, lower.

=> 1 + 2 = 3

Take two units higher,

=> 3 + 2 = 5

and is the another point (2,5), on the same parabola.

To know more about Axis of Symmetry here.

https://brainly.com/question/22495480

#SPJ1

Answer:

5,000

Step-by-step explanation:

Answer:

Money spent on playstation games per week: =$8169861

Money spent on other video games per week: = $5542467

Step-by-step explanation:

Hi to answer this first, we have to calculate how much Americans spend on non Playstation video games. So, we have to subtract the money spent on Sony Playstation games to the total money spent:

$1958904.00-$1167123.00= 791781 on other video games per day

Now, since each week has 7 days. We have to multiply each daily amount by 7.

Money spent on playstation games per week: $1167123.00 x 7=8169861

Money spent on other video games per week: $791781 x 7= 5542467

( - 1.5 , -5 ) is  a horizontal translation one unit right.

What is the formula for a vertical shrink?

Describe the transformation of the parent graph

f(x)=x^2 represented by g.

g(x)= -(2x+3)^2 - 5

Graph represents ( - 1.5 , -5 )

Learn more about vertical shrink

brainly.com/question/1447109

#SPJ4

here's the coordinates

b'= (4,5)

c'= (5,3)

Which flaw most accurately illustrates the graphed function's domain?

The inequality most accurately depicts the part's intended domain, which should be -9<x ≤2.

Domain here refers to the x change. The values of with regard to function should be the domain in this case. Additionally, we need to pay attention to the blank line that starts at -9 to 2 in x values.

Since 9 should not be filled however 2 should be.

Therefore, The inequality most accurately depicts the part's intended domain, which should be -9<x ≤2.

To learn more about inequality visit: https://brainly.com/question/20383699

#SPJ9

The constant of proportionality is $0.50.

A mathematical constant is a significant integer whose value is determined by an explicit definition. It is frequently denoted by a symbol or by the names of mathematicians to make it easier to use in a variety of mathematical situations.

The amount paid by Rocko is $12.50 for 25 game tickets.

The amount paid by Rocko is $17.50 for 35 game tickets.

A proportional relation can be written as:

y = k × x

where k is a constant, y is the cost, and x represents the number of tickets purchased in this instance.

Substituting the values, for Rocko

$12.50 = k × 25

Therefore

k = $12.50 / 25

k = $0.50

For Louisa,

$17.50 = K × 35

K = $17.50 / 35

K = $0.50

Now, k = K

So we have the same value of the constant in both cases, which means that the constant of proportionality is k = $0.50.

Learn more about proportionality here:

https://brainly.com/question/1496357

#SPJ9

Answer: n= -1/2 -3m

Step-by-step explanation:

Answer:

x = 39

Step-by-step explanation:

As we can see in the diagram, the triangle is a right-angled triangle, meaning that one of the angles inside the triangle has a measure of 90°.

Whenever we have a right-angled triangle and are given the lengths of two of its sides, and we are asked for the length of the third side, we must use the Pythagorean theorem, which states that:

[tex]\boxed{\mathrm{a^2 + b^2 = c^2}}[/tex],

where:

c = hypotenuse (longest side, opposite to 90° angle)

a, b = the two other sides of the triangle.

In this question, we are asked for the value of x, which is the hypotenuse of the given triangle, while the lengths of the other two sides are 15 and 36.

Therefore, using the Pythagorean theorem, we get:

[tex]15^2 + 36^2 = x^2[/tex]

⇒ [tex]x = \sqrt{36^2 + 15^2}[/tex]

⇒ [tex]x = \sqrt{1296 + 225}[/tex]

⇒ [tex]x = \sqrt{1521}[/tex]

⇒ [tex]x = \bf 39[/tex]

Learn more about the Pythagorean Theorem here:

https://brainly.com/question/26954703

Answer:

39

Step-by-step explanation:

This is called the Pythagorean Theorem. You are trying to find x or the hypotenuse. The a and b side are the two shorter side of the triangle(the a and b side can be interchangeable), these are the legs. The c side is the hypotenuse the long side. Plug in the numbers to the formula and get your answer.

Answer:

Ratios compare two numbers, usually by dividing them If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B. For example, if A is five and B is 10, your ratio will be 5/10

Step-by-step explanation:

hope this helps u :) have a good day! ^-^

The height of the mountain using the angles of elevation is 2.346 miles

let

x = distance from the mountain to your current position

h = height of the mountain

Therefore, using trigonometric ratios,

angle of elevation of the current position to the mountain = 8°

angle of elevation of the former position to the mountain = 4.5°

Therefore,

tan ∅ = opposite / adjacent

where

∅ = angle of elevation

tan 8  = h / x

tan 4.5 = h / x + 13

Hence,

x tan 8 = h

(x + 13) tan 4.5 = h

using substitution,

x tan 8  = (x + 13) tan 4.5

x tan 8 = x tan 4.5 + 13 tan 4.5

0.1405408347x = 0.07870170682x + 1.02312218872

0.1405408347x - 0.07870170682x =  1.02312218872

0.0613x = 1.02312218872

x = 1.02312218872 / 0.0613

x = 16.6900489396

x = 16.690 miles

Therefore,

h = 16.6900489396 × tan 8

h = 16.6900489396 × 0.1405408347

h = 2.34561947798

h = 2.346 miles.

Therefore, the height of the mountain using the angles of elevation is 2.346 miles

learn more on angle of elevation here: https://brainly.com/question/13636088

#SPJ4

It is true that if a and b are matrix functions such that the matrices a(0) and b(0) are the same, then a and b are the same matrix function.

Without further explanation, matrices represent linear maps and enable explicit computations in linear algebra. In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions arranged in rows and columns to represent a mathematical object or a property of such an object. As a result, a significant portion of linear algebra involves the study of matrices, and the majority of the characteristics and operations of abstract linear algebra may be described in terms of matrices. The composition of linear maps, for instance, is represented by matrix multiplication.

To learn more about matrix, Visit:

https://brainly.com/question/15250460

#SPJ4

The Volume generated when the region between the curves is rotated around the y - axis is 1216500335.46

Volume of the curves:

The volume of the solid formed by revolving the region bounded by the curve x = f(y) and the y-axis between y = c and y = d about the y-axis is given by

V = π ∫dc [f(y)]2dy.

The cross-section perpendicular to the axis of revolution has the form of a disk of radius R = f(y).

Given,

y = x³

Here we have to find the volume along to the y axis.

With limit as y = 0 and y = 27.

When we apply the values it can be written as,

=>[tex]V=\pi \int\limits^0_{27} {(x^3)^2} \, dx[/tex]

[tex]\implies V=\pi \int\limits^0_{27} {(x^6)} \, dx[/tex]

Apply the limits then we get,

[tex]\implies V = \pi [0^6 - (27)^6][/tex]

=> V = π [0 - 387420489]

=> V =   π x 387420489

=> V = 1216500335.46

To know more about Volume of the Curve here.

https://brainly.com/question/7008615

#SPJ4

we get that the total cost that Sara has to pay to mail these two mails will be equal to 4 6.12.

Sara has 2 items:

Weight of 1st item = 7 ounces.

Weight of second item = 6 3/5 ounces = 33 / 5 ounces.

Total Weight of items to be mailed = 7 ounces + 33 / 5 ounces

Total Weight = 35 + 33 / 5 ounces = 68 / 5 ounces.

Now, cost of mailing 1 ounce per mail = $ 0.45

Cost of mailing 68 / 5 ounce of mails = 68 / 5 × $ 0.45

Total cost = $ 6.12

Therefore, we get that the total cost that Sara has to pay to mail these two mails will be equal to 4 6.12.

Learn more about cost here:

https://brainly.com/question/2021001

#SPJ9

Answer:

< DGB = 101

Step-by-step explanation:

< CGB is equal to 79

< CGB is another name for < 1

We want to find < DGB which is another name for <2

< 1 and < 2 are a linear pair

<1 + <2 = 180

79 + <2 = 180

<2 = 180-79

<2 = 101

< DGB = 101

Answer:

The answer is 101

Step-by-step explanation:

Since a line has an angle of 180°

To know DGB we will just subtract 79 from 180

hence DGB=180°-79°

=101°

Answer: single random sample

Step-by-step explanation:

The population variance of the following set of numbers: 3, 5, 8, 9, 10 is 6.8

For given question,

We need to find  the population variance of the following set of numbers: 3, 5, 8, 9, 10

The formula for the Population variance is,

[tex]\sigma = \frac{\sum (x-\bar x)^2}{N}[/tex]

Here,

[tex]\bar x[/tex] = sample average

x = individual values in sample

N = count of values in the sample.

For given question,

[tex]\bar x=\frac{3+ 5+ 8+ 9+ 10}{5} \\\\\bar x=7[/tex]

Using the formula for variance,

[tex]\sigma = \frac{1}{5} [(3-7)^2 + (5 - 7)^2 + (8 - 7)^2 + (9 - 7)^2 + (10 - 7)^2]\\\\\sigma = \frac{1}{5} \times 34\\\\\sigma = 6.8[/tex]

Therefore, the population variance of the following set of numbers: 3, 5, 8, 9, 10 is 6.8

Learn more about the population variance here:

https://brainly.com/question/13708253

#SPJ4

The number of games that will be played in the first round will be 14 games.

It should be noted that the appropriate function to use in this scenario will be:

= (n - 1) × 2

where n = total number of people participating.

Therefore, this will be:

= (n - 1) × 2

= (8 - 1) × 2

= 7 × 2

= 14

Therefore, the number of games that will be played in the first round will be 14 games.

Learn more about functions on:

brainly.com/question/25638609

#SPJ1

Answer:

no

Step-by-step explanation:

it would be 87.5

Answer: 980.17691.

Step-by-step explanation:

Answer:

980.5714286 ft² or 979.68 ft²

Answer:

11.5

Step-by-step explanation:

Let [tex]x=2\cos(t)[/tex] and [tex]y=2\sin(t)[/tex], so that

[tex]x^2 + y^2 = 4\cos^2(t) + 4\sin^2(t) = 4[/tex]

is preserved. Then from the surface equation, we get

[tex]z = xy = 4\cos(t)\sin(t) = 2\sin(2t)[/tex]

The curve of intersection is then given by the vector function

[tex]\vec r(t) = 2\cos(t) \, \vec\imath + 2\sin(t)\,\vec\jmath + 2\sin(2t)\,\vec k[/tex]

We get the equation for the points of the data as x  y + 6 = 0

We are given the data as:

X              g(x)

10            - 16

11             - 17

12            - 18

13            - 19

We need to find the equation for the data.

Slope = ( - 17 + 16 ) / ( 11 - 10)

m = - 1 / 1 = - 1

Now, the equation will be:

y - y₁ = m (x - x₁)

Substituting the values, we get that:

y + 16 = - 1( x - 10)

y + 16 = - x + 10

x + y + 16 - 10 = 0

x + y + 6 = 0

Therefore, we get the equation for the points of the data as x  y + 6 = 0

Learn more about equation here:

https://brainly.com/question/1214333

#SPJ9

Answer:

£23

Step-by-step explanation:

£12 + £20 = £23

or

£20 - £12 = £8 difference.

As per the question, the study investigated the link between walking and the improved health. The researchers reported that the adults walked at an average of [tex]6.4[/tex] days that means [tex]9216[/tex] minutes in the past month for the purpose of health or recreation.

Now to claim for the null hypothesis, the true average number of days as well as minutes in the past months that the adults walked for the purpose of health or recreation is lower than the [tex]6.4[/tex] days as well as [tex]9216[/tex] minutes. That means [tex]u < 9216.[/tex]

And as per the standard theory of the null hypotheses which contains equal sign. And it can be represented as:

[tex]H(0):u = 9216[/tex] but [tex]H(0):u < 9216[/tex]

What are null hypotheses and alternative hypotheses?

The two hypotheses that is null hypotheses and alternative hypotheses are used in statistical testing. The test prediction based on the null hypotheses has no effect as well as no relationships between the variables. And the alternative hypotheses has both a relationship with the variables as well as effect on the variables.

To learn more about the null hypotheses and alternative hypotheses from the given link:

https://brainly.com/question/14016208

#SPJ4

The Equation representing the following inequality will be 2x + 8 < -18

In the given question, it is stated that a number is 8 more than twice a number that is less than -18.

Let the number be x.

The twice of a number = 2x

A number eight more than twice a number = 2x +8

With the following statements,  we get the Number = (2x+8). Also, we have a condition that this new number is lesser than -18. So we get our equation,

                 =>  2x + 8 < -18

Hence, This  2x + 8 < -18 represents the inequality mentioned in the question stating that a two number is created in which it is lesser than -18.

To know more about Linear Inequalities, Click here :

https://brainly.com/question/11897796

#SPJ1