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3 years ago

3x² + (4x – x) + 7 – (2x – 1) Which expression is equivalent to this

Mathematics

1 answer:

Airida [17]3 years ago

6 0

Answer:

3x² + x + 8

Step-by-step explanation:

3x² + (4x - x) + 7 - (2x - 1)

Solve what's inside the parenthesis first.

3x² + 3x + 7 - 2x + 1

Combine like terms.

3x² + x + 8

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An airport offers two shuttles that run on diffrent schedules. If both shuttles leave the airport at 4:00p.m., T what time will

Ghella [55]

We need to know the schedules . . . How often does each shuttle run ?

6 0

3 years ago

Owning a small and successful business isn't easy! There is a monthly cost of shipping supplies and

andriy [413]

Answer:

$C(x)=24,000+19,200x$

Step-by-step explanation:

<u>Mathematical Modeling</u>

To model a real-life situation, a mathematical model can be constructed in such a way it accurately represents the variables measured in the system.

This problem requires to build a model for the yearly cost of a small and successful business.

The first data is the fixed monthly cost or the money the owner must pay regardless of the number of employees he hires. This cost includes shipping supplies and products for $2,000. To operate for a full year, the fixed cost is 12*$2,000=$24,000.

The other component of the cost function is the variable cost of x employees. Given each employee costs $1,600 each month, having x employees cost 1,600x each month. For a full year, the variable cost will be

12*1,600x=19,200x.

We finally form the total cost function:

$\boxed{C(x)=24,000+19,200x}$

7 0

2 years ago

What is the solution to the system of equations below? -4x+6y=-18 and y=-2x+21

Verdich [7]

Answer:

x=9 and y=3

Step-by-step explanation:

Let's solve your system by substitution.

−4x+6y=−18 and y=−2x+21

Rewrite equations:

y=−2x+21;−4x+6y=−18

Step: Solve y=−2x+21for y:

y=−2x+21

Step: Substitute−2x+21foryin−4x+6y=−18:

−4x+6y=−18

−4x+6(−2x+21)=−18

−16x+126=−18(Simplify both sides of the equation)

−16x+126+−126=−18+−126(Add -126 to both sides)

−16x=−144

−16x

−16

−144

−16

(Divide both sides by -16)

x=9

Step: Substitute9forxiny=−2x+21:

y=−2x+21

y=(−2)(9)+21

y=3(Simplify both sides of the equation)

Answer:

x=9 and y=3

3 0

3 years ago

Two fences in a field meet at 120 degrees. A cow is tethered at their intersection with a 15-foot rope, as shown in the figure.

bija089 [108]

Answer:

Area of the field that the cow graze = 235.71 sq. ft

Step-by-step explanation:

Area of the field that the cow graze = (120 / 360) * πr²

= (1/3) * (22/7) * 15 * 15

= (22 * 5 * 15) / 7 = 1650 /7

= 235.71 sq. ft

5 0

3 years ago

Charlie runs a book rental business. He currently charges $3 per book and rents out an average of 38 books a day.

liberstina [14]

Answer:

b(x) = (3+0.5x) (38-4x)

Step-by-step explanation:

Let the generated revenue per day be b(x)

Let x be the number for every 50cents($0.5) price increase

Formula to be used to generate the revenue generated is expressed using the formula:

b(x) = Price × Quantity

Next is to derive the price and quantity function in terms of x.

For the price:

If he currently charges $3 per book

Let derive the price function for the model and x number of price increase for every 50 cents, then

Price = ($0.5 of x)+$3

Price = $3+$0.5x

Price = $(3+0.5x)

For the quantity:

Number of books rent out per day = 38

If for every 50cents increase in rental price x, the average business can expect to lose 4 rentals a day, then the total lost per quantity = 4x

Quantity per time = Number of books rent out daily - loss on each book

Quantity = $(38-4x)

Next is to substitute the price and quantity function into the revenue formula above:

Revenue = Price × Quantity

Revenue = (3+0.5x)(38-4x)

Hence the equation that models this scenario, where b(x) is the revenue generated and x is the number of 50 price increases is b(x) = (3+0.5x)(38-4x)

7 0

3 years ago