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zvonat [6]
2 years ago
5

TWO TRUTHS ONE LIE

Mathematics
1 answer:
Ivenika [448]2 years ago
5 0

Answer:

(3) A"B"C" can be mapped onto A'B'C' by rotating it 180 degrees

Step-by-step explanation:

well, the other two are true, so that only leaves one option, sorry if this is wrong

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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
the population of a city increased from 24500 to 41600 between 2003 and 2012 . find the change of population per year if we assu
AURORKA [14]
The change of population per year is 1,900

We'll start by subtracting; 41,600-24,500= 17,100
Then we'll divide 17,100 by 9 because there is a 9 year difference between 2003 and 2012.
17,100/<span>9=1,900</span>
5 0
3 years ago
Ill mark you brainlist plz help if you put something random I will report you!
julia-pushkina [17]

Answer:

11n - 5

Step-by-step explanation:

8 0
2 years ago
Tom ordered some books online and spent a total of $75. Each book cost $6 and he paid a total of $3 for shipping. How many books
BaLLatris [955]

Answer:

a)

_b+_=_

6B+3=75

B)

He ordered 12 books

Step-by-step explanation:

so each book (b) costs $6. he payed $75 total including the $3 shipping price

That gets us:

6b+3=75

6b=72

b=12

Therefore, Tom ordered 12 books

5 0
3 years ago
Select the graph that represents two quantities in a proportional relationship
dlinn [17]

The correct answer is option D.It is the graph that represents two quantities in a proportional relationship.

<h3>What is a graph?</h3>

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

As we can see graph D is showing the correct proportionality. We can also create an equation of proportionality as:-

Y = 2x

Put y = 0.5

0.5 = 2 x 0.5 = 1

As we put y=0.5 we get the value of x = 1 as shown in the graph.

Therefore the correct answer is option D.It is the graph that represents two quantities in a proportional relationship.

To know more about graphs follow

brainly.com/question/25020119

#SPJ1

3 0
2 years ago
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