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Natasha_Volkova [10]
3 years ago
9

Rewrite in a form that does not use exponents

Mathematics
1 answer:
emmainna [20.7K]3 years ago
4 0

Answer:

  \boxed{18}

Step-by-step explanation:

One of the rules of logarithms is ...

  log(a^b) = b·log(a)

So ...

6\log_5{x^3}=6(3\log_5{x})=\bf{18}\log_5{x}

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Mark wants to fence 4 rectangular gardens, each with a length of 9 1/4 feet and a width of 4 1/2 feet. What is the total length
juin [17]

Answer:

110 feet

Step-by-step explanation:

Given that,

Length of the rectangular garden = 9 1/4 feet = 37/4 feet

Width of the rectangular garden = 4 1/2 feet = 9/4 feet

We need to find the total length of fencing Mark needs to surround all 4 gardens.

The length for 1 garden = perimeter of the garden

The length for 4 garden = 4×perimeter of the garden

= 4×2(l+b)

=8(l+b)\\\\=8(\dfrac{37}{4}+\dfrac{9}{2})\\\\=8\times 13.75\\\\=110\ \text{feet}

Hence, 110 feet is the total length of the fencing Mark needs to surround all 4 gardens.

5 0
2 years ago
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
Plz hurry will mark brainliest
svetoff [14.1K]

Answer:

No they don't form a proportion

Step-by-step explanation:

Their denominatiors do not share a common multiple, therefore they can not form a proportion.

5 0
3 years ago
Write the ratio 69:75 as a fraction, decimal,and a percent.
LekaFEV [45]
As a fraction, 69:75 would become 96/75
As a decimal 69:75 would become 0.92
As a percentage 69:75 would become 92%
Hope this helps :) 
3 0
3 years ago
Read 2 more answers
jen and sarah go to lunch at the Green Grill.Their meals total $28.00 .The tax is 6%.What is the total cost including tax?
nordsb [41]
6%=0.06

28(0.06)
= 1.68 ---> tax

28+1.68
= 29.68

Jen and Sarah spent 29.68 dollars including tax

I hope this answer helped you and have a wonderful day!
5 0
3 years ago
Read 2 more answers
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