f(x) = cube root 2x
g(x) = 2x + 1
Find (f/g) (X) Include any restrictions on the domain

By solving a system of equations we can see that there are 400 main-floor seats and 500 balcony seats.

Let's define the two variables:

We know that if all the seats are sold, then the total income is $5,200, we can write the equation:

x*$8 + y*$4 = $5,200

And if 25% of the main-floor and 50% of the balcony seats are sold, then we get an income of $1800, then we can write:

0.25*x*$8 + 0.5*y*$4 = $1,800

x*$2 + y*$2 = $1,800

So we have a system of equations:

x*$8 + y*$4 = $5,200

x*$2 + y*$2 = $1,800

If we subtract twice the second equation for the first one we get:

(x*$8 + y*$4) - (x*$2 + y*$2) = $5,200 - 2*$1,800

x*$4 = $1,600

x = $1,600/$4 = 400

So there are 400 seats on the main-floor.

Using the first equation we can find:

x*$8 + y*$4 = $5,200

400*$8 + y*$4 = $5,200

$3,200 + y*$4 = $5,200

y*$4 = $5,200 - $3,200 = $2,000

y = $2,000/$4  = 500

So there are 500 balcony seats.

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Answer:

574

Step-by-step explanation:

Answer:

5261

Step-by-step explanation:

your welcome

Answer:

16

Step-by-step explanation:

The value of the inventory will be 4000

Bulbs in the warehouse: 2000 bulbs

Cost of each bulb to the manufacturer: 2

Average delivery cost = 0.30

The selling price of the bulb = 2.20

Value of inventory: The monetary value assigned to the items in inventory at the end of an accounting period is known as inventory valuation. The inventory is valued based on the expenses incurred to get it and prepare it for sale.

The biggest current business assets are inventories. You can assess your cost of goods sold (COGS) and, ultimately, your profitability, thanks to inventory valuation.

The value of the inventory is calculated on the cost price, therefore the value of the inventory will be:

= Cost of each bulb*Number of bulbs

= 2000*2

= 4000

So, the value of the inventory will be 4000

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Answer:

24

23fc

23

45jh4

66

35g

35

56

34

Answer:

720

Step-by-step explanation:

We are looking for the difference between 2/3 and 1/2, which we know to be 120. To subtract fractions of different denominators, we need to find the common denominator (this can be found by finding the LCM of both denominators)

120 = 2/3 - 1/2 = 4/6 - 3/6
1/6 = 120

We can multiply 120 by 6 to find the value of the full bank.

1/1 = 720

Jayden needs (C) 128 ft² cardboard to make a box.

The net is made up of six parallelograms, each representing one of the box's faces.

The area represented by the net can be used to estimate how much cardboard Jayden will need to make the box.

The calculations are as follows:

So, our rectangles and two squares:

Therefore, Jayden needs (C) 128 ft² cardboard to make a box.

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Answer:

  5 inches

Step-by-step explanation:

Whitney wants the greatest length that is an even divisor of both 45 inches and 20 inches.

The length Whitney is looking for is called the "greatest common divisor" (GCD) or "greatest common factor" (GCF) of the two numbers 45 and 20. There are a couple of different ways this can be found.

The prime factors of the two numbers are ...

  45 = 3×3×5

  20 = 2×2×5

The only factor common to the two products is 5. It is the greatest common factor.

Whitney can cut lengths of 5 inches.

Another way to find the GCD is to use Euclid's algorithm. That has you ...

Using this algorithm, we have ...

  45/20 = 2 r 5

  20/5 = 4 r 0 . . . . . The GCD is 5

Whitney can cut lengths of 5 inches.

Answer:

[tex]t = - \frac{1}{2} b + \frac{5}{2} [/tex]

Answer:

The answer to your question is 588

Answer:

588

Hope this helps

Answer: a=(V-4)/t

Step-by-step explanation:

V = 4 + at

V-4=at

a=(V-4)/t

Answer:

33

 messages

Step-by-step explanation:

x= 0.

[tex]3cosx = 2+cosx[/tex]

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

[tex]\frac{3cosx}{3} = \frac{2+cosx}{3} \\\\\frac{3cosx}{3} = \frac{2}{3} +\frac{cosx}{3} \\ \\cosx-\frac{cosx}{3}=\frac{2}{3} +\frac{cosx}{3}-\frac{cosx}{3}\\ \\\\cosx-\frac{cosx}{3}=\frac{2}{3}[/tex]

[tex]\frac{3cosx}{3} -\frac{cosx}{3}=\frac{2}{3}\\ \\\frac{3cosx-cosx}{3}=\frac{2}{3}[/tex]

[tex]3*\frac{3cosx-cosx}{3}=\frac{2}{3}*3\\ \\3cosx-cosx=\frac{6}{3}\\ \\3cosx-cosx=2[/tex]

[tex]2cosx=2[/tex]

[tex]\frac{2cosx}{2} =\frac{2}{2} \\ \\cosx=1[/tex]

[tex]cos^{-1}(cosx) =cos^{-1}(1)\\ \\x=cos^{-1}(1)\\ \\x=0.[/tex]

45 inches s the perimeter of a regular, triangular yield sign with aside length of 15 in

The perimeter of a shape is the sum of the lengths of all its edges. For example, a triangle has three edges, so its perimeter is equal to the sum of those three lengths.

The perimeter of a square can be easily calculated if one side and all other sides are given as being the same length; for example, a square with sides measuring 5 inches long has a perimeter of 20 inches because 5 x 4 = 20. By multiplying the sum of the length and width by two, one can determine a rectangle's perimeter.

We will use the simple perimeter formula as yield sign is equilateral triangle

So, 15 × 3 = 45 inches

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Answer:

x=27 or x= -8

Step-by-step explanation:

rearrange the terms

convert the expression

simplify the expression

rewrite the equation

solve the equation

formulate new equations

I can't show the full steps since there's no image

Answer:

this is answers

scan and see

the relationship between x and y when x varies directly is 4 x = y.

We know that when x varies directly with y, then:

x = k y

Now, we have x = 5 and y = 20

Substituting the values in the expression, we get that:

5 = 20 k

k = 5 / 20

k = 1 / 4

So, we get the relation as:

x = 1 / 4 y

4 x = y

Therefore, the relationship between x and y when x varies directly is 4 x = y.

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The graph of the compound inequalities with intersection points

(2.21, -0.63) is given below.

Please see the graph attached.

A compound inequality has two inequality statements joined either by the "or" or “and.”

We have,

6x+2y<12 or x-6y>6

We can graph each inequality.

And we also need to see the intersection between the inequalities.

Let,

6x + 2y = 12____(1)

x - 6y = 6_______(2)

From (1)

x = (12 - 2y ) / 6 put in (2)

(12 - 2y) / 6 - 6y = 6

2 - 1/3y - 6y = 6

2 - 6 = (1/3)y + 6y

-4 = 19y / 3

y = -12 / 19

y = - 0.63 put in (1)

6x + 2 x (-0.63) = 12

6x = 12 + 1.26

x = 13.26 / 6

x = 2.21

The point of intersection on the graph is (2.21, -0.63).

Thus the graph of the compound inequalities with intersection points (2.21, -0.63) is given below.

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The coordinates of the vertices E (-8,9), F(-4,9), G(-4,2), and D(2,-8) when rotated 90° counterclockwise around the origin of the new coordinates will be E'( - 9, - 8 ), F'( - 9, - 4 ), G'( - 2, - 4 ), and D'( 8, 2 ).

A point A( x, y ) becomes A' when a point is rotated 90 degrees counterclockwise about the origin ( - y, x ). To put it another way, flip x and y, and make y negative.

Therefore, when point E( - 8, 9 ) is rotated 90° counterclockwise around the origin will be:

E'( - 9, - 8 )

When point F( - 4, 9 ) is rotated 90° counterclockwise around the origin the new point will be:

F'( - 9, - 4 )

When point G( - 4, 2 ) is rotated 90° counterclockwise around the origin the new point will be:

G'( - 2, - 4 )

When point D( 2, - 8 ) is rotated 90° counterclockwise around the origin the new point will be:

D'( 8, 2 )

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Answer:

Step-by-step explanation:

Solve equation:

Answer: true

0.1=[tex]\frac{1}{10}[/tex]

Step-by-step explanation:

[tex]\frac{1}{5}/2[/tex]

Express  [tex]\frac{1}{5}/2[/tex]

 as a single fraction.

[tex]\frac{1}{5*2}[/tex]

Multiply 5 and 2 to get 10.

[tex]\frac{1}{10}[/tex]

FACTOR

[tex]\frac{1}{2.5}[/tex]     =0.1

Answer: [tex]7 \frac{13}{200}[/tex]

Step-by-step explanation:

7.065=

[tex]7 \frac{65}{1000}[/tex]=      ==> GCF of 65 and 1000 is 5

[tex]7 \frac{65/5}{1000/5}[/tex]=[tex]7 \frac{13}{200}[/tex]

Answer:

  g(x) = 3x +5

Step-by-step explanation:

You want the function that results from translating f(x) = 3x upward by 5 units.

The y-coordinate of a point tells how far above the x-axis it is. Adding 5 to the y-coordinate will move that point 5 units farther above the x-axis, which is to say 5 units upward.

The y-coordinate of a point on a graph is the value of the function of the x-coordinate of that point. That is, each point is (x, f(x)). If we want to translate that point 5 units upward, we add 5 to the function value:

  (x, f(x) +5) . . . . . graph translated 5 units up

Using the given definition of f(x), this becomes ...

  (x, 3x +5)

The translated function is defined as g(x), so we have ...

  (x, g(x)) = (x, 3x +5)

or ...

  g(x) = 3x +5

Answer:

Step-by-step explanation:

Let the initial salary be x.

Set equation and solve for x:

Answer:

The original salary is $11641.18.

Step-by-step explanation:

The equation will be,

→ x + (x × 2)/100 = 11874

Now the original salary will be,

→ x + (x × 2)/100 = 11874

→ x + 0.02x = 11874

→ 1.02x = 11874

→ x = 11874/1.02

→ x = 11641.1764706

→ [ x = 11641.18 ]

Hence, original salary is $11641.18.

The Three consecutive numbers will be 24.5, 25.5, 26.5

We have to take three consecutive numbers. Let the first number be 'x' and the consecutive two numbers be (x + 1), and (x + 2).

It is given that the square of the third number is greater than the square of the second number by 52. We need to create an equation that represents this situation. So, we get :

  => (x + 2)² = (x + 1)² + 52  

  =>  x² + 4x + 4 = x² + 2x + 1 + 52

  =>  x = 49/2      =>  x = 24.5

We get value of x = 24.5. Putting this value of x in consecutive numbers we get the first, second, and third numbers as 24.5, 25.5, and 26.5 respectively.

Hence, we get the three consecutive numbers: 24.5, 25.5, and 26.5

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Answer:

Step-by-step explanation:

You want the distances north and east of the origin that a plane ends up after flying 400 km at a bearing of 25°, then 700 km at 80°.

For some distance r and bearing angle θ, the (north, east) coordinates will be ...

  (north, east) = (r·cos(θ), r·sin(θ))

For the trip at hand, the final coordinates of the plane are ...

Distance north = (400 km)cos(25°) +(700 km)cos(80°)

  = 362.52 km +121.55 km = 484.07 km

B is about 484 km north of O.

Distance east = (400 km)sin(25°) +(700 km)sin(80°)

  = 169.05 km +689.37 km = 858.41 km

B is about 858 km east of O.

__

Additional comment

Rectangular coordinates of a point at distance r from the origin and an angle θ measured CCW from the +x axis are given by ...

  (x, y) = (r·cos(θ), r·sin(θ))

You may notice the similarity to the coordinates described above. That is why we can use a calculator the way we have in the attachment. The imaginary part of the complex number represents the distance east.

The down payment is $112,000.

And, Amount of the mortgage loan is $168,000.

Here,

Alvira and Barry Gomez purchased a home priced at $280,000.

They put down 40%.

We have to find down payment.

And, Amount of the mortgage loan.

What is Down payment?

A sum of money that a buyer pays in the early stages of purchasing an expensive good or service is called down payment.

Now,

Alvira and Barry Gomez purchased a home priced at $280,000.

They put down 40%.

Hence, The down payment = $280,000 x 40%

                                          = $280,000 x 40 / 100

                                          = $112,000

And, Amount of the mortgage loan = Total amount - Down payment

                                                      = $280,000 - $112,000

                                                      = $168,000

Therefore, The down payment is $112,000.

And, Amount of the mortgage loan is $168,000.

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The picture of the triangle ΔDEF is attached below.

A triangle can be defined as a basic polygon which has 3 sides.

In the given ΔABC we see that AC is the hypotenuse and the two sides AB and AC are the legs of the triangle.

m∠B=90°

The ΔDEF is drawn such that m∠E=90° and AB=DE and EF=BC .

Therefore we can say that the two triangles are congruent by SAS axiom of congruency.

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