A movie theater sells popcorn in bags that open to form similar prisms, as shown. The large bag has a volume of 576 cubic inches. What is the volume of the small bag?

Answer:

i think its 6

Step-by-step explanation:

The length of the diagonal of the rectangular prism will be √35 units. Then the correct option is B.

A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The dimension of the rectangular prism will be 3 units long, 5 units wide, and 1 unit high. Then the diagonal of the prism is given as,

D² = 3² + 5² + 1²

Simplify the equation, then we have

D² = 3² + 5² + 1²

D² = 9 + 25 + 1

D² = 35

D = √35 units

The length of the diagonal of the rectangular prism will be √35 units. Then the correct option is B.

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Answer:

Option (4)

Step-by-step explanation:

The given system of equations is,

y = -2x + 4 ------ (1)

6x + 3y = a --------(2)

We have to find the value of a for which the system of equations will have infinitely many solutions.

Option (1). If a = -12

                6x + 3y = -12

                2x + y = -4

                        y = -2x - 4

Both the equations have same slope, therefore, they are parallel and will have no solutions.

Option (2). If a = -4

                 6x + 3y = -4

                         3y = -6x - 4

                           [tex]y=-2x-\frac{4}{3}[/tex]

Then equation (1) and (2) will intersect each other at least at one point Or there is exactly one solution of the system of the equations.

Option (3). If a = 4

                 6x + 3y = 4

                         3y = -6x + 4

                           y = -2x + [tex]\frac{4}{3}[/tex]

Then equation (1) and (2) will intersect each other at least at one point Or there is exactly one solution of the system of the equations.

Option (4). If a = 12

                  6x + 3y = 12

                           3y = -6x + 12

                             y = -2x + 4

Therefore, both the equations (1) and (2) are same for a = 12 and they will have infinitely many solutions.

This question is based on system of linear equation .Thus, for a=12 will have infinitely many solution.

Given:

y = -2x + 4 ------ (a)  

6x + 3y = a ------(b)

We need to determined the value of a for which the system gives infinitely many solution.

Now check all the options as given below:

Option(1)  a = -12 and put it in (b) we get,

6x + 3y = -12

 2x + y = -4

y = -2x - 4

Both the equations have same slope, therefore, they are parallel to each other and have no solutions.

Option(2)  a= -4 and put it in (b) we get,

6x + 3y = -4

3y = -6x - 4

[tex]y=-2x-\dfrac{4}{3}[/tex]

Therefore, the equation has unique solution. Thus, both lines intersect each other at one point and there is unique value of x and y.

Option(3) a= 4

6x + 3y = 4

3y = -6x + 4

[tex]y=-2x+\dfrac{4}{3}[/tex]

Therefore, the equation has unique solution. Thus, both lines intersect each other at one point and there is unique value of x and y.

Option(4) a= 12

6x + 3y = 12

3y = -6x + 12

y = -2x + 4

Both the  equation are same for a= 12.

Thus, for a=12 will have infinitely many solution.

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Answer:

They very according to the wealth of a country because the wealth of the country also reflects on how much supply there is, and if for example, there is a shampoo factory they will use less quality items because they don't have enough money or supplies to make good quality shampoo. The wealth of the country also affects how many sales are made from those lower quality items. Since the country is so poor, they don't have enough money to buy expensive products from overseas so they will buy the lower quality items, even if they know that they aren't the best quality. This might result to diseases in some serious cases, like in food industries of poor countries.

Step-by-step explanation:

it vary because if the country in which the company is being operated is a wealthy country it means that the company or industry will gain more customers than a country that is poor. Because if the country is wealthy people will come to that country because of it's rich economy but it also differs if the country in which the company is operating and does not offer quality service that industry will not be successful  

Answer:

90°

Step-by-step explanation:

cosx = y=1

Therefore cosx =1

For cosx= 1

x= 90°, 450°, 810° ... etc.

Now 0° ≤ x ≤ 360°

The only value that satisfies both relations is 90°

Therefore, x= 90°

Answer:

[tex] \frac{9c + 160}{5} [/tex]

Step-by-step explanation:

C = 5(F - 32)/9

so we do a little algebra here

9C = 5F - 160

we move both side

5F - 160 = 9C

5F = 9C + 160

so in the end

F =

[tex] \frac{9c + 160}{5} [/tex]

a = 9

b = 160

c = 5

Answer:

[tex]F=\frac{9C+160}{5}[/tex]

Step-by-step explanation:

[tex]C=\frac{5(F-32)}{9}[/tex]

Multiply both sides with 9.

[tex]9C=5(F-32)[/tex]

Use distributive property.

[tex]9C=5F-160[/tex]

Add 160 to both sides.

[tex]9C+160=5F[/tex]

Divide 5 to both sides.

[tex]\frac{9C+160}{5}=F[/tex]

Answer: 84 people

Step-by-step explanation:

From the question, 240 people are going to a charity event and 3/5 of the guests have ordered chicken for their meals. This means (3/5 × 240) = 144 people ordered chicken. Since 144 people have ordered, the number of remain people left will be:

= 240 - 144

= 96 people.

Out of the remaining guests which is 96, 12.5% have ordered gluten free meals. This means (12.5% × 96) = 12 ordered gluten free meals.

The people who haven't ordered their meals yet will be:

= 96 - 12

= 84 people.

Using the appropriate arithmetic operations, the number of guests who haven't made an order yet is 126

Chicken orders = 3/5 × 240 = 144

Number left = 240 - 144 = 96

Gluten free meat = 12.5% × 144 = 18

Not yet ordered = 144 - 18 = 126

Therefore, the Number of guests who haven't made an order yet is 126

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Answer:

Read below

Step-by-step explanation:

x is always the smaller number

y is always the larger number

underlined means it's the question

bolded means it's the answer

1.

One number is 6 times as large as another. Their sum is 42. Find the numbers.

The numbers need to fit the criteria:

A. 6+36=42 (correct)

B. 7+42=49 (incorrect)

C. 7+35=42 (incorrect because it doesn't follow the 1st rule)

D. 6+42=48 (incorrect)

Only A. 6, 36 fits the criteria.

2.

One number is 3 less than another. Four times the smaller is 4 more than 3 times the larger. Find the numbers.

The numbers need to fit the criteria:

A.

4+3=7

12-6≠21 (incorrect)

B.

7+3=10

28-3≠30 (incorrect)

C.

13+3=16

52-4=48 (correct)

D.

9+3≠13 (incorrect)

Only C. 13, 16 fits the criteria.

3.

One number is 4 less than another. Five times the smaller is 3 less than 4 times the larger. Find the numbers.

The numbers need to fit the criteria:

A.

13+4=17

65+3=68 (correct)

B.

-23+4= -19

-115+3≠ -76 (incorrect)

C.

17+4=21

85+3≠84 (incorrect)

D.

-11+4+ -7

-35+3≠ -33 (incorrect)

Only A. 13, 17 fits the criteria.

4.

The sum of two numbers is 23. When three times the smaller is subtracted from the larger, the result is 3. Find the numbers.

The numbers need to fit the criteria:

A.

5+18=23

18-15=3 (correct)

B.

8+15=23

15-24≠3 (incorrect)

C.

-13+36=23

36+39≠3 (incorrect)

D.

-5+28=23

28+15≠3 (incorrect)

Only A. 5, 18 fits the criteria.

5.

The sum of two numbers is 26. When twice the smaller is subtracted from the larger, the result is 2. Find the numbers.

The numbers need to fit the criteria:

A.

8+18=26

18-16=2 (correct)

B.

9+17=26

17-18≠2 (incorrect)

C.

7+19=26

19-14≠2 (incorrect)

D.

6+20=26

20-12≠2 (incorrect)

Only A. 8, 18 fits the criteria.

Answer:

x = -8/3

Step-by-step explanation:

1/2x+3 = 2/3+1

Combine like terms

1/2x+3 = 2/3 + 3/3

1/2x + 3 = 5/3

Subtract 3 from each side

1/2x + 3-3 = 5/3 - 3

1/2x = 5/3 - 9/3

1/2x = -4/3

Multiply each side by 2

1/2x *2 = -4/3*2

x = -8/3

Answer:

Step-by-step explanation:

V= π(8)^2(12/3)

V= 64(4)π

V= 256π

V= 804.3 cm^3

Answer:

a) 6

b) 37.5

c) 6th term

Step-by-step explanation:

a) plug in 2 for n

3(2)^2/2

6

b) plug in 5 for n

3(5)^2/2

37.5

c) since 5 is 37.5, I am going to check 6

3(6)^2/2

54

The 6th term will be the first to have a value higher than 50

Answer:

D

Step-by-step explanation:

A function of x means that there can only be one value of y per x value.  Therefore, D does not match this because there are 4 values of y per x value (3).

Answer:

D

Step-by-step explanation:

Each x value can have only ONE y value

this means that there cannot be more than one of the same x value:

think of the x values as an input, each input has one output right?

ex:

input: 7

output:8

input:3

output:2

how is it possible that the same input has different outputs?

input: 5

output: 6,7

this does not make any sense, one input should only have one output hence, one value of x(input) should have only one value of y(output)

Hope this helps!

Answer:

Step-by-step explanation:

Answer:

The mileage of the car is 30 miles per gallon

Step-by-step explanation:

Here, we are interested in calculating the gas mileage of the car.

The gas mileage refers to the number of kilometers the car can travel on a particular amount of fuel.

The full capacity of the car tank is 15 gallon

Now after traveling 300 miles, it stops for gas and 10 gallons of fuel are added to make the car full again.

What this means is that the car used up a total of 10 gallons of fuel for the 300 miles

Thus, the gas mileage of the car is that it used 10 gallons to travel a total of 300 miles

Expressing this as a ratio, we have 300 miles/10 gallons = 30 miles/ gallon

This means that on a gallon of fuel, the car can travel 30 miles

Answer:

1 < x < 7.5

Step-by-step explanation:

This problem can be solved using given below property of triangle.

Sum of two sides is always greater than third side of triangle.

Difference of two sides is always lesser than third side of triangle.

_______________________________________________

Given

sides length

6.5 units

3.5 units

Third side is 2.5 +  x

using the property, Sum of two sides is always greater than third side of triangle.

6.5 + 3.5 > 2.5 +x

=>10 >2.5 + x

=>2.5 + x< 10

=> x< 10 -2.5

=> x < 7.5

using the property, Difference of two sides is always lesser than third side of triangle.

6.5 - 3.5 >  2.5 +x

=>3.5 >  2.5 +x

=> 2.5 +x  > 3.5

=> x  > 3.5 - 2.5

=> x  > 1

combining both we have

1 < x < 7.5

out of the given option none is 1 < x < 7.5

hence, correct answer will be 1 < x < 7.5 and wrong option can be claimed by student.

The inequality that represents the values of x that ensure triangle ABC exists is A. 0.5 < x < 7.5

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

Given that the side lengths of a triangle are as; 6.5 units, 3.5 units, and 2.5 + x units

By using the property, the Sum of two sides is always greater than third side of triangle, then;

6.5 + 3.5 > 2.5 +x

=>10 >2.5 + x

=>2.5 + x< 10

=> x< 10 -2.5

=> x < 7.5

Also, by using the property, Difference of two sides is always lesser than third side of triangle then we get;

6.5 - 3.5 >  2.5 +x

=>3.0 >  2.5 +x

=> 2.5 +x  > 3.0

=> x  > 0.5

Now combining both we have;

. 0.5 < x < 7.5

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Answer:

Which expressions are equal to 0 when x = –1? Check all that apply.

StartFraction 4 (x plus 1) Over (4 x plus 5) EndFraction

StartFraction 4 (x minus 1) Over (5 minus 4 x) EndFraction

StartFraction 4 (x minus (minus 1)) Over (4 x plus 5) EndFraction

StartFraction 4 (x plus (minus 1)) Over (4 x plus 5) EndFraction

StartFraction 4 (x plus 1) Over (5 minus 4 x) EndFraction

Step-by-step explanation:

Answer:

diameter = two times the radius

2r

the area = πr²

the circumference= 2πr

hope it helps

Answer:

B, x=40 is the right answer

Step-by-step explanation:

DAC is one half of the right angle and CAB is another half. So, you know that since a right angle is 90 degrees, DAC + CAB must equal 90.

They have given you equations for both angles, so now its just a matter of rearranging and solving for x.

DAC = x

CAB = 2x - 30

DAC + CAB = 90

Using the equations above, we can come up with this final equation:

x + 2x - 30 = 90

If we add the x together:

3x - 30 = 90

If we move the 30 to the other side by adding it to 90

3x = 90 + 30

3x = 120

If we divide 120 by 3:

x= 40

Therefore, the answer is B

Hope this helped : )

Answer:

The area of the shaded region is [tex]49.5 cm^{2}[/tex] to 3. significant figures

Step-by-step explanation:

Step one: find the two diagonals of the kite.

The Horizontal diagonal can be obtained using the cosine rule:

[tex]AC^{2}=OA^{2}-OC^{2}- 2\times (OA)\times (OC)cos (\theta)[/tex]

[tex]AC^{2}=8^{2}+8^{2}- 2\times 8 \times 8 \times cos (120)= 212\\AC =\sqrt{212}=14.56cm[/tex]

The vertical diagonal of the kite can be obtained by Pythagoras' Theorem:

Please note the law in circle geometry which states that a radius and a tangent always meet at right angles.

This implies that triangle OBC is a right-angled triangle, with angle OCB being 90 degrees, and COB being 60 degrees. This is because the diagonal divides the 120-degree angle into half.

[tex]cos 60 = \frac{8}{OB}\\OB=\frac{8}{cos 60}= 16cm[/tex]

Step two: Use the dimensions of the two diagonals of the Kite to find the area:

The area of a Kite is obtained using this formula:

[tex]Area = \frac{pq}{2}[/tex], where p and q are the two diagonals.

hence,

[tex]Area = \frac{14.56 \times 16}{2}= 116.48cm^{2}[/tex]

Step three: Calculate the area of the sector of the circle.

Area of the sector is obtained using this formula

[tex]Area = \frac{\theta}{360}\times \pi\times r^{2}\\Area = \frac{120}{360} \times \pi \times 8^{2}=67.03cm^{2}[/tex]

Step Four: Subtract the area of the sector from the area of the kite:

Area of the shaded region will be [tex]116.48cm^{2} -67.03cm^{2} = 49.45cm^{2}[/tex]

This will be[tex]49.5 cm^{2}[/tex] to 3. significant figures

Answer:

43.8 cm²

Step-by-step explanation:

1. Split the kite in two and find the length of OB

When split the kite in two, you will find that the 120° becomes 60°, as they are divided into two.

Then, use the sine rule we can find out the length of OB. It goes like this:

[tex]\frac{OB}{sin90} = \frac{8}{sin30}\\ \\{OB} = \frac{8sin90}{sin30}\\\\ {OB} = 16cm[/tex]

2. Calculate the area of the kite

Since we have split the kite into two triangles and we know two side of the triangles, then we can calculate the area of one triangle using the formula of [tex]area of triangle=\frac{1}{2}absinc[/tex].

[tex]\frac{1}{2}[/tex]×8×16×sin60 = [tex]32\sqrt{3}[/tex]

But as there are two triangles, we duplicate the answer.

2×[tex]32\sqrt{2}[/tex] = [tex]64\sqrt{3}[/tex]

2. Calculate the area of the sector

area of sector =[tex]\frac{angle of sector}{360} \\[/tex]×πr²

[tex]\frac{120}{360}[/tex]×8²π = [tex]\frac{64}{3}[/tex]π

3. Subtract the area of the sector from the area of the kite

[tex]64\sqrt{3}[/tex] - [tex]\frac{64}{3}[/tex]π = 43.83060841 ≈ 43.8 cm² (to 3 s.f.)

HOPE THIS WILL HELP YOU :)

Answer:

C. (4,0)

Step-by-step explanation:

Given a graph of the system of equations

3x+4y=12; and

2x-y=8.

We can see that both lines pass through (4,0). Therefore, (4,0) is a point of intersection of the two lines.

It is therefore a solution to the system of equations.

Answer:

[tex](7x - 9) + (3x + 14) = 10x + 5[/tex]

Step-by-step explanation:

[tex]\left(7x-9\right)+\left(3x+14\right)[/tex]

Remove parentheses: [tex]\left(a\right)=a[/tex]

[tex]=7x-9+3x+14[/tex]

Group like terms:

[tex]=7x+3x-9+14[/tex]

Add similar elements: [tex]7x+3x=10x[/tex]

[tex]=10x-9+14[/tex]

Add/Subtract the numbers: [tex]-9+14=5[/tex]

[tex]=10x+5[/tex]

Hope I helped. If so, may I get brainliest and a thanks?

Thank you. Have a good day! =)

Answer:

pls refer to the pic

Step-by-step explanation:

Answer: 3 years

Step-by-step explanation:

The following can be gotten from the question:

Principal = $1600

Rate = 5%

Simple interest = $240

Time = Unknown

Interest = Principal × Rate × Time /100

240 = (1600 × 5 × Time)/100

240 = (8000 × Time)/100

240 × 100 = 8000 × Time

24000 = 8000 × Time

Time = 24000/8000

Time = 3 years

Answer:

49

Step-by-step explanation:

y = 7^2

= 49

Answer:

C = 25.1 cm

Step-by-step explanation:

C = 2(3.142r)

C = 2(3.142*4)

C = 2(12.568)

C = 25.136

Round to the nearest hundredth

C = 25.1

Answer:

6:12=1:2

Step-by-step explanation:

as we will cut 6:12 by 6 . please mark me as brainliest and follow me

Answer:

1:2

Step-by-step explanation:

6 and 12 are divisible by 6

6 ÷ 6 = 1

12 ÷ 6 = 2

Answer:

y- intercept = 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

[tex]\frac{x}{3}[/tex] + [tex]\frac{y}{2}[/tex] = 1

Multiply through by 6 to clear the fractions

2x + 3y = 6 ( subtract 2x from both sides )

3y = - 2x + 6 ( divide all terms by 3 )

y = - [tex]\frac{2}{3}[/tex] x + 2 ← in slope- intercept form

with y- intercept c = 2

Answer:

If the radius is 10mi, height is 22mi, the answer is V≈6911.5

If the radius is 22mi, height is 10mi,  the answer is V≈15205.31

ΔABC is an equilateral triangle.

All 3 angles must be equal in an equilateral triangle.

[tex]180/3[/tex]

[tex]=60[/tex] °

Answer:

x5

Step-by-step explanation:

Answer:

(x - 1) (x + 4)

Step-by-step explanation: