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stepladder [879]
2 years ago
14

List the potential solutions to 2 ln x = 4 ln 2 from least to greatest.

Mathematics
2 answers:
Contact [7]2 years ago
6 0
X = -4 and X = 4
then the answer to the solution is 4


svp [43]2 years ago
3 0

We have to find the potential solutions to 2 ln x = 4 ln 2 from least to greatest.

Using the properties of ln function.

a \times ln b = ln b^{a}

Therefore, we get

ln x^{2} = ln 2^{4}

ln x^{2} = ln 16

taking antilog on both the sides, we get

x^{2} = 16

So, x = \pm 4

Therefore, the potential solutions to 2 ln x = 4 ln 2 from least to greatest is -4 and 4.

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BLUEPRINTS Abby’s family is building a new house. On the blueprints of the house, Abby’s bedroom measures
mariarad [96]

Answer:

A scale drawing or floor plan is a representation of an actual object or space drawn in two-dimensions. For a floor plan, you can imagine that you are directly above the building looking down. The lines represent the walls of the building, and the space in between the lines represents the floor.

In order to find the actual dimensions from a floor plan, you can set up and solve a proportion. The scale given in the drawing is the first ratio. The unknown length and the scale length is the second ratio.

Let’s look at an example.

The floor plan below shows several classrooms at Craig’s school. The length of Classroom 2 in the floor plan is 2 inches. What is the actual length, in feet, of Classroom 2?

First, set up a proportion. The scale in the drawing says that

12′′=3′

, therefore the proportion is:

0.5 inches3 feet

Next, write the second ratio. You know the scale length is 2 inches. The unknown length is

x

. Make sure that the second ratio follows the form of the first ratio: inches over feet.

0.5 inches3 feet=2 inchesx feetThen, cross-multiply.

0.530.5x0.5x===2x2×36Then, divide both sides by 0.5 to solve for

x

.

0.5x0.5x0.5x===660.512The answer is 12.

The actual length of the classroom is 12 feet.

8 0
3 years ago
What is the median of 76, 84, 93, 67, 82, 87, and 76?
Ahat [919]
The median of a set of numbers is the midpoint of the set if you were to organize the numbers from least to greatest or greatest to least. So, all we have to do is rearrange the numbers from least to greatest and find the midpoint:
67   76   76   82   84   87   93
count 3 in from both sides and the remaining number is 82, which is the median.
8 0
3 years ago
HELP QUICK 30 POINTS!!
vlada-n [284]

Answer:

B

Step-by-step explanation:

For answer A it is stretching the graph of function f by a factor of 15.

For answer C and D it is changing the function itself and that is not what the question is asking.

5 0
3 years ago
Read 2 more answers
PLEASE PLEASE PLEASE HELP ME WITH ALGEBRA 1 PLEASE!?!?!?!?!!!?!?!?!?!?! I WILL GIVE LOTS OF POINTS AND BRAINLEST
Damm [24]

<span>1.1 What are the different ways you can solve a system of linear equations in two variables? 

</span><span>A linear equation can be written in many ways, so the way we can use to solve a system of linear equations depends on the form the system is written. There are several methods to do this, the more common are: Method of Equalization, Substitution Method, Elimination Method. 

<span>1.2. Method of Equalization

</span>a. Write the two equations in the style [variable = other terms] either variable x or y.<span>
</span>b. Equalize the two equations 
c. Solve for the other variable and then for the first variable.

</span>

<span> 1.3. Substitution Method

a. Write one of the equations (the one that looks the simplest equation) in the style [variable = other terms] either variable x or y.
b. Substitute that variable in the other equation and solve using the usual algebra methods.
c. Solve the other equation for the other variable.<span>

1.4. Elimination Method

Eliminate</span> means to remove, so this method works by removing variables until there is just one left. The process is:
<span>
</span>a. Multiply an equation by a constant "a" such that there is a term in one equation like [a*variable] and there is a term in the other equation like [-a*variable]
b. Add (or subtract) an equation on to another equation so the aim is to eliminate the term (a*variable)
c. Solving for one variable and the for the other.
</span>

2.1 Benefits of Method of Equalization<span>
</span>


It's useful for equations that are in the form [variable = other terms] (both equations). In this way, it is fast to solve the system of linear equation by using this method. The limitations come up as neither of the equations are written in that way, so it would be necessary to rewrite the two equations to achieve our goal


2.2. Benefits and limitations of Substitution Method


This method is useful for equations that at least one of them is in the form [variable = other terms]. So unlike the previous method, you only need one equation to be expressed in this way. Hence, it is fast to solve the system of linear equation by using this method. The limitations are the same that happens with the previous method, if neither of the equations is written in that way, we would need to rewrite one equation to achieve our goal.


2.3. Benefits and limitations of Elimination Method


It's useful for equations in which the term [a*variable] appears in one equation and the term [-a*variable] appears in the other one, so adding (or subtracting). 


3.1. What are the different types of solutions


When the number of equations is the same as the number of variables there is likely to be a solution. Not guaranteed, but likely.

One solution: It's also called a consistent system. It happens as each equation gives new information, also called Linear Independence.

An infinite number of solutions: It's also called a consistent system, but happens when the two equations are really the same, also called Linear Dependence.

No solutions: It happens when they are actually parallel lines. 


3.2. Graph of one solution system


See figure 1, so there must be two straight lines with different slopes.


3.3. Graph of infinite number of solutions system


See figure 2. So there must be two straight lines that are really the same.


3.4. Graph of no solution system


See figure 3. So there must be two straight lines that are parallel.


4. Explain how using systems of equations might help you find a better deal on renting a car?


Q. A rental car agency charges $30 per day plus 10 cents per mile to rent a certain car. Another agency charges $20 per day plus 15 cents per mile to rent the same car. If the car is rented for one day in how many miles will the charge from both agencies be equal?

A. Recall: 10 cents = 0.1$, 15 cents = 0.15$

If you rent a car from the first car agency your cost for the rental will be:

(1) 30D+0.1M

<span>If you rent a car from the second car agency the total amount of money to pay is:

(2) 20D+0.15M</span>

Given that the problem says you want to rent the car just for one day, then D = 1, therefore:

First agency: 30(1)+0.1M=&#10;\boxed{30+0.1M}

Second agency: 20(1)+0.15M=&#10;\boxed{20+0.15M}

<span>At some number of miles driven the two costs will be the same:

30+0.1M=20+0.15M

Solving for M:

10=0.05M
M=200mi

There is a representation of this problem in figure 4. Up until you drive 200 miles you would save money by going with the second company.</span>

<span>

5. Describe different situations in the real world that could be modeled and solved by a system of equations in two variables </span>

<span>
</span>

For example, if you want to choose between two phone plans. The plan with the first company costs a certain price per month with calls costing an additional charge in cents per minute. The second company offers another plan at a certain price per month with calls costing an additional charge in cents per minute. So depending on the minutes used you should one or another plan.


3 0
3 years ago
What is the sum of the series? Write in expanded form making sure to show all steps used to find the sum
pantera1 [17]

Answer:

-16

Step-by-step explanation:

k = 3

-2(3) + 5 = -1

k = 4

-2(4) + 5 = -3

k = 5

-2(5) + 5 = -5

k = 6

-2(6) + 5 = -7

(-1) + (-3) + (-5) + (-7)

= -16

3 0
2 years ago
Read 2 more answers
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