Find the volume of the sphere. Express your answer in terms of pi.

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Answer:

x = 3.

Step-by-step explanation:

Begin by setting up a ratio comparing the small triangle to the large triangle. Remember, combine the values of the parts of the sides given to find the total lengths of the sides:

2x + x + 5 = 3x + 5

4 + 3 = 7

Now, we can set up a ratio:

[tex]\frac{x+5}{4}=\frac{3x+5}{7}[/tex]

Cross multiply:

7(x + 5) = 4(3x + 5)

Distribute:

7x + 35 = 12x + 20

Subtract 7x from both sides:

35 = 5x + 20

Subtract 20 from both sides:

15 = 5x

Divide both sides by 5:

x = 3.

Answer:

Step-by-step explanation: You can find the value of x with a little knowledge about proportions between similar polygons. The sides with lengths relative to x are similar to each other meaning that you can use the proportion: x/3x+5 = 4/7 solve for x by cross multiplying and you will get the value of x.

Answer: Semi-regular tessellations are made of more than one kind of regular polygon. There are only 8 semi-regular tessellations.

A semi-regular tessellation is a tiling of the plane using regular polygons where the arrangement at each vertex is the same but the types of polygons may vary.

There are 8 known semi-regular tessellations.

There is a finite number of possibilities due to the constraints on the arrangements of polygons.

We have,

A semi-regular tessellation, also known as a uniform tessellation or Archimedean tessellation, is a type of tessellation or tiling of the plane where regular polygons are used to fill the space.

In a semi-regular tessellation, the arrangement of polygons at each vertex is the same, but the types of polygons may vary.

To create a semi-regular tessellation, two conditions must be met:

- Each vertex (or corner) of the tessellation must have the same arrangement of polygons around it.

- The sequence of polygons around each vertex must be the same, although the actual polygons may differ.

There are exactly 8 known semi-regular tessellations, which are formed using regular polygons.

These tessellations include combinations of triangles, squares, hexagons, and dodecagons (12-sided polygons). Some examples of semi-regular tessellations include the honeycomb pattern and the tiling known as "Truchet tiles."

As for the question of why there aren't infinitely many semi-regular tessellations, it is because the arrangement and combination of regular polygons at each vertex are constrained.

The conditions for a semi-regular tessellation limit the possibilities for the types and arrangements of polygons. While there are many ways to arrange polygons around a vertex, the number of distinct arrangements is finite.

Thus,

A semi-regular tessellation is a tiling of the plane using regular polygons where the arrangement at each vertex is the same but the types of polygons may vary.

There are 8 known semi-regular tessellations, and there is a finite number of possibilities due to the constraints on the arrangements of polygons.

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Answer:

[tex] {3x}^{2} + 2x[/tex]

Solution,

[tex]x(3x + 2) \\ = x \times 3x + x \times 2 \\ = {3x}^{2} + 2x[/tex]

hope this helps...

Good luck on your assignment..

Answer:

3x²+2x

Step-by-step explanation:

=> x(3x+2)

Using distributive property

=> (x*3x)+(x*2)

=> 3x²+2x

Answer:

Cornor should divide the total length of the road on which there is traffic by the length of each of the cars

Step-by-step explanation:

The best calculation he can use is to divide the total length of the road on which we have the traffic by the length of each of the cars

Mathematically, the best way to go about this is to convert the miles to feet then divide by the length of each of the cars

Mathematically 1 mile = 5280 feet

so 5.5 miles will be = 5280 * 5.5 = 29,040 feet

It is this length we shall now divide by 12.5 ft

And that is 29,040/12.5 = 2,323.2

Which is approximately 2,323 cars

Answer:

2730

Step-by-step explanation:

We want to determine the greatest common divisor of the elements of the set  [tex]S = \{ n^{13} - n \mid n \in \mathbb{Z} \}.[/tex]

We apply the Fermat's little theorem which states that if p is a prime number, then for any integer a, the number aᵖ − a is an integer multiple of p.

Now, [tex]n^{13} \equiv n \mod p [/tex] if p-1 divides 12.

Since the  of 12 are 1,2,3,4, 6, 12, the corresponding primes are 2, 3, 5, 7, 13.

Therefore, the gcd of the elements in [tex]2^{13}-2[/tex] and [tex]3^{13}-3$ is 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13.[/tex]

2*3*5*7*13=2730

Therefore, the gcd of the elements in set S is 2730.

Answer:

5[tex]\sqrt{2}[/tex]

Step-by-step explanation:

prime factorising 50 inside root,

[tex]\sqrt{50}[/tex]=[tex]\sqrt{5*5*2}[/tex]

      5*5 is a perfect square

    So root of 5*5(or 25) is 5.

Hence 5 comes outside and 2 remains in bracket.

=5[tex]\sqrt{2}[/tex]

Answer:

Obi's age is 18 and Oba's age is 9

Step-by-step explanation:

Let Obi's age be x and Oba's age be y

Condition 1:

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

Condition 2:

(x-4) = 3(y-4)

=> x -4 = 3y-12

=> x - 3y = -9  -----(2)

Putting eq (1) in (2)

2y - 3y = -9

=> -y = -9

=> y = 9

Now,

x = 2y

=> x = 2(9)

=>  x= 18

Answer:

[tex]8\\4[/tex]

Step-by-step explanation:

Obi's age is [tex]x[/tex].

Oba's age is [tex]2x[/tex].

4 years ago, Obi's age was [tex]x-4[/tex].

4 years after, Obi's age is [tex]2x-4[/tex]

3 times more than Oba's, so [tex]3(x-4)[/tex]

[tex]2x - 4 = 3( x - 4)[/tex]

[tex]2x - 4 = 3x-12[/tex]

[tex]2x - 3x = -12+4[/tex]

[tex]-1x=-8[/tex]

[tex]x=8[/tex]

[tex]x-4\\(8)-4=4[/tex]

Hi,

Complete the steps to solve the equation 4e2 + 2x = x − 3 by graphing.

The equation 4e2 + 2x = x - 3 has

x-3

x -coordinates

has no solution

Answer:

6

Step-by-step explanation:

=> 2x-2y

Taking 2 common

=> 2(x-y)

Given that x-y = 3

=> 2(3)

=> 6

Answer:

1

[tex] - y = 3x \\ \frac{ - y}{ - 1} = \frac{3 - x}{ - 1} \\ y = \frac{3 - x}{1 } \\ y = x - 3[/tex]

2

[tex]2x - 2y \\ factor \: out \: 2 \\ 2(x - y) \\ [/tex]

Answer:

8.3 to the nearest tenth.

Step-by-step explanation:

The mean = (6 + 13 + 14 + 3 + 5 + 8) / 6

= 8 .33.

Answer:

8.3

Step-by-step explanation:

The mean is 8.333...

So rounded to the nearest tenth would get your answer...

8.3

Hope this helps!

Answer:

∠ A ≈ 16.67°

Step-by-step explanation:

Using the Sine rule in Δ ABC

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex] , substitute values

[tex]\frac{8}{sinA}[/tex] = [tex]\frac{16}{sin35}[/tex] ( cross- multiply )

16 sinA = 8 sin35° ( divide both sides by 16 )

sin A = [tex]\frac{8sin35}{16}[/tex] , thus

∠ A = [tex]sin^{-1}[/tex] ( [tex]\frac{8sin35}{16}[/tex] ) ≈ 16.67° ( to 2 dec. places )

Answer:

435 pgs

Step-by-step explanation:

29 pgs per hr

29(15) pgs per 15 hr

435

Answer:

435 pgs

Step-by-step explanation:

29 x 15 = 435

188 is the answer of questions

Answer:

8

Step-by-step explanation:

A) mean = average. Find the total of the ages and dive by number of people:

19x 2 = 38

20x3= 60

21x1= 21

22x4 = 88

23x1=23

38 +60 +21+88+23= 230

230/ 11= 20.9

Mean = 20.9

B ) 1 more person makes the total 12 people. The mean becomes 22, so total of the ages would be 12x22= 264

Subtract the two totals 264 - 230 = 34

The person would be 34

Answer:

the answer is 6 just check it

The volume of the given figure is 288 cubic units.

Given a prism with the base dimension of 8×12 units and the height of 3 units.

From the general formula of the volume of the prism,

The volume of a prism is the product of the area of the base and the height of the prism. Prism volume (V) = B × h,

where, B is the area of the base and h is the height of the prism. = l × w × h,

where l, w, and h are the length, width, and height of the rectangular prism.

In our case,

l = 12

w =8

h =3

Volume of the prism = 12 *8 * 3

Volume of the prism = 288

Therefore, the volume of the prism will be 288 cubic units.

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Answer: There were 78 red apples at the party.

Step-by-step explanation:

This situation can be represented by the equation  

x + 3x + 2(3x) = 130    where x is the number of green apples, 3x is the number of  yellow apples and 2(3x) is the number  of red apples.

Now solve for x

x +3x +2(3x) =130

4x + 6x = 130

10x  = 130

x =  13  

Now we know that x is 13 so put it into the expression for red apples and solve for the actual number of red apples.

2 * (3*13)  = ?

2 * 39 = 78  

Answer:

Actually the correct answer is the last option.

Step-by-step explanation:

I just took the quiz on edge

The function given in the option (4) has the steepest slope.

For option (1)

Let's calculate the slope for given values of x and y in option (1)

First, let's consider the points (3,10) and (6,13):

[tex]x_1=3, x_2 =6[/tex] and [tex]y_1 = 10, y_2=13[/tex]

[tex]x_2-x_1=6-3=3[/tex]

and [tex]y_2-y_1= 13-10 =3[/tex]

Now, the formula for slope is:

[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

So, for these points,

[tex]m=\dfrac{3}{3}[/tex]

[tex]m=1[/tex]

Next, for points (6,13) and (9,16):

[tex]x_2-x_1=9-6=3[/tex]

and [tex]y_2-y_1=16-13 =3[/tex]

then, slope is:

[tex]m=\dfrac{3}{3}[/tex]

[tex]m=1[/tex]

Similarly, for points (9,16) and (12,19):

Slope is 1.

Hence, for the data given in option (1), slope is 1.

Now for option(2);

From the given graph, we can see the co-ordinates are (1,0) and (0,-2)

[tex]x_1=1,y_1=0[/tex] and [tex]x_2=0, y_2=-2[/tex]

[tex]x_2-x_1= -1[/tex] and [tex]y_2-y_1=-2[/tex]

Thus, the slope is:

[tex]m = \dfrac{-2}{-1}[/tex]

[tex]m=2[/tex]

Now for option (3):

From the given graph, it is clear that the co-ordinates are (0.5,0) and (0,1)

[tex]x_1= 0.5, x_2=0[/tex] and [tex]y_1=0, y_2=1[/tex]

[tex]x_2-x_1=0.5[/tex] and [tex]y_2-y_1= 1[/tex]

Thus, the slope is

[tex]m = \dfrac{1}{0.5}[/tex]

[tex]m =2[/tex]

Now, for option (4):

First, let's consider the points (2, -4) and (4, -12)

[tex]x_1= 2, x_2= 4[/tex] and [tex]y_1= -4, y_2=-12[/tex]

[tex]x_2-x_1= 2[/tex] and [tex]y_2-y_1=- 8[/tex]

slope is:

[tex]m = \dfrac{-8}{2}[/tex]

m =-4

Now, for points  (4, -12) and (6, -20):

[tex]x_2-x_1= 2[/tex] and [tex]y_2-y_1= -8[/tex]

Then, the slope is:

[tex]m= \dfrac{-8}{2}[/tex]

m = -4

Similarly, for points (6, -20) and (8, -28):

Slope is -4.

That means for the data given in  option (4)  slope is -4.

Hence, the slope for the option (4) is steepest.

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Answer:

Total Surface Area =

148cm²

Explanation:

in the picture

The total surface area of cuboid is 158 cm².

The surface area of a cuboid is the total area of all of the faces of a cuboid.

If, the length (l), width (w), and height (h) of the cuboid

then, use the formula: surface area (SA)=2lw+2lh+2hw.

Here, given that,

l = 6cm

w = 4cm

h = 5cm

So, required total SA = 2( 24+30+20)

                                   =158 cm²

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Answer:

3n

Step-by-step explanation:

Answer:

5/6x - 1/3 > 4/3

Multiply through by 6 you will get

5x - 2 > 8

5x > 8 +2

5x > 10

= x > 2

{ x : x > 2 }

Hope this helps.

Answer:

C x > 2

Step-by-step explanation:

Took the quiz

Answer:

A

Step-by-step explanation:

In a function no X's can repeat which is what the vertical line test is. And in this case no X's repeat therefore, making it a function.

Answer:

No, it fails the vertical line test

Step-by-step explanation:

This is not a function.  It does not have a one to one correspondence.  There are x values that have more than one y value.  It fails the vertical line test

Answer:

[tex]3t^9[/tex]

Step-by-step explanation:

Image attached below.

Answer:

976 cm^2.

Step-by-step explanation:

The surface area consists of 2 congruent triangles + 2 congruent sloping rectangles  + a rectangular base.

Area of the 3 triangles 1/2*base*height * 2

= base * height

= 14*24 cm^2

Area of the 2 rectangles = 2*25 * 10

= 20*25 cm^2

Area of the base = 14 * 10 cm^2

So total surface area = 14*24 + 20*25 + 14*10

= 976 cm^2.

Answer:

x = 3

Step-by-step explanation:

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

10x + 2 is an exterior angle of the triangle, thus

10x + 2 = 2x + 1 + 25

10x + 2 = 2x + 26 ( subtract 2x from both sides )

8x + 2 = 26 ( subtract 2 from both sides )

8x = 24 ( divide both sides by 8 )

x = 3

Answer:

£160.

Step-by-step explanation:

Mario receives 3 / (4+3+9) = 3/16 of the money.

So by proportion the total amount of money

=  96 * 16/3 = £512

So Rachel receives  4/16 = 1/4

= 512 / 4

= £128.

- and Sanjit receives 9/16

= 512 * 9/16

= £288

The difference is 288 - 128 = £160.

Answer:

equilateral acute

Step-by-step explanation:

Answer:

Equilateral Acute Triangle

Step-by-step explanation:

Answer:

280 kg

Step-by-step explanation:

279.98... so it rounds up to 280

Answer:

58kg

Step-by-step explanation:

127 pounds to kg is 57.606 kgs

divide pounds by 2.205

The amount of mix would be 16 and the amount of milk would be 8 work is in the picture