A rectangular prism has a width of x cm. Its length is 3 cm more than its width, and its height is 4 cm more than its length. Write an algebraic expression, in simplified form, for the volume of the prism.

As we know that angle of semi circle is 180°.

Here,

FLG = 40°

GLH = ?

HLJ = 60°

FLG + GLH + HLG = 180°

40° + GLH + 60° = 180°

GLH + 100° = 180°

GLH = 180° - 100°

GLH = 80°

Now,

FLH = 40° + 80° = 120°

[tex] \sf \: Length \: of \: an \: arc \: of \: GHF = \dfrac{ \theta}{360} \times 2 \pi \: r[/tex]

[tex] = \dfrac {120}{360} \times 2 \times \dfrac{22}{7} \times r[/tex]

[tex] = \frac{1}{3} \times \frac{44}{7} \times r[/tex]

[tex] = \frac{44}{21} \times r[/tex]

[tex] = 2.09r[/tex]

Given:

The expression is:

[tex]12\div \dfrac{3}{5}[/tex]

To find:

The correct statement for solution of the given expression.

Solution:

We have,

[tex]12\div \dfrac{3}{5}[/tex]

If a number is divided by a fraction, then we need to multiply the reciprocal of the fraction with the number.

It can be written as

[tex]12\div \dfrac{3}{5}=12\times \dfrac{5}{3}[/tex]

[tex]12\div \dfrac{3}{5}=\dfrac{12\times 5}{3}[/tex]

[tex]12\div \dfrac{3}{5}=\dfrac{60}{3}[/tex]

[tex]12\div \dfrac{3}{5}=20[/tex]

To simplify the given expression, we need to multiply 12 by 5, then divide by 3.

Therefore, the correct option is D.

Answer:

x = 9

Step-by-step explanation:

24 divided by 8 is equal to 3.

12 = x + 3 (subtract three from both sides)

9 = x

Answer:

y = 3/4x + 7

Step-by-step explanation:

Put it in point-slope form:

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

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

y - 4 =3/4x + 3

y = 3/4x + 7

Answer: 43.75%

Step-by-step explanation:

The percentage change is given by:

= [Final value - initial value / Initial value] x 100

The percentage increase in the average number of people from 2005 to 2012 is 56.25%.

The percentage is calculated by dividing the required value by the total value and multiplying it by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

The average number of people in 2005 = 8000.

The average number of people in 2012 = 12500.

The change in the average number of people from 2005 to 2012.

= 12500 - 8000

= 4500

The percentage change in the average number of people at the games from 2005 to 2012.

= [Change in the average number of people / Average number of people in 2005] x 100

= (4500 / 8000) x 100

= 450/8

= 56.25%

Thus,

The percentage increase in the average number of people from 2005 to 2012 is 56.25%.

Learn more about percentages here:

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Answer:

E'(-2, -3), F'(-1, -5), G'(1, -5) and H'(2, -3).

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

If a point A(x, y) is translated a units right and b units down, the new location of the point is at A'(x + a, y - b)

The location of the vertices of quadrilateral EFGH is E(-5, -1), F(-4, -3), G(-2, -3) and H(-1, -1). If quadrilateral EFGH is translated 3 units right and 2 units down, the new location would be:

E'(-2, -3), F'(-1, -5), G'(1, -5) and H'(2, -3).

Answer:

Number of miles= 13

Step-by-step explanation:

Giving the following information:

He is receiving total contributions of $65 plus $20 for every mile he walks.

To calculate the number of miles to reach $325, we need to use the following formula:

Total collection= fixed contribution + variable contribution per mile*number of miles

325= 65 + 20*number of miles

260/20 = number of miles

number of miles= 13

Answer:

Simple: C. 70% = Rs. 84

Step-by-step explanation:

cause it can't be 120% if Rs.120 is the 100%

Answer:

En 2001 el pueblo poseía 45.826 habitantes.

Step-by-step explanation:

Un pueblo tenía 13.578 habitantes en 1970. En 1988 la población se incrementó 1,5 veces con respecto a 1970. Para calcular entonces la población en 1988 debes realizar el siguiente cálculo:

13.578*1,5= 20.367

Por lo que en 1988 el pueblo poseía 20.367 habitantes.

En 2001 se incrementó la población 2,25 veces en relación a 1988. Para calcular entonces la población en 2001 debes realizar el siguiente cálculo:

20.367* 2,25= 45.825,75≅ 45.826

Por lo que en 2001 el pueblo poseía 45.826 habitantes.

Answer:

Step-by-step explanation:

.

4

2

Answer:

x = 4, -4

Step-by-step explanation:

You can do this by simply pressing the calculator OR by simplify

4x^2 - 64 = 0

(2x)^2 - 8^2 = 0

(2x - 8)(2x + 8) = 0

∴ 2x - 8 = 0 or 2x + 8 = 0

x = 4 or x = -4

Answer:

245 degrees

Step-by-step explanation:

The circle is 360 degrees and you have only found 55 and 60  you add those together and you will get 115 to find jk you first add the numbers you have then minus them with 360 because its a circle. 360-115 will be 245 that would be your answer.

Answer:

120 degree

Step-by-step explanation:

jn-60 vwrtical oopsite angle

nk 180

jk 180-60

Answer:

A) y = 5

Step-by-step explanation:

30 / 6 = 5

y = 5

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Answer:

34

Step-by-step explanation:

:)

Answer:

34

Step-by-step explanation:

Remember that the sum of the angles of a triangle is 180

And since two sides are congruent b = 73

So 180-(73+73) = 34

Answer:

Sorry I don't know that one

Answer:

36

Step-by-step explanation:

devide 105 by 3 then add one 34+35+36=105

Answer:

It's 37 because the three are 33, 35, and 37. 37 is the largest of all of them.

Step-by-step explanation:

105/3 = 35, therefore the middle number is 35, and the 3 numbers are 33, 35, and 37.

Answer:

The answer is B

Step-by-step explanation:

3/4

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Answer: x = -4

Step-by-step explanation:

-4 + 4 = 0

if  y = 0 then X will be -4

Answer:

hello

Step-by-step explanation:

answer is x=-4

because if we add

4-4=0

x+4=0

-4+4=0

Answer:

r = 8

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to 3

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, - 6) and (x₂, y₂ ) = (r, 6)

m = [tex]\frac{6+6}{r-4}[/tex] = [tex]\frac{12}{r-4}[/tex] , then

[tex]\frac{12}{r-4}[/tex] = 3 ( multiply both sides by (r - 4))

12 = 3(r - 4) ← divide both sides by 3

4 = r - 4 ( add 4 to both sides )

8 = r

Answer:

45.44units^3

Step-by-step explanation:

Volume of the shaded part = Volume of the triangular based prism - Volume of square based prism

Volume of prism = Base area * Height

Volume of the triangular based prism = (5 * 4 * 5.7)/2

Volume of the triangular based prism = 57units^3

Volume of square based prism = 1.7* 1.7 * 4

Volume of square based prism = 11.56units^3

Taking the difference

Volume of the shaded solid = 57 - 11.56

Volume of the shaded solid  = 45.44units^3

Answer:

B

Step-by-step explanation:

Answer:

= 0.0471 or 4.71%

Step-by-step explanation:

(5/52) x (25/51)

= 0.04713423831

Answer:

Rounding to the nearest whole number, 49 moons can fit in the earth.

Rounding to the tenth place, 50 moons can fit in the earth.

Step-by-step explanation:

To find how approximately how many moons could fit inside the earth, you would need yo find the volumes the earth and the moon.

V = 4/3 π r^3

Earth:

d = 2r

d = 7926 miles

7926 = 2r

3963 miles = r

V = 4/3 π (3963)^3

V = 4/3 π (62240377347)

V = 82987169796π cubic miles

Moon:

d = 2r

d = 2159 miles

2159 = 2r

1079.5 miles = r

V = 4/3 π (1079.5)^3

V = 4/3 π (1257963209.88)

V = 1677284279.83π cubic miles

Now you divide the volume of earth by the volume of moon to find how many moons can fit in earth

82987169796π ÷ 1677284279.83π =

approx 49

Answer:

(a) Infinite

(b) 6 (because a to z contains 26 letters so we can only take 26 letters or less otherwise the letter can be repeated so we have to take the num which is coming in table of 4 so 24then we can make 6passwords)

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