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I am Lyosha [343]
3 years ago
14

*15 points help easy question*

Mathematics
1 answer:
DIA [1.3K]3 years ago
8 0

Answer:

x = 12

Step-by-step explanation:

The segment from the vertex to the base is a perpendicular bisector.

Using Pythagoras' identity on the right triangle on the right.

(\frac{1}{2} x )² + 3² = (\sqrt{45} )² , that is

\frac{1}{4} x² + 9 = 45 ( subtract 9 from both sides )

\frac{1}{4} x² = 36 ( multiply both sides by 4 )

x² = 144 ( take the square root of both sides )

x = \sqrt{144} = 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
Find the quotient of the problem using the area model strategy. After you have worked out your problems on a sheet of paper, you
Artist 52 [7]

Answer:

56 with re9

Step-by-step explanation make a square on a paper make 3 line on top of each line put 800 40 and 9 on the side put 15 search up 15 dived by 800 and 40 dived by 15 then 9 add it all up the yo go give me brainlist

8 0
3 years ago
Read 2 more answers
-5x– 8< -53 and -63 < -5x – 8
baherus [9]

Answer:

x>9 and x<11

Step-by-step explanation:

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3 years ago
Create your own word problem that results in a negative integer
mestny [16]

Answer:

In Buffalo, New York, the temperature was -14°F in the morning. If the temperature dropped 7°F, what is the temperature now?

Step-by-step explanation:

You just need to get a situation where there would be negative increase. My example was temperature, but other easy examples could be money (debt, etc) or sea level.

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3 years ago
Solve this problem using substitution
Sergeeva-Olga [200]
Solving for (x,y)
(x-y=8)
(x=y-8) & (y=x-8)

solving for (y,x)
(2y=2x-16)
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