The length of a rectangle is represented by the function L(x) = 2x. The width of that same rectangle is represented by the function W(x) = 8x2 − 4x + 1. Which of the following shows the area of the rectangle in terms of x?

(L + W)(x) = 8x2 − 2x + 1
(L + W)(x) = 8x2 − 6x + 1
(L ⋅ W)(x) = 16x3 − 4x + 1
(L ⋅ W)(x) = 16x3 − 8x2 + 2x

If you draw all the diagonals of a normal hexagon, there are 3*6=18 possible triangles; however, three of those are identical (the equilateral triangles), leaving us with 18-3=15 triangle possibilities.

In terms of geometry, a hexagon is a closed, six-sided polygon in two dimensions. A hexagon has six angles and six vertices. Hexa and gonio both denote the number six. A hexagon can be found in the shapes of a honeycomb, a football, a pencil face, and floor tiles. a standard hexagonal 2D geometric polygon with six equal-length sides and six equal-sized angles. All of the lines are closed, and there are no curving edges. A regular hexagon has 720 degrees of internal angles. Additionally, these shapes have six rotating and six reflective symmetries.

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Answer:

I believe the solution is -12

Step-by-step explanation:

The radius of the ball which is the each of the smaller balls is R = 2r.

The formula for the volume of a sphere is V = 4/3 π r³, where V = volume and r = radius. The radius of a sphere is half its diameter. So, to calculate the surface area of a sphere given the diameter of the sphere, you can first calculate the radius, then the volume.

We can use the following formula to get the volume of a sphere whose radius is "r": A sphere's volume is equal to 4/3r³.

here, we have,

Given,

A steel ball which is melted down to make eight smaller identical balls.

If the radius of the original steel ball was 20 cm:

Let the spherical ball's radius be R.

And with r being the radius of 8 similar balls,

According to the inquiry,

Volume of 8 similar balls = the volume of a larger sphere

3/4πR³ = 8 × 3/4πr³

R³ = 8r³

R = 2r

Hence, The radius of the ball which is the each of the smaller balls is R = 2r.

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Answer: B - $6,098.35

Step-by-step explanation:

This is a compound interest question. The compound interest formula is:

A = P ( 1 + r/n)^nt

A = Future amount of investment

P = Starting amount of investment

r = Rate of interest

n = Number of times interest compounds per year

t = Time (Years)

You must turn the percentage (1%) into a decimal by dividing by 100

1/100=.01

So, the equation for this question is:

A = 4,800(1+[tex]\frac{.01}{2}[/tex])^(2)(24)

A = 4800(1.005)^48

A = 4800(1.2704891611)

A = 6,098.35

⇒ 75° and (4x+9)° are co-interior angles which means when they are added they give 180°

[tex]75+(4x+9)=180\\4x=180-75-9\\4x=96\\\frac{4x}{4} =\frac{96}{4} \\x=24[/tex]

this simply means that x=24°

75° and 3y are corresponding angles, corresponding angels are equal.

this means that :

[tex]3y=75\\\frac{3y}{3} =\frac{75}{3} \\y=25[/tex]

this means that y=25°

goodluck

The length of the equilateral triangle = 4.8m

Given that,

The area of the equilateral triangle = 10.2 m²

The formula for the area of an equilateral triangle = [tex]\sqrt{3} /4 a^{2}[/tex]

Therefore,  

[tex]\sqrt{3} /4 a^{2}[/tex] = 10.2

[tex]a^{2}[/tex] = 10.2 × [tex]4/\sqrt{3}[/tex]

[tex]a^{2}[/tex] = 10.2 × 4/ 1.732

[tex]a[/tex] = 4.85

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[tex] \sf \frac{5^{4} \times {10}^{4x ^{7} } }{8 \times 43 \times {5}^{3} } [/tex]

The equation of this circle include the following: C. (x - 8)² + (y - 4)² = 16.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²

Where:

Substituting the given points into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - 8)² + (y - 4)² = 4²

(x - 8)² + (y - 4)² = 16.

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Answer:

Below

Step-by-step explanation:

N, the number can be anything   greater than or equal to 11.5 and less than 12.5  

11.5 ≤  n < 12.5

The value of x in the triangle s 16√2

From the question, we have the following parameters that can be used in our computation:

The triangle

The vertical side (y) can be calculated using the following equation

y/2 = (18 - 2)/y

So, we have

y^2 = 32

Take the square roots

y = 4√2

The length x is then calculated as

x^2 = y^2 + (18 - 2)^2

Substitute the known values in the above equation, so, we have the following representation

x^2 = (4√2)^2 + (18 - 2)^2

Evaluate

x^2 = 288

Take the square root

x = 16√2

Hence, the value of x is 16√2

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Answer:

$43.77

Step-by-step explanation:

The total price without tax is $41.69. To add tax, we take 5% of this total (which ends up being $2.08) and add it to the total. This makes the final price $43.77.

Answer: The line y = 3x - 5 can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, m = 3 and b = -5.

When a line is reflected across the x-axis, the slope of the line changes sign, but the y-intercept remains the same. This means that if the original line has slope m and y-intercept b, the reflected line will have slope -m and y-intercept b.

For the image, y = 1 - 3x, the slope is -3 and the y-intercept is 1.

To find the value of a, we can set the two lines equal to each other and solve for x:

3x - 5 = 1 - 3x

Solving for x, we get:

4x = 6

x = 3/2

So the line of reflection, x = a, passes through

Step-by-step explanation:

If the wax cost $1.38 a square foot, the cost of wax to cover the area of the floor is $1,569.75.

The correct option is B.

The total area of the floor is calculated from the shape of the floor.

The floor is made up of a trapezoid and a rectangle.

The area of a trapezoid can be calculated as:

A = (a + b)/2 * h

where

a and b are the lengths of the bases and h is the height.

The trapezoid has a height of 15 feet and bases of 35 feet and (20 - 20) or 10 feet. So its area is:

A = (35 + 10)/2 * 15

A = 337.5 square feet

The rectangle has a base of 20 feet and a height of 40 feet. So its area is:

A =20 * 40

A = 800 square feet

The total area of the figure is the sum of the areas of the trapezoid and triangle:

A = 337.5 + 800

A = 1137.5 square feet

Finally, to find the cost of the wax, we multiply the area by the cost per square foot:

Cost = 1137.5 * $1.38

Cost  = $1569.75

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Absolutely, because they show how big a number is, average leading zeros are regarded as significant digits. Leading zeros are counted as important figures since they help determine the decimal point's location and the size of the number.

Leading zeros in a number are important figures. This implies that when counting the total number of significant figures in a number, they are taken into account. The reason for this is that preceding zeros reveal the location of the decimal point and, hence, the size of the number. Because the leading zero signifies that the number is in hundredths, the number 0.002, for instance, has three significant figures. The number would be read as two rather than two hundredths without the leading zero. Due to their significance in assessing a number's precision, leading zeros should always be counted among the significant figures.

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The correct statements about the given isosceles triangle are: (B) YQ = XP, (C) ∠WXY = ∠WYX, (D) WQ/QX = WP/PY, (E) PQ ║ XY, and (F) ∠PXY = ∠QYX.

An isosceles triangle in geometry is a triangle with two equal-length sides.

It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

The isosceles right triangle, the golden triangle, the faces of bipyramids, and some Catalan solids are all examples of isosceles triangles.

Isosceles triangles were first studied mathematically in Babylonian and Egyptian mathematics.

Isosceles triangles are commonly employed in architecture and design, such as in building pediments and gables, and have been utilized as ornamentation since much earlier periods.

Then, according to the given image, the true statements for the following isosceles triangle can be:

YQ = XP

∠WXY = ∠WYX

WQ/QX = WP/PY

PQ ║ XY

∠PXY = ∠QYX

Therefore, the correct statements about the given isosceles triangle are: (B) YQ = XP, (C) ∠WXY = ∠WYX, (D) WQ/QX = WP/PY, (E) PQ ║ XY, and (F) ∠PXY = ∠QYX.

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K'(-2, 1) is the coordinate of the image of point K, found by multiplying the original x-coordinate of the point K (2) by -1. To reflect the triangle over the y-axis, the x-coordinate of each point is multiplied by -1.

Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.

The coordinate of the image of point K is K’(-2, 1). This means that the x-coordinate of the point is -2 and the y-coordinate of the point is 1. This can be found by multiplying the original x-coordinate of the point K (2) by -1. The y-coordinate of point K remains the same, so the y-coordinate of the image of point K is 1.

Therefore, the coordinate of the image of point K is K’(-2, 1).

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Answer: The pants cost more than $34.5

Step-by-step explanation:

Triangle PST is congruent to triangle QSR based on side-angle-side congruency theorem

A triangle is a polygon that has three sides and three angles. Types of triangles are equilateral, isosceles, scalene, right angled triangle. In an equilateral triangle, two sides are equal.

Two triangles are said to be congruent, if all angles and all sides are congruent to each other.

From the diagram:

ΔPQR is equilateral (given)

QR = PT (Given)

∠SPT = ∠RQS (Given)

PS = QS (Definition of equilateral triangle)

ΔPST ≅ ΔQSR (Side angle side congruency theorem)

Triangle PST is congruent to triangle QSR

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The graph of the function is attached below.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given a function x +4y -3 = 0

To graph the equation x + 4y - 3 = 0, we need to find at least two points that satisfy the equation and plot them on a coordinate plane. To do this, we can use the intercept method.

First, we can find the x-intercept by setting y = 0 in the equation and solving for x:

x + 4(0) - 3 = 0

x = 3

So the x-intercept is (3, 0).

Next, we can find the y-intercept by setting x = 0 in the equation and solving for y:

0 + 4y - 3 = 0

4y = 3

y = 3/4

So the y-intercept is (0, 3/4).

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The graph of the function [tex]g(x) = 6.(\frac{8}{3})^x[/tex] is an exponentially growing function.

The formula for exponential growth is [tex]y = y_0.e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_0.e^{(-kt)}[/tex].

Given, An exponential function [tex]g(x) = 6.(\frac{8}{3})^x[/tex].

The graph of the function has a y-intercept of 6 and it is an exponentially growing function for all positive values of 'x'.

To obtain the intercept we set x = 0, Therefore, [tex]g(0) = 6.(\frac{8}{3})^0[/tex],

[tex]g(0) = 6[/tex].

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Answer: WVZ=84 XVW=84   IFH= 14 EFG= 58

Step-by-step explanation:

9x-15=5x+29- do 9-5 to get 4x then 29+5 to get 44 then divide 44 by 4

6x+25=2x+3- do 6-2 to get 4x then 3-25 to get -22 then divide -22 by 4

Answer:

y = -3 or (2, -3)

Step-by-step explanation:

For x = 2 :

(2 ⋅ 2) + y = 1

4 + y = 1

4 − 4 + y = 1 − 4

0 + y =−3

y = −3 or (2, -3)

The equation of the line is y = ( 1/2 )x + 1 and the y intercept is b = 1

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 0 , 1 )

Let the second point be Q ( 4 , 3 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 3 - 1 ) / ( 4 - 0 )

Slope m = 2/4

Slope m = 1/2

Now , the equation of line is y - y₁ = m ( x - x₁ )

y - 1 = ( 1/2 ) ( x - 0 )

y - 1 = ( 1/2 )x

Adding 1 on both sides , we get

y = ( 1/2 )x + 1

Hence , the equation of line is y = ( 1/2 )x + 1

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The statements supported by the random samples of the amount of time spent shopping, as shown on the box plot are :

For Group A, the box begins at 30 minutes. This means that 25 % of those in group A spent 30 minutes or less when shopping. For Group B, this can be said to be less than 25 %.

Group A had a longer box than Group B and what this is meant to show is that Group A had greater variability in the data ( number of minutes spent shopping ) than Group B.

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The 30th term value is 2900.

A series of integers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Given:
A sequence,

10, 110, 210, 310, …

To find the common difference:

110 - 10 = 100

So, d = 100

Remember that,

aₙ= a₁ + (n-1)d

aₙ=a₁+(n−1)d

So,

aₙ = 10 +(n−1)100.

a₃₀ = 10 + (30 - 1)100

a₃₀ = 10 + 29(100)

a₃₀ = 10 + 2900

a₃₀ = 2910.

Therefore, a₃₀ = 2910.

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The largest palindrome less than 600 is 599. The fifth smallest prime number is 11. The sum of these two numbers is 599 + 11 = 610, so the answer is (E) 611.

Palindromes are often used in literature, poetry, and wordplay, and are considered a form of symmetrical writing. Palindromes can be simple or complex, and can be made up of individual words or phrases. For example, "Madam I'm Adam" is a famous palindrome made up of individual words, while "Able was I ere I saw Elba" is a palindrome made up of a complete sentence.

Palindromes have been a source of fascination and inspiration for centuries, and have been studied by mathematicians, linguists, and computer scientists. Palindromic sequences have been found in DNA, and have been used in the study of genetics and molecular biology. Some palindromes are also considered to be puzzles, and are used in problem solving and critical thinking exercises.

In summary, a palindrome is a sequence of characters that reads the same backward or forward, and has been a source of interest and inspiration for centuries. They are found in literature, poetry, and mathematics, and are considered a form of symmetrical writing.

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a) The shape of the histogram appears to be roughly symmetric and bimodal.

b) The histogram appears to have two modes, explanation is given below.

c) D option is correct.

a) The shape of the histogram appears to be roughly symmetric and bimodal.

b) The histogram appears to have two modes, which may be due to the fact that the data includes both male and female students. The two modes may correspond to the average shoe sizes for men and women, respectively.

c) D option is correct. The distribution has two modes from 38 to 40 and from 44 to 46. This may be due to having data for both men and women. The lower mode might be for women and the upper for men.

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____ The given question is incomplete, the complete question is given below:

In the U.S., shoe sizes are defined differently for men and women, but in Europe, both genders use the same shoe size scale. The accompanying histogram shows the European shoe sizes of 269 male and female college students, converted from their reported U.S. shoe sizes.

a) Describe the shape.

view the histogram (The distribution is roughly symmetric and bimodal.)

b) How many modes does the histogram have? What might explain that?

c) Choose the correct answer below.

A. The distribution is multimodal, with modes from 38 to 40, from 44 to 46, and from 48 to 50. This may be due to having data for both men and women. The first two modes might be for women and the third for men.

B. The distribution has one mode from 44 to 46. This is due to the students having roughly the same mean shoe size.

C. The distribution has one mode from 38 to 40. This is due to the students having roughly the same mean shoe size.

D. The distribution has two modes from 38 to 40 and from 44 to 46. This may be due to having data for both men and women. The lower mode might be for women and the upper for men.

E. The distribution has two modes from 34 to 36 and from 44 to 46. This may be due to having data for both men and women. The lower mode might be for women and the upper for men.

F. The distribution is multimodal, with modes from 34 to 36, from 40 to 42, and from 43 to 50. This may be due to having data for both men and women. The first two modes might be for men and the third for women

G. The distribution does not have any modes, because it is uniform i Shoe Sizes Count.

By using effective text features and text structure, the author can help the reader to better understand and remember the central idea of the text. These elements can also make the text more engaging and interesting to read. Overall, text features and text structure are essential tools for conveying information effectively and conveying the author's intended message to the reader.

Generally, Text features and text structure are important components of a written text that contribute significantly to its overall meaning. The central idea of a text is the main message or thesis that the author wants to convey to the reader. The text structure is the way the author organizes the information within the text, and the text features are the visual and organizational elements of the text that help the reader navigate and understand the content.

Text features such as headings, subheadings, and bullet points help the reader to quickly identify the main ideas and subtopics of the text. Bold and italicized fonts may be used to emphasize important concepts or ideas. Images, charts, and graphs can provide visual aids that help the reader understand complex information. In addition, text features like footnotes, citations, and a bibliography can help to establish the credibility of the author and the information presented in the text.

Text structure also plays a critical role in conveying the central idea of a text. The author may use a variety of text structures, such as chronological order, cause and effect, problem-solution, or compare and contrast, to organize the information and present it in a logical and coherent manner. For example, a text about the causes and effects of climate change might use a cause and effect structure to explain how human activities are contributing to global warming and the impacts that result from this phenomenon.

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