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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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Step-by-step explanation:

3 consecutive integers = x, y and z

1st number is X

2nd number is Y which is X +1

3rd number is Z which is X +2

Write equation

X + 2Y = 16 + 2Z

Replace Y with X + 1 and Z with X + 2

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X + 2(X + 1) = 16 + 2(X + 2)

Distribute

X + 2X + 2 = 16 + 2X + 4

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3X + 2 = 2X + 20

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5 0
3 years ago
Interest.
nikitadnepr [17]

Answer:

Interest: $390 | Total: $715

Step-by-step explanation:

To answer the first question, we can use the simple interest formula provided:

I=Prt

<em>P = initial balance</em>

<em>r = annual interest rate</em>

<em>t = time</em>

<em />

First, change 8% into the decimal form:

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Now, plug in the values:

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Charlie made $390 of interest. To find the total, just add that number to $325.

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3 years ago
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answer
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3 years ago
Describe a situation that fits each equation. Describe more than one situation for each equation, if possible.
lisabon 2012 [21]

Answer:

Step-by-step explanation:

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4 0
2 years ago
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9966 [12]

The given question is wrong.

Question:

Which expression is equivalent to the given expression using commutative property of addition? 2(x + b) + 3(xa).

Answer:

Option C:

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Solution:

Given expression is 2(x + b) + 3(xa).

To find the equivalent expression using commutative property of addition.

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Now, write the given expression using commutative property.

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