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Dmitrij [34]
3 years ago
5

a phone company offers two monthly plans. plan A costs 13 plus an additional 0.16 for each minute of calls. Plan B costs 24 plus

an additional 0.14 for each minute of calls
Mathematics
1 answer:
vladimir1956 [14]3 years ago
5 0

Answer:

Let x represent number of calling minutes

Step-by-step explanation:

17 + .11x = 22 + .07x

      .04x = 5

         x = 5/.04  = 125 minutes, is the number of minutes the two plans cost the same

 17 + .11*125 = $30.75 is the cost when the two plans cost the same  

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Giving 100 points.
Nitella [24]

Answer:

1.   <u>Cost per customer</u>:  10 + x

     <u>Average number of customers</u>:  16 - 2x

\textsf{2.} \quad  -2x^2-4x+160\geq 130

3.    $10, $11, $12 and $13

Step-by-step explanation:

<u>Given information</u>:

  • $10 = cost of buffet per customer
  • 16 customers choose the buffet per hour
  • Every $1 increase in the cost of the buffet = loss of 2 customers per hour
  • $130 = minimum revenue needed per hour

Let x = the number of $1 increases in the cost of the buffet

<u>Part 1</u>

<u></u>

<u>Cost per customer</u>:  10 + x

<u>Average number of customers</u>:  16 - 2x

<u>Part 2</u>

The cost per customer multiplied by the number of customers needs to be <u>at least</u> $130.  Therefore, we can use the expressions found in part 1 to write the <u>inequality</u>:

(10 + x)(16 - 2x)\geq  130

\implies 160-20x+16x-2x^2\geq 130

\implies -2x^2-4x+160\geq 130

<u>Part 3</u>

To determine the possible buffet prices that Noah could charge and still maintain the restaurant owner's revenue requirements, solve the inequality:

\implies -2x^2-4x+160\geq 130

\implies -2x^2-4x+30\geq 0

\implies -2(x^2+2x-15)\geq 0

\implies x^2+2x-15\leq  0

\implies (x-3)(x+5)\leq  0

Find the roots by equating to zero:

\implies (x-3)(x+5)=0

x-3=0 \implies x=3

x+5=0 \implies x=-5

Therefore, the roots are x = 3 and x = -5.

<u>Test the roots</u> by choosing a value between the roots and substituting it into the original inequality:

\textsf{At }x=2: \quad -2(2)^2-4(2)+160=144

As 144 ≥ 130, the <u>solution</u> to the inequality is <u>between the roots</u>:  

-5 ≤ x ≤ 3

To find the range of possible buffet prices Noah could charge and still maintain a minimum revenue of $130, substitute x = 0 and x = 3 into the expression for "cost per customer.  

[Please note that we cannot use the negative values of the possible values of x since the question only tells us information about the change in average customers per hour considering an <em>increase </em>in cost.  It does not confirm that if the cost is reduced (less than $10) the number of customers <em>increases </em>per hour.]

<u>Cost per customer</u>:  

x =0 \implies 10 + 0=\$10

x=3 \implies 10+3=\$13

Therefore, the possible buffet prices Noah could charge are:

$10, $11, $12 and $13.

8 0
2 years ago
Hello can someone help me with this?
zalisa [80]

Answer:

  1. 1
  2. 1/2
  3. 1/5
  4. 2
  5. 10
  6. 0
  7. -1
  8. -1/2
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3 years ago
3. Is the relation {(1,2), (3, 10), (2,8), (5,<br> 10)} a function?<br> a) yes<br> b) no<br> a
Sedaia [141]

Answer:

the answer is yes

Step-by-step explanation:

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3 years ago
What is the slope intercept form of (13x − 5x) + 12 − 2y = 6? SHOW YOUR WORK
vlabodo [156]
Here is the work:
(13x - 5x) + 12 - 2y = 6
(8x) + 12 - 2y = 6
-2y = -8x - 12 + 6
-2y = -8x - 6
y = 4x + 3
3 0
3 years ago
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9/6=x/10 what is x? How to figure it out.
skelet666 [1.2K]

Answer:

x=15

Step-by-step explanation:

(10*9)/6=10*x/10

90/6=x

15=x

4 0
3 years ago
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