what's the circumference of a circle is C centimetres. which expression best represents the value of pie?

Answer:

see explanation

Step-by-step explanation:

Expand both factors and collect like term

Using Pascal' triangle with n = 6 to obtain the coefficients

1  6  15  20  15  6  1

Decreasing powers of 1 from [tex]1^{6}[/tex] to [tex]1^{0}[/tex]

Increasing powers of 3x from [tex](3x)^{0}[/tex] to [tex](3x)^{6}[/tex]

[tex]1+3x)^{6}[/tex]

= 1.[tex]1^{6}[/tex][tex](3x)^{0}[/tex] + 6.[tex]1^{5}[/tex][tex](3x)^{1}[/tex] + 15.[tex]1^{4}[/tex][tex](3x)^{2}[/tex] + 20.[tex]1^{3}[/tex][tex](3x)^{3}[/tex] + 15.1²[tex](3x)^{4}[/tex] + 6.[tex]1^{1}[/tex][tex](3x)^{5}[/tex] + 1.[tex]1^{0}[/tex][tex](3x)^{6}[/tex]

= 1 + 18x + 135x² + 540x³ + 1215[tex]x^{4}[/tex] + 1458[tex]x^{5}[/tex] + 729[tex]x^{6}[/tex]

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

[tex](1-3x)^{6}[/tex]

= 1.[tex]1^{6}[/tex][tex](-3x)^{0}[/tex] + 6.[tex]1^{5}[/tex][tex](-3x)^{1}[/tex] + 15.[tex]1^{4}[/tex][tex](-3x)^{2}[/tex] + 20.[tex]1^{3}[/tex][tex](-3x)^{3}[/tex] + 15.1²[tex](-3x)^{4}[/tex] + 6.[tex]1^{1}[/tex][tex](-3x)^{5}[/tex] + 1.[tex]1^{0}[/tex][tex](-3x)^{6}[/tex]

= 1 - 18x + 135x² - 540x³ + 1215[tex]x^{4}[/tex] - 1458[tex]x^{5}[/tex] + 729[tex]x^{6}[/tex]

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

Collecting like terms from both expressions

[tex](1+3x)^{6}[/tex] + [tex](1-3x)^{6}[/tex]

= 2 + 270x² + 2430[tex]x^{4}[/tex] + 1458[tex]x^{6}[/tex]

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

(2)

Using Pascal's triangle with n = 5

1  5  10  10  5  1

Decreasing powers of 1 from [tex]1^{5}[/tex] to [tex]1^{0}[/tex]

Increasing powers of 2x from [tex](2x)^{0}[/tex] to [tex](2x)^{5}[/tex]

[tex](1+2x)^{5}[/tex]

= 1.[tex]1^{5}[/tex][tex](2x)^{0}[/tex] + 5.[tex]1^{4}[/tex][tex](2x)^{1}[/tex] + 10.[tex]1^{3}[/tex][tex](2x)^{2}[/tex] + 10.[tex]1^{2}[/tex][tex](2x)^{3}[/tex] + 5.[tex]1^{1}[/tex][tex](2x)^{4}[/tex]+ 1.[tex]1^{0}[/tex][tex](2x)^{5}[/tex]

= 1 + 10x + 40x² + 80x³ + 80[tex]x^{4}[/tex] + 32[tex]x^{5}[/tex]

Answer:

5 15 10/3 7

3 12 12/3 5

Step-by-step explanation:

The missing values in the ratio table will be;

Pies         5       20      10/3   25/3

Cakes      3       12        2      5

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

The ratio table is;

Pies         5       x      10/3   z

Cakes      3       12     y       5

Now,

Since, The ratios are equivalent to each other.

Thus, We can solve to find the value of x, y and z as;

⇒ 5 : 3 = x : 12

⇒ 5/3 = x/12

Multiply by 12;

⇒ 5 × 12 / 3 = x

⇒ 20 = x

And, 5 : 3 = 10/3 : y

⇒ 5/3 = 10/ (3× y)

⇒ 5/3 = 10/3y

Multiply by 3;

⇒ 5 = 10/y

⇒ y = 10/5

⇒ y = 2

And, 5 : 3 = z : 5

⇒ 5/3 = z/5

Multiply by 5;

⇒ 25/3 = z

⇒ z = 25/3

Therefore, The missing values in the ratio table will be;

Pies         5       20      10/3   25/3

Cakes      3       12        2      5

Learn more about the ratio visit:

https://brainly.com/question/277887

#SPJ5

Step-by-step explanation:

228 ÷12 =19

So 19 dollars per hour

Now 133÷19= 7 hours

Answer:

x=5, y=2. (5, 2).

Step-by-step explanation:

3x-2y=11

x+2y=9

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

4x=20

x=20/4

x=5

5+2y=9

2y=9-5

2y=4

y=4/2

y=2

Answer:

y ≤ 1

Step-by-step explanation:

Answer:

50:1

Step-by-step explanation:

Rs50=Rs50

100 paise= Rs1

Ratio = 50:1          [ cant be simplified further]

I hope im right!!

Another way:

Rs50= 50 x 100 = 5000 paise

100 paise= 100 paise

Ratio = 5000: 100

[tex]\frac{5000}{100}[/tex] ÷ [tex]\frac{100}{100}[/tex] = [tex]\frac{50}{1}[/tex]

Ratio = 50:1

Answer:

I think the equation would be 345 = 121 + p

Answer:

A. Add -2 to both sides

Step-by-step explanation:

The reason you need to add -2 to both sides is because if you add -2 to -2 it cancels out and you are left with x=18. But you need to add -2 to 18 too because them the equation won't be equal anymore.

Answer:

[tex]V=502.5\ cm^3[/tex]

Step-by-step explanation:

The area of the pentagonal base, A = 33.5 cm²

The height of the prsim,h = 15 cm

We need to find the volume of the pentagonal base prism. The formula for the volume of the pentagonal base prism is given by :

[tex]V=A\times h\\\\V=33.5\times 15\\\\V=502.5\ cm^3[/tex]

So, the required volume is [tex]502.5\ cm^3[/tex].

Answer:

See below, please!

Step-by-step explanation:

We can set up a system of equations to model this problem. Let's consider the student's ticket as x, and y for the adult ticket.

So since the student ticket is $1.50, and adult is $4, we can set up the following equation: [tex]1.5x+4y=5050[/tex], since they collected $5050 total.

We can set up another equation modeling the number of people who came to the game. This would be x+y=2200.

Solve this, and we get x= 1500 and y=700. So, they sold 1500 student tickets and 700 adult tickets.

Hope this helped!

Answer:

2

Step-by-step explanation:

9x=8+5x

9x-5x=8

4x=8

x=8/4

x=2

Answer:

3.5

Step-by-step explanation:

hope it helps

Answer:

A

Step-by-step explanation:

Answer:

the awnser to your question is letter c

Answer:

127/495

Step-by-step explanation:

Turning repeating decimals into fractions is a little like surgery: you need to make sure to "cut out" just the right part to let you simplify. In this case, it'd be very nice if we could deal with that repeating 0...565656... part. Let's start by giving our decimal a name:

[tex]x=0.25656...[/tex]

We're gonna split this into two parts: a number we can operate on, and "knife" to make the incision. For both, we'd like the only part to the right of the decimal to be the repeating part. To make our "knife," we'll multiply both sides of the equation by 10:

[tex]10x=2.5656...[/tex]

To make the number we'll be cutting from, we can shift the decimal point by any multiple of two more to the right. I'll keep things simple and stick with 2. This corresponds to multiplying the "knife" equation by 100 on both sides:

[tex]1000x=256.5656...[/tex]

Surgery time! To cut out the repeating bit, we can now just subtract the "knife" equation from the one above:

[tex]1000x-10x=256.5656...-2.5656...\\990x=254[/tex]

And just like that, it's gone! All that's left to do now is divide both sides by 990 and simplify:

[tex]x=254/990=127/495[/tex]

Answer:

Grace's triangle is an obtuse triangle and a scalene triangle.

Step-by-step explanation:

Hope I helped!

Answer:

obtuse triangle and a scalene triangle

Step-by-step explanation:

:)

Answer:

B ?

Step-by-step explanation:

Answer:

5 pounds = 80 ounces

Hope it helps!!!

Answer:

x=9

Step-by-step explanation:

Since ABCD is a square, we know that AC bisects ∠BCD(=90), and therefore ∠ACB=45.

8x-27=45

8x=72

x=9

Answer:

x = 9°

Step-by-step explanation:

∠ACB = 45° because line AC bisects ∠BCD which is 90° (because square).

8x - 27° = 45°

add 27° to each side:

8x = 72°

divide both sides by 8:

x = 9°

Answer:

235.6

Step-by-step explanation:

A=πr2

=π·52

=78.53982x3=235.61946

235.6

Answer:

for the first answer your answer was correct, it was the second answer that was wrong. So the first answer is 2 3/4. The second answer would be 81 centimeters because it grew that much.

Step-by-step explanation:

To find the first answer add the starting height and ending height. To find how much it grew convert the total ending height of the tree to cm by multiply by 100, so 275. Then subtract 356 by 275 because you are finding out how much it grew. Take away 275 from 356 and you get 81

Answer:

3

Step-by-step explanation:

Answer:

8.164

Step-by-step explanation:

The circumference of the ball is 8.164 inches.

Since the diameter of the tennis ball is 2.6 inches

So here the radius should be half i.e. 1.3 inches

Now we know that

Circumference = [tex]2\pi r\\\\[/tex]

= 2(3.14)(1.3)

= 8.164 inches

Therefore, we can conclude that The circumference of the ball is 8.164 inches.

Learn more about circumference here: https://brainly.com/question/15673093

the answer will be thirty three cm.

Answer:

5.50 per pond

3.5 pound

3.5 × 5.50

$19.25

Answer:

{-2, - 1, 0, 1}

Step-by-step explanation:

The integer solutions will be {-2, - 1, 0, 1}

Answer:

<3<3<3<3<3<3<3

{-2, - 1, 0, 1}

<3<3<3<3<3<3<3

Answer:

5 1/3

Step-by-step explanation:

2 times 8 is 16 and 16 over 3 is 5 with a remainder of one. So it's 5 1/3

Answer:

[tex] \boxed{ 5} \frac{ \boxed{1}}{ \boxed{3}}\: miles [/tex]

Step-by-step explanation:

Total distance ran

[tex] = \frac{2}{3} \times 8 \\ \\ = \frac{16}{3} \\ \\ = \boxed{ 5} \frac{ \boxed{1}}{ \boxed{3}}\: miles [/tex]

Answer:

[tex]x = 9.9[/tex]

[tex]y= 7[/tex]

Step-by-step explanation:

Given

See attachment for triangle

Required

Find x and y

Considering  [tex]\theta = 45[/tex]

From the attached triangle, length x is the hypotenuse and length y is the adjacent

Solving for x

[tex]Sin\theta = \frac{Opp}{Hyp}[/tex]

[tex]Sin\theta = \frac{7}{x}[/tex]

So, we have:

[tex]Sin45 = \frac{7}{x}[/tex]

[tex]x= \frac{7}{Sin45 }[/tex]

[tex]x = \frac{7}{0.7071}[/tex]

[tex]x = 9.9[/tex]

Solving for y

Considering  [tex]\theta = 45[/tex]

[tex]Tin\theta = \frac{Opp}{Adj}[/tex]

So, we have:

[tex]Tin45= \frac{7}{y}[/tex]

[tex]y= \frac{7}{Tan45}[/tex]

[tex]y= \frac{7}{1}[/tex]

[tex]y= 7[/tex]

The value of x and y is 9.9 and 7.

Since theta is 45 degrees

So, we know that

Sin theta = opp/hyp

Sin theta = 7 /x

x = 7 / 0.7071

= 9.9

Now the value of Y should be

Tin theta = opp/hyp

y = 7 \tan 45

= 7 /1

= 7

Therefore, we can conclude that The value of x and y is 9.9 and 7.

Learn more about length here: https://brainly.com/question/19021872

Answer:

Step-by-step explanation:

If you picture this scene in your head, you will get a simple 3x4x5 right triangle. 4 times 2 is 8, 5 times 2 is 10, so Sarah should, by now, have traveled 3 times 2 miles.

Final answer: Sarah has traveled 6 miles after an hour.

Hope this helped! :)

Helping tip: The reason it is not 4 is because they are not traveling west and east away from each other. They are traveling north and east, so they are moving in two directions to form a right triangle, and the hypotenuse would be 10 (miles). The side, or distance, that Beth has traveled is 8. So as this is a typical variation of a 3x4x5 triangle, Sarah will have traveled  6 miles.

Answer:

10.6

Step-by-step explanation:

Answer:

x = 122°

Step-by-step explanation:

since it is a right triangle, the sum of the other 2 interior angles = 90°

the angle opposite x = 90° - 32° = 58°

58° and angle x are supplementary angles. Their sum is 180°.

180° - 58° = 122°