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stiks02 [169]
3 years ago
15

Why are inequalities important in equations

Mathematics
1 answer:
Delicious77 [7]3 years ago
4 0
Because the tell if he number is big or small
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You have just opened a new dance club, Swing Haven, but are unsure of how high to set the cover charge (entrance fee). One week
bonufazy [111]

Answer:

a) The demand function is

q(p) = -4 p + 107

b) The nightly revenue is

R(p) = -4 p^2 + 107 p

c) The profit function is

P(p) = -4 p^2 + 133.75 p - 939

d) The entrance fees that allow Swing Haven to break even are between 10.03 and 23.41 dollars per guest.

Step-by-step explanation:

a) Lets find the slope s of the demand:

s = \frac{79-43}{7-16} = \frac{36}{-9} = -4

Since the demand takes the value 79 in 7, then

q(p) = -4 (p-7) + 79 = -4 p + 107

b) The nightly revenue can be found by multiplying q by p

R(p) = p*q(p) = p*( -4 p + 107) = -4 p^2 + 107 p

c) The profit function is obtained from substracting the const function C(p) from the revenue function R(p)

P(p) = R(p) - C(p) = p*q(p) = -4 p^2 + 107 p - (-26.75p + 939) = \\\\-4 p^2 + 133.75 p - 939

d) Lets find out the zeros and positive interval of P. Since P is a quadratic function with negative main coefficient, then it should have a maximum at the vertex, and between the roots (if any), the function should be positive. Therefore, we just need to find the zeros of P

r_1, r_2 = \frac{-133.75 \,^+_-\, \sqrt{133.75^2-4*(-4)*(-939)} }{-8} = \frac{-133.75 \,^+_-\, 53.526}{-8} \\r_1 = 10.03\\r_2 = 23.41

Therefore, the entrance fees that allow Swing Haven to break even are between 10.03 and 23.41 dollars per guest.

7 0
3 years ago
Use the diagram to determine which statement is true
Dahasolnce [82]

The answer is d.

Finding area of ABCD :

  1. Find side length
  • side = √3² + 4²
  • side = 5

    2. Apply formula to find area

  • area = 5²
  • area = 25

Finding area of GHIA :

  • area = 4²
  • area - 16

Finding area of DEFG :

  • area = 3²
  • area = 9

Now, let's see whether is true.

  • Area (ABCD) - Area (GHIA) = Area (DEFG)
  • 25 - 16 = 9
  • 9 = 9

∴ Hence, it is proved √

7 0
1 year ago
Calculate the area of the shape below.
Vsevolod [243]

Answer:

24ft²

Step-by-step explanation:

divide up the shape:

big triangle:

(looking for base)

9.8²= 4² + b²

b  = 8.95ft

(finding area)

0.5*8.95*4 = 17.9ft²

small triangle:

(looking for base)

12-8.95=3.05ft

(finding area)

0.5*3.05*4 = 6.1ft²

Whole Shape:

17.9+6.1 = 24ft²

3 0
3 years ago
How do i simplify this problem?<br><br>12r+5s-7T+9s-4r​
Nimfa-mama [501]

Answer: To simplify this problem you combine the like terms in the equation (numbers with the same variables.)

Demo: 12r + -4r = 8r

4 0
3 years ago
Read 2 more answers
Solve 4(10x - 2) = 192​
MAXImum [283]

Answer:

5

Step-by-step explanation:

4*10x=40x

4*2=8

40x-8=192

40x=192+8

=200

X= 200/40

=5

5 0
3 years ago
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