The area of this square is one hundred twenty-one square centimeters. What is the length of one side of this square?

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 current temperature is 48°F, in expected to drop 1.5°F each hour, then the hours per word 8 hours the temperature will be 36°F.

The current temperature is = 48°F.

It is expected to drop = 1.5°F each hour.

We can assume, temperature = 36°F

Let x hours the temperature will be 36°F.

Temperature is a measure of the average kinetic energy of the particles in an object. When the temperature increases, the motion of these particles also increases. Temperature is measured with a thermometer or a calorimeter.

Then,

48 - 1.5x = 36

It's expected to drop 1.5F per hour,

We can list the equation,

So,

We can write,

48 - 1.5x = 36

48 - 36 = 1.5x

We can sum or difference of the product,

1.5x = 12

x = 12/1.5

We can divide the products,

x = 8 hours

Therefore,

In expected to drop 1.5°F each hour, then the hours per word 8 hours the temperature will be 36°F.

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Answer:

The present temperature is 48°F; it is anticipated to decrease by 1.5°F every hour, reaching 36°F in 8 hours.

Step-by-step explanation:

48°F is the current temperature.

An hourly decrease of 1.5°F is anticipated.

We'll assume that it's 36°F.

The temperature will be 36°F in x hours.

The average kinetic energy of the particles in an object is measured by its temperature. The velocity of these particles likewise increases as the temperature rises. A thermometer or a calorimeter is used to determine the temperature.

Then,

48 - 1.5x = 36

It's expected to drop 1.5F per hour,

We can list the equation,

So,

We can write,

48 - 1.5x = 36

48 - 36 = 1.5x

We can sum or difference of the product,

1.5x = 12

x = 12/1.5

We can divide the products,

x = 8 hours

Therefore,

In expected to drop 1.5°F each hour, then the hours per word 8 hours the temperature will be 36°F.

The fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

The volume of a rectangular prism can be calculated using the formula:

V = l x b x h..........(i)

where,

V ⇒ Volume

l  ⇒ length

b ⇒ width

h ⇒ height

From the question, we are given the values,

l = 8 inches

b = 4 inches

h = 9 inches

Putting these values in equation (i), we get,

V = 8 x 4 x 9

⇒ V = 288 in³

Therefore, the fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

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Answer:− -19s

Step-by-step explanation:

Move  

Answer: x = 70

Step-by-step explanation:

We are looking at the supplementary angles so 180-45 = 2x -5

135 = 2x-5 add 5 to both sides

135+5 = 2x

140 = 2x Divide both sides by 2

70=x

Check: 2(70)- 5 = 135

135 + 45= 180

OK!

Answer: option D

Step-by-step explanation:

Given equation:

P = 6 w + 8 [eq1]

l=2w+4 [where l is length]

using eq1 we have:

6w=P-8

w=(P-8)/6

hence  option D

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Here we have a dilation of scale factor 2.

We can see that bot figures we have the same slope, so we just have a dilation of scale factor K to go from figure A to figure B.

To find the value of K, notice that for some side length L in figure A, the correspondent length L' in figure B must be:

L' = K*L

Here if we use the left sides, we will get:

for figure A; L= 2

for figure B: L = 4

4 = K*2

4/2 = K

2 = K

So this is a dilation of scale factor k = 2.

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Answer:

shape is how it looks like Square is a shape and size is how big something in like my size of my foot is 6 inches

Step-by-step explanation:

well idk your real question i think it is that your shape and size can change

Answer:

If a system is graphed and does not intersect, the systems are parallel.

Step-by-step explanation:

The constructions which must be completed in order to construct the inscribed circle to triangle QRS is; Choice A; The perpendicular bisectors of QR.

It follows from the task content that;

On this note, it follows that the first construction in order to construct the inscribed circle to triangle QRS is; The perpendicular bisectors of QR.

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The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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The statement can be written using absolute value notation as follows:

| x - 76 | ≤ 24

The notation, ( | x - 76 | ≤ 24 ) represents that the absolute value of the difference between x and 76 is less than or equal to 24. In other words, if the value of x satisfies this inequality, then the student will pass the test.

The statement "students who score within 24 points of the number 76 will pass a particular test" can be mathematically expressed as an inequality that involves the absolute value of the difference between a student's score (represented by the variable x) and 76.

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Answer: two integers are 5 and 14.

Step-by-step explanation:

Let x be the smaller integer, then the larger integer is x+9. We can set up the equation:

1/x + 2/(x+9) = 6/5

Multiplying both sides by the least common multiple of the denominators:

5(x+9) + 10x = 6x(x+9)

Simplifying and rearranging:

6x^2 - 17x - 45 = 0

We can use the quadratic formula to solve for x:

x = [17 ± √(17^2 - 4(6)(-45))] / (2(6))

x ≈ 4.5 or x ≈ -1.667

Since we are looking for a positive integer, we can discard the negative solution.

Therefore, the smaller integer is x ≈ 4.5, but since it must be a positive integer, the smaller integer is 5. The larger integer is x+9, or 14.

Checking our answer:

1/5 + 2/14 = 6/70 + 20/70 = 26/70 = 13/35

13/35 is equal to 6/5 when multiplied by 6/7:

(13/35) * (6/7) = 78/245 = 6/5

Therefore, our solution is correct, and the two integers are 5 and 14.

Answer:

7, 2, -3, -8

Step-by-step explanation:

y = -5x + 2  Substitute in -1 for x

y = -5(-1) + 2

y = 5 + 2

y = 7

y = -5x + 2  Substitute in 0 for x

y = -5(0) + 2

y = 0 + 2

y = 2

y = -5 + 2 substitutes in 1 for x

y = -5(1) + 2

y = -5 + 2

y = -3

y = -5x + 2  Substitute in 2 for x

y = -5(2) + 2

y = -10 + 2

y = -8

Helping in the name of Jesus.

Answer:

y+2=-4(x+9)

Step-by-step explanation:

Point slop form: y-y₁=m(x-x₁)

X-coordinate is -9 and the y-coordinate is -2.

slope is -4.

y-(-2)=-4(x-(-9))

y+2=-4(x+9)

Hope this helps!

Answer:

1: You need to provide more information for people to be able to answer your question.

2: Is this a question or a statement? Please clarify.

Step-by-step explanation:

The value of h can be any value other than 2.

The augmented matrix of a consistent linear system must have a unique solution, which means the determinant of the coefficient matrix must be non-zero.

       [1 h

        3 6]

The determinant of this matrix is (1 * 6) - (3 * h) = 6 - 3h.

For the determinant to be non-zero and the system to be consistent, 6 - 3h must not be equal to zero, so h cannot be equal to 2.

Therefore, the value of h can be any value other than 2.

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Answer:

y = 1/3x + 14/3

Step-by-step explanation:

y = mx + b

we know the slope, so the equation would be --> y = 1/3x + b

Now we plug in the coordinates of the given point (4, 6) the line goes through, and solve for b:

y = 1/3x + b

6 = 1/3(4) + b

6 = 4/3 + b

-4/3   -4/3

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

14/3 = b

Answer:

A

Step-by-step explanation:

Answer:

Don't agree with 1 and 2, agree with 3

Step-by-step explanation:

1: -35 degrees Fahrenheit is colder than 35 degrees Fahrenheit.

2: A distance of 15 meters is greater than a distance of 10 meters, not less, so it is not closer to sea level.

3: A distance of 17 meters is less than a distance of 40 meters, so it is closer to sea level.

To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

Answer:

Variable terms: 4a and 6a

Constant terms: 4 and 11

Step-by-step explanation:

A constant term is one that is NOT multiplied by any variables.

At this level of math, think of constants as terms that are only numbers.

(for example: 1, 68.9, -42, etc.)

Note that a term in « a + bi » form can also be a constant.

A variable term is a one that IS multiplied by a variable.

(for example x, -3y, 8z, etc.)

In question 1, the variable terms are:

4a and 6a because they are multiplied by the variable a

The constant terms are:

4 and 11 because they are simply integers

Note that the constant terms could also be written as -4 and -11 depending on how the operations are viewed (subtracting vs adding a negative)

Answer:d

Step-by-step explanation:

Answer:

B & D

Step-by-step explanation:

Since the point negative 4.5 (-4.5) is labeled on this number line representing temperature change, the absolute value of the point labeled in the image means that: B. the temperature equals 4.5 degrees.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

In conclusion, the absolute value of a number is always positive and it can be used for describing the distance of a number from zero (0) on the number line, without taking its direction into consideration.

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Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Answer:

2x - 2 = 0

Step-by-step explanation:

2(x - 1) = 5.0 - 2 - 3.0

2x - 2 = 5.0 - 2 - 3.0

2x - 2 = 0

Answer:

a) .38 × 2,450 = 931 people buy the local newspaper.

b) 2,450 - 931 = 1,519 people do not buy the local newspaper.

Answer:

x > -3

Step-by-step explanation:

4 - 4x < 16

- 4x < 16 - 4

- 4x < 12 (note that both can be divided by -4)

x > -3

That's the final answer.

AND if you're co fused about why the sign changed, you should always remember this

By negative num I mean any number that starts with a minus for example -2, -3, -5, -100

Answer:

f(x) = -2.5x + 4

Step-by-step explanation:

If you go down 5 units and 2 units to the right then there is another point so the slope is -5/2 which is the same thing as -5 divided by 2. So it’s -2.5 as the slope and for the y- intercept, there is only one point on there and it is on 4. So the function is

f(x) = -2.5x + 4

I hope this helps

(I deserve to be marked the brainliest)

Answer:

f(x)=−5/2x+4

Step-by-step explanation:

other answer is wrong, i took the test