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Vikentia [17]
2 years ago
6

Help. I can’t seem to figure out how to get the answer.

Mathematics
1 answer:
liubo4ka [24]2 years ago
8 0

Answer:

  15. 80 benches

  16. 45 cost units

Step-by-step explanation:

The two problems together are asking you to find the coordinates of the vertex of the cost function. To do this you can use the procedure for writing a quadratic in vertex form.

  C(x) = 0.1x^2 -16x +685

  = 0.1(x^2 -160x) +685 . . . . . . factor out the leading coefficient

  = 0.1(x^2 -160x +6400) +685 -(0.1)(6400) . . . add and subtract 0.1(6400)

  C(x) = 0.1(x -80)² +45 . . . cost function in vertex form

__

<h3>15.</h3>

The number of benches that minimizes the cost function is the x-coordinate of the vertex. That is the value that makes the square equal to zero.

  x = 80 . . . benches

__

<h3>16.</h3>

The minimum value of the cost function is the value obtained when the squared term is zero:

  C(80) = 0.1(80 -80)² +45

  C(80) = 45

The minimum cost per bench is 45. (The problem statement gives no units for cost. It could be pesos, or millions of rubles. We can't tell.)

_____

<em>Additional comment</em>

The square of a binomial is ...

  (x +a)² = x² +2ax +a²

You will notice that the constant (a²) is the square of half the x-coefficient. To "complete the square", we put the equation in a form where we have (x² +2ax) in parentheses. Then we divide the x-coefficient by 2, and add its square inside parentheses: (x² +2ax +a²) and rewrite to the form of a square: (x +a)².

In order to keep the expression the same, we must subtract the same quantity elsewhere in the equation. Outside parentheses, it must be multiplied by the coefficient in front of the parentheses. In the above, we added (0.1)(6400) and subtracted (0.1)(6400) so that we could rearrange the cost function to vertex form: a(x -h)² +k has vertex (h, k).

__

We find a graphing calculator to be an extremely handy tool for dealing with polynomial functions. The attached shows the graph of the cost function. The calculator marks the vertex for us. Since it is a plot of cost versus number of benches, the units of the vertex are (benches, cost units).

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Wewaii [24]
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40% decrease

7 0
3 years ago
What is 5+3y-8x-(-2)-5y
Vilka [71]
3-2y-8x is it's most simplified form I think. 
4 0
3 years ago
What is the solution to the following system of equations? x − 4y = 6 2x + 2y = 12 (0, 10) (10, 0) (6, 0) (0, 6)
frozen [14]

Answer:

(6,0)

Step-by-step explanation:

The given system has equations:

x-4y=6

2x+2y=12

Multiply the top equation by 2 to get:

2x-8y=12

2x+2y=12

Subtract the top equation form the bottom equation to get:

2x-2x+2y--8y=12-12

\implies 10y=0

\implies y=0

Put y=0 into x-4y=6

x-4*0=6

\implies x=6

Therefore the solution is (6,0)

4 0
3 years ago
A total of $2,000 is invested at an annual interest rate of 2%. Find the balance in the account after
Anit [1.1K]

Answer:

<u>The balance in the account after 10 years is US$ 2,442.81</u>

Step-by-step explanation:

1. Let's review the data given to us for answering the question:

Investment amount = US$ 2,000

Duration of the investment = 10 years

Annual interest rate = 2% compounded continuously

2. Let's find the future value of this investment after 10 years, using the following formula:

FV = PV * eˣ ⁿ

PV = Investment = US$ 2,000

number of periods (n) = 10 (10 years compounded continuously)

rate (x) = 2% = 0.02

e = 2.71828 (Euler's number)

Replacing with the real values, we have:

FV = 2,000 * (2.71828)^0.02*10

FV = 2,000 * 2.71828^0.2

FV = 2,000 * 1.2214027

<u>FV = US$ 2,442.81</u>

8 0
3 years ago
Ateacher uses 36 centimeters of tape to hang up 9 student projects. At that rate
Troyanec [42]

The teacher would need 40 centimeters of tape to hang 10 student projects.

Step-by-step explanation:

Given,

Tape used to hang projects = 36 centimeters

Number of projects hanged = 9

We will find unit rate;

9 projects = 36 centimeters

1 project = \frac{36}{9}\ centimeters

1 project = 4 centimeters

Therefore,

Tape needed to hang 10 projects = 4*10 = 40 centimeters

The teacher would need 40 centimeters of tape to hang 10 student projects.

Keywords: unit rate, multiplication

Learn more about unit rate at:

  • brainly.com/question/11203617
  • brainly.com/question/11253316

#LearnwithBrainly

3 0
3 years ago
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