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alex41 [277]
3 years ago
13

Solve: (x + 5)^2 + 15 = 64

Mathematics
1 answer:
ch4aika [34]3 years ago
5 0
(x+5)^2 = 49;
Then x + 5 = 7 or x + 5 = -7 ;
Finally, x = 2 or x = -12.
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You have just opened a new nightclub, Russ' Techno Pitstop, but are unsure of how high to set the cover charge (entrance fee). O
Neko [114]

Answer:

a)q(p)=-15p+ +300

b)R(p)=-15p²+300p

c)C(p)=-30p+1600

d.1)P(p)=-15p²+330p-1600

d.2)p=$11

Step-by-step explanation:

(a).Before getting started, we are going to consider  the cartesian plane, where x-axis corresponds to the cover charge and y-axis corresponds to number of guests per night . There, we will locate the following coordinates according to the previous information:

(9,165)  (10,150).

Remember that  the slope-intercept form of the  linear equation is y=mx+b where m is the slope and b  is te intercept.

The slope can be calculated  by the next formula:

m=\frac{y2-y1}{x2-x1}

In this case we will assign  (9,165) as the first coordinate and (10,150) as the second one. The order does not matter. At the end we get the same value for m.

Therefore:

m=\frac{150-165}{10-9} = -15

Now, we have the slope and two poitns. According to this, and taking into account that  point-slope form of the equation of a line is y-y1=m(x-x1),   find a linear demand equation.

Any of two coordintates can be selected. In this case we will select the second one.

y-150=-15(x-10)   equation 1

Solve equation 1 for y

y=-15x+150+150

y=-15x+300

Above we had defined x as cover charge (p) and y as number of guests (q). Thus, rewrite equation 1.

q(p)=-15p+ +300.  

it equation shows the number of guests per night as a function of the cover charge,

(b). The nightly revenue can be calculated multplying the price of the cover charge by  the number of guests. So, we just have to multiply the equation 1 by p.

p*q(p)=p*(-15p +300)

R(p)=-15p²+300p   equation 2

(c) To get the cost function of the nightclub  we just have to multiply the cost of the two non-alcoholic drinks   by the number of the guests ( equation 1) and add to it  nightly overheads.

C(p)=2*(-15p+300)+1000

C(p)= -30p+600+1000

C(p)=-30p+1600  equation 3

(d) In order to find the profit in terms of the cover charge we will  subtract nightly costs ( equation 3) from nightly revenue (equation 2)

P(p)=R(p)-C(p)

P(p)=-15p²+300p - (-30p+1600)

P(p)=-15p²+300p+30p-1600

P(p)=-15p²+330p-1600

To determine that  the entrance fee we should charge for a maximum profit we are going to use the first derivative test (y'(x)=0) in order to find an extremum point.

Compute the first derivative of P(p)

P'(p)=-30p+330=0

30p=330

p=330/30

p= $11

The entrance fee that we should charge for a maximum profit is p=$11 per guest.

5 0
3 years ago
A long year end status report for work is 108 pages long. You need to print 19 copies for a meeting next week. How much is the p
maks197457 [2]
A total of
  108*19 = 2052
pages will be printed. We suppose paper will be purchased in reams of 500 pages each, so
  ceiling(2052/500) = ceiling(4.104) = 5
reams will be needed. The the cost will be
  (5 reams)*($3.69/ream) = $18.45

The paper for the reports will cost $18.45.
7 0
3 years ago
PLEASE HELP ME! I gotta get this done before the 1st!!!
Hunter-Best [27]

Answer:

A)6x-18, B)They are not equal, since 6xx18 is not equal to 6x-9

Step-by-step explanation:

2(3x-9) = 2(3x)-2(9) =6x-18.

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2 years ago
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maria [59]

Answer:

c) √121 is the rational number.

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2 years ago
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Answer:

its 22 because it is going by 3

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3 years ago
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