a. Bared an the information in the figure, which of the two cities have nearest to each other?
Select choice
b. Based on the information in the figure, which of the two cities are farthest apart from each other?
Select Choice
c. If you were going to use the information from 5 Sate's sketch to plan a road trip between these cities, what is an assumption that you would have to make?
Select Choice

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2.

The five regular polyhedra, also known as the Platonic solids, are the only convex polyhedra where all faces are congruent regular polygons, and the same number of polygons meet at each vertex.

The five regular polyhedra are:

1. Tetrahedron: It has four triangular faces, and three triangles meet at each vertex.

2. Cube: It has six square faces, and three squares meet at each vertex.

3. Octahedron: It has eight triangular faces, and four triangles meet at each vertex.

4. Dodecahedron: It has twelve pentagonal faces, and three pentagons meet at each vertex.

5. Icosahedron: It has twenty triangular faces, and five triangles meet at each vertex.

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that:

"for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2".

For regular polyhedra, each face has the same number of sides (n) and each vertex is the meeting point of the same number of edges (k). Therefore, we can rewrite Euler's formula for regular polyhedra as:

V - E + F = 2  

=>  kV/2 - kE/2 + F = 2  

=>  k(V/2 - E/2) + F = 2

Since each face has n sides, the total number of edges can be calculated as E = (nF)/2, as each edge is shared by two faces. Substituting this into the equation:

k(V/2 - (nF)/2) + F = 2  

=>  (kV - knF + 2F)/2 = 2  

=>  kV - knF + 2F = 4

Now, we need to consider the conditions for a valid polyhedron:

1. The number of faces (F), edges (E), and vertices (V) must be positive integers.

2. The number of sides on each face (n) and the number of edges meeting at each vertex (k) must be positive integers.

Given these conditions, we can analyze the possibilities for different values of n and k. By exploring various combinations, it can be proven that the only valid solutions satisfying the conditions are:

(n, k) pairs:

(3, 3) - Tetrahedron

(4, 3) - Cube

(3, 4) - Octahedron

(5, 3) - Dodecahedron

(3, 5) - Icosahedron

Therefore, there exist only five regular polyhedra.

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The members of the given set in this problem are given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

The union and intersection sets of multiple sets are defined as follows:

The intersection of the sets Y and Z for this problem is given as follows:

Y ∩ Z = {0, 6, 23, 26}

(which are the elements that belong to both of the sets).

The union of the above set with the set X is given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

(elements that belong to at least one of the sets).

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Answer:

B

Step-by-step explanation:

Because they took the correct steps to answer the equation.They also got the right answer (-2).

At the begining they added 4 to both sides (to cancel out the 4)

C would be wrong because they subtracted 4 from a negative four and this does NOT cancel it out.

Have a Supercalifragilisticexpialidocious day, I hope you like my explination. If you do please give rating or brainliest :)

Answer: 24

Step-by-step explanation:

To find the area of the composite figure, we need to find the area of the sector and the area of the triangle and then add them together.

Area of sector = (θ/360) * π * r^2, where θ is the angle of the sector in degrees, r is the radius of the circle.

The angle of the sector can be found by subtracting the angle of the triangle from 360 degrees. The radius of the circle can be found by dividing the length of the arc by the angle of the sector.

Length of the arc = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 4 = 4.19

Radius of the circle = 4.19/60 = 0.07

Angle of sector = 360 - 60 = 300 degrees

Area of sector = (300/360) * 3.14 * 0.07^2 = 0.0041

The area of the triangle can be found using the formula:

Area of triangle = (1/2) * base * height = (1/2) * 8 * 6 = 24

Therefore, the total area of the composite figure is:

0.0041 + 24 = 24.0041

Rounding to the nearest hundredth, the area of the composite figure is approximately 24.00.

Answer:

L = 16

w = 10

Step-by-step explanation:

Givens

Area = 160 sqr inches

width = x

length = x + 6

Equation

Area = L * w

Solution

Substitute in the equation all of the givens.

160 = x(x + 6)                     Remove the brackets

160 = x^2 + 6x                   Subtract 160 from both sides.

160-160 = x^2 + 6x - 160

0 = x^2 + 6x - 160

This equation factors. Turn it around first

x^2 + 6x - 160 =  0

(x - 10)(x + 16) = 0

Answer

x (width) = 10

x + 16 = 16

Answer:

The length is 16 inches and the width is 10 inches.

Step-by-step explanation:

f(x) = 3x + 2 reflected about y - axis is:  f(x) = g(x) = 3.(-x) +2

Given,

In the question;

g(x) is the reflection across the y-axis of f(x)=3x+2.

To find the g(x) and write the answer in the form mx + b, where m and b are integers .

Now, According to the question:

f(x) = 3x +2

The reflection over the x-axis means multiply f(x) by -1

f(x) = 3x + 2 reflected about y - axis is:

Here, f(x) = g(x) = 3.(-x) +2

Hence, f(x) = 3x + 2 reflected about y - axis is:  f(x) = g(x) = 3.(-x) +2.

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Answer:

  C.  1889

Step-by-step explanation:

Given fixed weekly costs of $3778 and a variable cost per handle of $1, you want to know how many handles must be produced weekly for sale at $3 each to break even.

The "contribution margin" of each handle is the difference between its variable cost and its selling price:

  $3 -1 = $2

The enterprise will break even when the sum of contribution margins is equal to the fixed costs. If h is the number of handles produced and sold, then to break even, we must have ...

  2h = 3778

  h = 1889

1889 handles must be molded weekly to break even.

__

Additional comment

You get the same result if you write the profit equation and solve for the number of handles that makes profit be zero.

  profit = revenue -cost

  0 = (3h) -(3778 +1h)

  3778 = 2h . . . . . as above

  1889 = h

Answer:

16/40 = 40%

Step-by-step explanation:

I divided 16/40 and got 0.4,

To turn a decimal into a percentage, either multiply by 100 or move the decimal to the right 2 times.

Answer:

3/4 of a tank =3/4(13) gal

=39/4 almost 10 gal

An equation can be written to determine the number of students that went on this trip is: C. \(\frac{1259}{s} + 12=\frac{1259}{s+9}\)

In order to write an equation to determine the number of students that went on this trip, we would have to assign a variable and an expression to the number of students who went on the trip and the original number of students who had planned to go on the trip as follows;

Since a total of $1259 was collected from all of the students with 9 students dropping out and their portion of the money collected given back to them while the students that are all still going must contribute an additional $12, an equation to determine the number of students that went on this trip is given by;

\(\frac{1259}{s} + 12=\frac{1259}{s+9}\)

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Complete Question:

A high school class is planning a field trip to an art museum in their city. The class collected a total of $1259 from all of the students, which will go towards renting a bus, museum admission, and lunch.

However, a week before the trip 9 students had to drop out and their portion of the collected money had to be given back to them. Due to this, the students that are all still going must contribute an additional $12 each to cover all of the cost.

Now let s be the number of students who went on the trip and s + 9 be the original number of students who had planned to go on the trip

What equation can be written to determine the number of students that went on this trip?

I don't think I can do it. sorry

Answer:

80.

Step-by-step explanation:

The answer is A.

An indefinite integral is a function that, when differentiated, equals the original function. It is denoted by ∫f(x)dx, where f(x) is the function to be integrated. An indefinite integral always has an arbitrary constant of integration, which is denoted by C. This is because the derivative of any constant is zero, so the derivative of ∫f(x)dx+C is still equal to f(x).

A definite integral is the limit of a Riemann sum as the number of terms tends to infinity. It is denoted by ∫

a

b

​

f(x)dx, where a and b are the limits of integration. A definite integral does not have an arbitrary constant of integration, because the limits of integration specify a unique value for the integral.

In other words, an indefinite integral is a family of functions that share the same derivative, while a definite integral is a single number.

Answer:

  14 ft

Step-by-step explanation:

After the sides are folded up, the depth of the box is 2 ft, so the area of the square bottom is ...

  (200 ft^2)/(2 ft) = 100 ft^2

The edge dimension of the bottom is then ...

  √(100 ft^2) = 10 ft

Each side adds 2+2=4 ft to the bottom dimension in each direction, so the original square piece of metal was 14 ft square.

Answer:

∆SMK is similar to ∆RMT by AA.

The function f (x) =0.5(2)ˣ represents the growth in square centimeters of a fungus after X days F (85)

Function:

Function, in mathematics, expression, rule or law that defines the relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics and essential for establishing physical relationships in science.

According too the Question:

Given That:

f (x) =0.5(2)ˣ

(B) When, x= 8

f(8) = 0.5(2) ⁸

    = 128

Therefore, the Function is true.

(c) When, x = 10

f(10) = 0.5 (2)¹⁰

      = 512

That is, the value of functions after 10 days.

Therefore, C is Correct.

(D) when, x = 64

f(64) = 0.5(2)⁶⁴

This functions represents the growth in square centimeters at a function after 64 days not the answer at fungi.

(E) When, x = 85

f(85) = 0.5(2)⁸⁵

The functions represents the growth in square centimeter of a fungi after 85 days x.

Therefore, we choose B and C.

Complete Question:

The function f (x) =0.5(2)^x represents the growth in square centimeters of a fungus after X days F (85)?

Select all that apply: D A f (8) = 1 f (8) 128 f (10) 512 represents the value of the function after 10 days f (64) represents the amount of fungi after 64 days E f (85) represents the amount of days it takes for the fungi to reach 85 cm?'

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I'm sorry I have No clue

Step-by-step explanation:

lol but I honestly d0n7 kno

Answer:

7/30

Step-by-step explanation:

7/10 x 2/6

= 14/60

= 7/30

So, the answer is 7/30

Answer:

Alternate interior angles

Step-by-step explanation:

Angles 4 and 5 are alternate interior angles

Answer:

x = 3

Step-by-step explanation:

x - 1.2 = 1.8

  +1.2  +1.2

---------------

x = 3

The value of the angle θ is approximately 24.2 degrees to 1 decimal place.

In a right-angled triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. Given that tan θ = 23/52, we can find the value of the angle θ.

To find the value of θ, we can use the inverse tangent or arctan function. Taking the inverse tangent of both sides of the equation, we have:

θ = arctan(23/52)

Using a calculator or trigonometric tables, we can evaluate the inverse tangent of 23/52. The result is approximately 24.2 degrees.

Note that in the context of a right-angled triangle, the tangent function is defined for acute angles (less than 90 degrees). Since 0 degrees is the smallest possible angle, it is considered an acute angle in this case.

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Answer:

Step-by-step explanation:

This is a linear function (a line), meaning it can be modeled in the form y=mx+b.

Taking two points that lie on the line, say (-1, 2) and (3, -1),

m=(-1-2)/(3-(-1))=-3/4.

So we have y=(-3/4)x+b.

Substituting in the point (-1, 2), we get that 2=(-3/4)(-1)+b

2 = 3/4 + b
b = 5/4

Therefore, y=(-3/4)x + 5/4.

Answer:

.20x = 72, so x = 360

.30(360) = 108

The triangle with all sides is are given below

What is a triangle?

Triangles are three-sided closed polygon formed by the intersection of three lines. It is encountered a lot in everyday life. It is one of the basic shapes of geometry. It has three sides, three angles, and three vertices.

Given, angle A =30, b=6

we know cos 30 = √3/2

√3/2 = b/c

√3/2=6/c

c =6/√3/2= 6.9

Similarly for a=13, b =13

using pythagoras theorem,

c^2=a^2+b^2

=18.38

Hence, we can write the rest part

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Answer:

x= 16 ft

length = 4 ft

width = 11 ft

Step-by-step explanation:

The area is length* width

so the length is ( x - 12 )

and the width is ( x - 5 )

the area is 44ft

so now set up an equation and solve for x

( x - 12 ) ( x - 5 ) = 44

distribute

x^(2) - 17x + 60 = 44

inverse operations

x^(2) - 17x + 60 = 44

                - 60     - 60

x^(2) - 17x = -16

factor

x^(2) - 17x = -16

x ( x - 17 ) = -16

now it is pretty clear that the answer is:

x = 16

just substitute it into the equation and check

( x - 12 ) ( x - 5 ) = 44

( 16 - 12 ) ( 16 - 5 ) = 44

( 4 ) ( 11 ) = 44

44 = 44

this also shows that

the length is 4

because:

( x - 12 )

= ( 16 - 12 )

= 4

and the width is 11

because:

( x - 5 )

= ( 16 - 5 )

= 11