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GuDViN [60]
4 years ago
6

What is the solution to log2 (9x)- log2^3=3?

Mathematics
1 answer:
Svet_ta [14]4 years ago
3 0

Answer:

x = \frac{8}{3}

Step-by-step explanation:

Using the rule of logarithms

log x - log y = log (\frac{x}{y} )

log_{b} x = n ⇒ x = b^{n}

Given

log_{2} (9x) - log_{2} 3 = 3

log_{2} (\frac{9x}{3} ) = 3

log_{2} 3x = 3

3x = 2³ = 8 ( divide both sides by 3 )

x = \frac{8}{3}

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according to a recent survey, in 2000, 64% of households had one or more pets.Throughout the next decade, this decreased by appr
ehidna [41]

Answer:

Year 2034

Step-by-step explanation:

In 2000, 64% had one or more pets

<em>Since decreasing at 1% per year, we can say:</em>

<em>In 2001, 63%</em>

<em>In 2002, 62%</em>

<em>In 2003, 61%</em>

<em>In 2004, 60%</em>

<em>And so on</em>

<em />

To go to 30% from 60% in 2004, we would need to decrease 60 - 30 = 30%, and that will occur after 30 more years. So that would be the year

2004 + 30 = 2034

So, year 2034

3 0
3 years ago
Someone help me with this math homework please!
Reil [10]

Answer:

Option number B

Step-by-step explanation:

As per the statement:

Pieter wrote and solved an equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level.

Given the equation as:

7h - 5 ( 3h -8 ) = -72

Using distributive property, 

a ⋅ ( b + c ) = a ⋅ b + a ⋅ c

7h - 15h + 40 = - 72

Combine like terms;

-8h + 40 = -72

Subtract 40 from both sides we have;

-8h 8= -112

Divide both sides by -8 we have;

h = 14 hours

Therefore, the statement is true about Pieter’s solution is, It must be a positive number since it represents a number of hours.

3 0
3 years ago
Hannah has a jar filled with 150 coins made up of quarters and nickels. The total value of the coins is $28.30
Sonja [21]
Based on the given details above, here are the answers to your question.
If x represents the number of quarters in the jar, the equation that can be used to find the number of quarters is this <span>0.25x + 0.05(150 x) = 28.30.
Then, for the how many quarters and how many nickels are there, the answer is </span><span> 46 quarters; 104 nickels. Hope this answer helps. </span>
5 0
4 years ago
Expand. If necessary, combine like terms. (x+3)(x-3)=
Ne4ueva [31]

Answer:

{x}^{2}  - 9

Step-by-step explanation:

(x−3)(x+3)

x(x+3)−3(x+3)

x \times x+x \times 3−3x−3   \times 3

x \times x−3 \times 3

{x}^{2}  - 9

<h3>Hope it is helpful....</h3>
8 0
3 years ago
The owners of a recreation area are filling a small pond with water. Let WB the total amount of water in the pond(in liters). Le
alexira [117]

Answer:

As we can see the domain is the: "number of minutes water has been added". And from the information given the values for T are between 0 and 60 so then the set of values would be "the set of all real numbers from 0 to 60", and we start from 0 because the time can't be negative.

For the range who represent "amount of water in the pond (in liters)" we need to analyze the possible values for W, since T is defined between 0 and 60 the limits for W are:

W(0)=35*0+300=300

W(60)=35*60+300=2400

So then the set of values for the range are "the set of all real numbers from 300 to 2400" liters.

Step-by-step explanation:

Assuming this complete problem: "The owners of a recreation area are filling a small pond with water. Let W be the total amount of water in the pond (in liters). Let T be the total number of minutes that water has been added. Suppose that  gives as a W function of during the next 60 minutes.

Identify the correct description of the values in both the domain and range of the function. Then, for each, choose the most appropriate set of values. "

Solution to the problem

As we can see the domain is the: "number of minutes water has been added". And from the information given the values for T are between 0 and 60 so then the set of values would be "the set of all real numbers from 0 to 60", and we start from 0 because the time can't be negative.

For the range who represent "amount of water in the pond (in liters)" we need to analyze the possible values for W, since T is defined between 0 and 60 the limits for W are:

W(0)=35*0+300=300

W(60)=35*60+300=2400

So then the set of values for the range are "the set of all real numbers from 300 to 2400" liters.

8 0
2 years ago
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