What is the relationship between the radius and the diameter?

Answer:

V = 396 cm³

Step-by-step explanation:

the volume (V) of the prism is calculated as

V = Ah ( A is the area of the triangular face and h the height of prism )

A = [tex]\frac{1}{2}[/tex] bh ( b is base and h perpendicular height )

here b = 9, h = 8 , then

A = [tex]\frac{1}{2}[/tex] × 9 × 8 = 4.5 × 8 = 36 cm² , so

V = 36 × 11 = 396 cm³

Answer:

x^3 + 9 x^2 + 21 x + 9 = (x^2 + 6 x + 3)×(x + 3) + 0

Step-by-step explanation:

Set up the polynomial long division problem with a division bracket, putting the numerator inside and the denominator on the left:

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

To eliminate the leading term of the numerator, x^3, multiply x + 3 by x^2 to get x^3 + 3 x^2. Write x^2 on top of the division bracket and subtract x^3 + 3 x^2 from x^3 + 9 x^2 + 21 x + 9 to get 6 x^2 + 21 x + 9:

| | | x^2 | | | |

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

| -(x^3 | + | 3 x^2) | | | |

| | | 6 x^2 | + | 21 x | + | 9

To eliminate the leading term of the remainder of the previous step, 6 x^2, multiply x + 3 by 6 x to get 6 x^2 + 18 x. Write 6 x on top of the division bracket and subtract 6 x^2 + 18 x from 6 x^2 + 21 x + 9 to get 3 x + 9:

| | | x^2 | + | 6 x | |

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

| -(x^3 | + | 3 x^2) | | | |

| | | 6 x^2 | + | 21 x | + | 9

| | | -(6 x^2 | + | 18 x) | |

| | | | | 3 x | + | 9

To eliminate the leading term of the remainder of the previous step, 3 x, multiply x + 3 by 3 to get 3 x + 9. Write 3 on top of the division bracket and subtract 3 x + 9 from 3 x + 9 to get 0:

| | | x^2 | + | 6 x | + | 3

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

| -(x^3 | + | 3 x^2) | | | |

| | | 6 x^2 | + | 21 x | + | 9

| | | -(6 x^2 | + | 18 x) | |

| | | | | 3 x | + | 9

| | | | | -(3 x | + | 9)

| | | | | | | 0

The quotient of (x^3 + 9 x^2 + 21 x + 9)/(x + 3) is the sum of the terms on top of the division bracket. Since the final subtraction step resulted in zero, x + 3 exactly divides x^3 + 9 x^2 + 21 x + 9 and there is no remainder.

| | | x^2 | + | 6 x | + | 3 | (quotient)

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9 |

| -(x^3 | + | 3 x^2) | | | | |

| | | 6 x^2 | + | 21 x | + | 9 |

| | | -(6 x^2 | + | 18 x) | | |

| | | | | 3 x | + | 9 |

| | | | | -(3 x | + | 9) |

| | | | | | | 0 | (remainder) invisible comma

(x^3 + 9 x^2 + 21 x + 9)/(x + 3) = (x^2 + 6 x + 3) + 0

Write the result in quotient and remainder form:

Answer: Set up the polynomial long division problem with a division bracket, putting the numerator inside and the denominator on the left:

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

To eliminate the leading term of the numerator, x^3, multiply x + 3 by x^2 to get x^3 + 3 x^2. Write x^2 on top of the division bracket and subtract x^3 + 3 x^2 from x^3 + 9 x^2 + 21 x + 9 to get 6 x^2 + 21 x + 9:

| | | x^2 | | | |

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

| -(x^3 | + | 3 x^2) | | | |

| | | 6 x^2 | + | 21 x | + | 9

To eliminate the leading term of the remainder of the previous step, 6 x^2, multiply x + 3 by 6 x to get 6 x^2 + 18 x. Write 6 x on top of the division bracket and subtract 6 x^2 + 18 x from 6 x^2 + 21 x + 9 to get 3 x + 9:

| | | x^2 | + | 6 x | |

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

| -(x^3 | + | 3 x^2) | | | |

| | | 6 x^2 | + | 21 x | + | 9

| | | -(6 x^2 | + | 18 x) | |

| | | | | 3 x | + | 9

To eliminate the leading term of the remainder of the previous step, 3 x, multiply x + 3 by 3 to get 3 x + 9. Write 3 on top of the division bracket and subtract 3 x + 9 from 3 x + 9 to get 0:

| | | x^2 | + | 6 x | + | 3

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

| -(x^3 | + | 3 x^2) | | | |

| | | 6 x^2 | + | 21 x | + | 9

| | | -(6 x^2 | + | 18 x) | |

| | | | | 3 x | + | 9

| | | | | -(3 x | + | 9)

| | | | | | | 0

The quotient of (x^3 + 9 x^2 + 21 x + 9)/(x + 3) is the sum of the terms on top of the division bracket. Since the final subtraction step resulted in zero, x + 3 exactly divides x^3 + 9 x^2 + 21 x + 9 and there is no remainder.

| | | x^2 | + | 6 x | + | 3 | (quotient)

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9 |

| -(x^3 | + | 3 x^2) | | | | |

| | | 6 x^2 | + | 21 x | + | 9 |

| | | -(6 x^2 | + | 18 x) | | |

| | | | | 3 x | + | 9 |

| | | | | -(3 x | + | 9) |

| | | | | | | 0 | (remainder) invisible comma

(x^3 + 9 x^2 + 21 x + 9)/(x + 3) = (x^2 + 6 x + 3) + 0

Write the result in quotient and remainder form:

Answer: x^3 + 9 x^2 + 21 x + 9 = (x^2 + 6 x + 3)×(x + 3) + 0

A) multiply by 2 both sides, canceling the ÷ by 2

4x - 1 = 2x + 14

+1

4x = 2x +15

-2x

2x. = 15

÷2

x = 7.5

B) mutiply 3 both sides

9x + 6 = 2x + 13

-6

9x. = 2x + 7

-2x

7x. = 7

÷1

x = 1

Hope this helps!

Answer:

Sale Price = $36

Step-by-step explanation:

To find the sale price, you need to find what 10% of the original price is. 10% of $45 is $4.50. Now we need to find what 20% is, 20% is double 10% so we multiply the answer we got by 2. This equals to $9. The question is asking for the sale price, to find it you have to subtract $9 (the discount) from $45 (regular price). The answer you should get is $36.

Equation:
$45 ÷ 10 = $4.50
$4.50 × 2 = $9
$45 - $9 = $36

Answer:

[tex]x = \frac{2}{539} [/tex]

Step-by-step explanation:

[tex] \frac{x + 2}{3x} = 180[/tex]

[tex]180(3x) = x + 2[/tex]

[tex]540x = x + 2[/tex]

[tex]540x - x = 2[/tex]

[tex]539x = 2[/tex]

[tex] \frac{539x}{539} = \frac{2}{539} [/tex]

[tex]x = \frac{2}{539} [/tex]

Answer:

x = 4

Step-by-step explanation:

x + 1 = 5

   - 1     -1

5 - 1 = 4

x = 4

Answer: C

Step-by-step explanation:

4/8 ×3/1

Answer:

192π

Step-by-step explanation:

cylinder volume is base times height

2πr^2 = base = 64π

height = 3

64π*3 = 192π

The volume of the given cylinder is 192π cubic units. Therefore, option C is the correct answer.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

From the given figure, radius of a cylinder = 8 units and radius of a cylinder = 3 units.

We know that, volume of a cylinder is πr²h.

Now, volume = π×8²×3

= π×64×3

= 192π cubic units.

Therefore, option C is the correct answer.

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Answer:

57/10 is the simplest form

Step-by-step explanation:

To divide fractions you need to do the reciprocal rules.

You also need to convert any mixed numbers to improper to make them easier to divide.

4 3/4 and 5/6 are your fractions.

4 3/4 converted into an improper fraction is 19/4

This is because the rule with this is that you take your whole number multiply it by the denominator and take the product and add it to the numerator.

19/4 divided by 5/6.

You need to flip 5/6 to 6/5 due to the reciprocal rules and also change the division sign to a multiplication sign.

19/4 x 6/5

You can multiply straight across!

19 x 6 and 4 x 5

19 x 6 = 114

4 x 5 = 20

Our answer: 114/20

We still need to simplify this answer

We can divide this result into 2/2.

114/20 = 57/10

57/10 is the simplest form. If you were to divide more, you will get involved with decimals.

Answer: 57/10 is the simplest form

Step-by-step explanation:

You also need to convert any mixed numbers to improper to make them easier to divide.

4 3/4 and 5/6 are your fractions.

4 3/4 conerted into an improper fraction is 19/4

This is because the rule with this is that you take your whole number multiply it by the denominator and take the product and add it to the numerator.

19/4 divided by 5/6.

You need to flip 5/6 to 6/5 due to the reciprocal rules and also change the division sign to a multiplication sign.

19/4 x 6/5

19 x 6 and 4 x 5

19 x 6 = 114

4 x 5 = 20

Our answer: 114/20

We still need to simplify this answer

We can divide this result into 2/2.

114/20 = 57/10

57/10 is the simplest form. If you were to divide more, you will get involved with decimals.

Answer:

x= 7 1/2

Step-by-step explanation:

Subtract the 1/2 to get it out of the way (whatever you do on one side of the = sign you have to do to the other)

So 10- 1/2= 9 1/2

Subtract the 2 to get it out of the way

9 1/2-2=

7 1/2

Hope it helped :)

Answer:

here, hope it helps

Step-by-step explanation:

17. A

18. B

19. A

Answer:

$45/4hrs

Step-by-step explanation:

450/40 divide both sides with 10

Answer:

$64.83.

Step-by-step explanation:

Each year the multiplier fffor her new rate will be 1.05.

So after 30 years her hourly rate will be  15 * 1.05^30

= $64.83

Answer:

-5,6,-2/3,1 1/3,0

Step-by-step explanation:

I think this how it goes try it out or not i need help to

Answer:

the first choice :)

Step-by-step explanation:

Answer:

Option A:   A = {CBA, CAB, BCA, ACB}

Answer:

475 km

Step-by-step explanation:

(40 + 45 + 50 + 35 + 55  km +  50 *5 km)  

Answer:

third side ≈ 19.8

Step-by-step explanation:

using Pyjthagoras' identity in the right triangle.

the square on the hypotenuse x is equal to the sum of the squares on the other 2 sides, that is

x² = 13² + 15² = 169 + 225 = 394 ( take square root of both sides )

x = [tex]\sqrt{394}[/tex] ≈ 19.8 ( to the nearest tenth )

Answer:

Sector AOB: 3.87

Sector BOC: 7.74

Sector COD: 5.16

Sector DOE: 3.01

Sector AOE: 11.19

Explanation:

Equation used: [tex]S=\frac{r^2*a}{2}[/tex]

Answer:

14, 16, 18

Step-by-step explanation:

Three even numbers means they are seperated by a distance of 2

Write this equation

x-2+x+x+2=48

x=16

So the three even numbers are 14, 16, 18

Answer:

14, 16, 18

Step-by-step explanation:

Thats the answer the guy above me is correct

Answer:

Step-by-step explanation:

8x⁴y⁴ = 4×2×x³×x¹×y⁴ = 4x³×(2xy⁴)

12x³z² = 4×3×x³×z² = 4x³×(3z²)

Then the greatest common factor is of the two terms 8x⁴y⁴ and 12x³z² is:

4x³

Answer:

No

Step-by-step explanation:

1240/24 = 51.6

It will give you a decimal so therefore it will not go evenly

Since mass is neither created nor destroyed, the missing items are;

The term nuclear reaction has to do with the transformation of one nucleus to another. On this case, we are going to transform P u to c m.

Since mass is neither created nor destroyed, the missing items are;

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Answer:

A: 242
B: 96
C: 1
D: 0

Step-by-step explanation:

Answer:

109

Step-by-step explanation:

as we can see x is an outer exterior angle and according to its property sum of an interior angle and an outer exterior angle = 180

The interior angle is 40+31 = 71

71 + x = 180

x = 180 -71

therefore x = 109

Answer:

Step-by-step explanation:

It is given that the area of a circle is 36.43cm² and we have to find the length of the radius.

So, first of we must know this formula :

⇒ πr² = Area(Circle)

Now, Substituting the given values in the formula :

⇒ 3.14 × r² = 36.43

⇒ r² = 36.43/3.14

⇒ r² = 11.60

⇒ r = √11.60

⇒ r = 3.40

Therefore,

Hey ! there

Answer:

Step-by-step explanation:

In this question we are given with area of circle that is 36.43 cm² . And we are asked to find the length of radius of circle rounded to two decimal points .

We know that ,

[tex] \qquad \quad \frak{Area_{(Circle)} = \pi r {}^{2} } \quad \bigstar[/tex]

Where ,

Solution : -

According to question , area of Circle is equal to 36.43 . So ,

[tex] \longrightarrow \qquad \: \pi r {}^{2} = 36.43[/tex]

Step 1 : Substituting value of π :

[tex] \longrightarrow \qquad \:3.14 \times r {}^{2} = 36.43[/tex]

Step 2 : Transposing 3.14 to right side :

[tex] \longrightarrow \qquad \: r {}^{2} = \cancel{\dfrac{36.43}{3.14} }[/tex]

On dividing 36.43 by 3.14 , We get :

[tex] \longrightarrow \qquad \: r {}^{2} = 11.60[/tex]

Step 3 : For removing square from r , We are applying root on both sides :

[tex] \longrightarrow \qquad \: \sqrt{r {}^{ 2 }} = \sqrt{ 11.60}[/tex]

We get :

[tex] \longrightarrow \qquad \:r = \sqrt{11.60} [/tex]

Step 4 : Finding square root of 11.60 , We get :

[tex] \longrightarrow \qquad \: \purple{\underline{\boxed{\frak{r = 3.40 \: cm}}}} [/tex]

The solution tothe logarithmic function log₃([3x+2] = log₃(4x - 6) is 8

Given the logarithm expression

log(3)[[3x+2] = log(3)[4x - 6]

The logarithm on both sides of the equation will cancel out to have:

3x + 2 = 4x - 6

Collect the like terms

3x - 4x = -6 - 2

-x = -8

x =8

Hence the solution tothe logarithmic function log₃([3x+2] = log₃(4x - 6) is 8

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Answer:

8

Step-by-step explanation:

Answer:

1 yard

Step-by-step explanation:

If the ribbon to begin with is 3 yards then if cut in to 3 pieces each peace would be 1 yard.

Answer:

k = 60°

Step-by-step explanation:

y and z are parallel with each other against x line.

So we can make (2k+11)° = 131° and then solve for k.

2k + 11 = 131°

2k = 131° - 11°

2k = 120°

k = 60°

Using proportions, it is found that it will take 4 hours for Phoebe to catch Candice.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Given their velocities, and the fact that they travel in the same direction, each hour, Phoebe gets 10 mph closer to Candice.

The initial distance is of 40 miles, 40/10 = 4, hence it will take 4 hours for Phoebe to catch Candice.

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