Mathematics College

What is the first step in solving ln(x − 1) = ln6 − lnx for x?

Answers

Answer 1

Answer:

[tex]ln(x - 1) = ln(\frac{6}{x})[/tex]

Step-by-step explanation:

[tex]ln(x - 1) = ln6 - lnx[/tex]

To solve for x we need to simplify the ln

To simplify logarithmic function we use log property

[tex]ln(a) - ln(b) = ln(\frac{a}{b})[/tex]

we apply the same property on the right hand side of the given equation

[tex]ln(x - 1) = ln6 - lnx[/tex]

[tex]ln(6) - ln(x) = ln(\frac{6}{x})[/tex]

[tex]ln(x - 1) = ln(\frac{6}{x})[/tex]

This is the first step in solving the given equation

Related Questions

Which expression is equivalent to 10x^6y^12/-5x^-2y^-6? Assume .x=0.y=0.

Answers

For this case we have the following expression:
 (10x ^ 6y ^ 12) / (- 5x ^ -2y ^ -6)
 Rewriting we have:
 (10 / -5) * ((x ^ 6y ^ 12) / (x ^ -2y ^ -6))
 (-2) * ((x ^ 6y ^ 12) / (x ^ -2y ^ -6))
 Then, for power properties:
 (-2) * (x ^ (6 - (- 2)) and ^ (12 - (- 6)))
 (-2) * (x ^ (6 + 2) and ^ (12 + 6))
 (-2) * ((x ^ 8y ^ 8)
 For x = 0, y = 0, we have:
 (-2) * ((0 ^ 8) (0 ^ 8))
 0
 Answer:
 An expression that is equivalent when x = 0 and y = 0 is:
 0

Answer:B on edge

Step-by-step explanation:

Andrew drove 55 mph on his trip. Which of the following equations best represents the distance he drove if x stands for the number of hours?

Answers

55*x
X= The hours 
I hope this helps!!

Answer

Using speed formula:

[tex]\text{Speed} = \frac{\text{Distance}}{\text{Time}}[/tex]

Let y represents the distance in miles and x represents the time in hours.

As per the given statement:

Andrew drove 55 mph on his trip.

Using formula;

we have;

[tex]55 = \frac{y}{x}[/tex]

Multiply both sides by x we have;

[tex]y = 55x[/tex]

Therefore, the equation best represents the distance he drove is [tex]y = 55x[/tex]

Dynatashia has a list of items she needs to buy at the store. She has written down the items and the advertised prices as shown: Hamburger – $3.99 per pound Hamburger buns – $1.29 2-liter soda – 3 for $2.00 Dynatashia buys 1.5 pounds of hamburger, 1 package of buns and 3 of the 2-liter bottles of soda. Her receipt is shown below. 2-ltr soda 2@3/$2 $1.34 Hambrg 1.5 lb@3.99 $5.99 Hbuns 1@1.69 $1.69 2-ltr soda 1@3/$2 $0.67 Determine if Dynatashia's receipt is correct. a. Yes, Dynatashia's receipt is correct. b. No, Dynatashia paid too much for soda. c. No, Dynatashia paid too much for hamburger. d. No, Dynatashia paid too much for buns.

Answers

Answer:

D. No, Dynatashia paid too much for buns.

Step-by-step explanation:

We are given that,

The actual cost of the items are,

Items                                          Cost

Hamburger                         $3.99 per pound

Buns                                    $1.29 per packet

2-liter soda                          $2 per 3 bottle

As, she bought 1.5 pounds of hamburgers, 1 packet of buns and 3 bottles of 2-liter soda.

So, she has to pay,

For hamburger = 1.5 × 3.99 = $5.99

For buns = 1.29 × 1 = $1.29

For soda bottles = $2

But from the receipt, we see that she pays,

For hamburger = 1.5 × 3.99 = $5.99

For buns = 1.69 × 1 = $1.69

For soda bottles = 1.34 + 0.67 = $2

That is, she has to pay $1.29 for the packet of the buns but she paid $1.69 for the buns.

Hence, the receipt is not correct as Dynatashia paid too much for the buns.

Answer: D

Step-by-step explanation:

edg

What is the mode of these numbers? A 40. B 43. C 26 and 31. D. 31 and 43

Answers

31 and 43. (the mode is the number(s) that occurs the most frequently)

What are the zeros of the polynomial function f(x) = (x – 6)(x – 2)(x + 7)?

Answers

The given polynomial is in factored form. So in order to find the zeros of the polynomial, set each factor equal to zero and find the value of x. All such values of x will be the zeroes of the polynomial.

So,
x - 6 = 0 
⇒ x = 6

x - 2 = 0
⇒ x = 2

x + 7 =0
⇒ x = -7

Thus the zeros of the given function are x = 6, x = 2 and x = -7

Simplify (3x+8)(x+1) using a table, the Distributive Property, and the FOIL
method. Which method is most efficient? Explain.

Answers

Foil method:
FOIL stands for
first-multiply the first term in each set of parenthesis
outer-multiply the outer term in each of the perenthesis
inner- multiply the inner term in each of the parenthesis
last- multiply the last term in each of the parenthesis
(3x+8)(x+1)
(3x*x)=3x^2
(3x*1)=3x
8*x=8x
8*1=8
thus we shall have:
3x^2+3x+8x+8
=3x^2+11x+8

Distributive property:

(3x+8)(x+1)
3x(x+1)+8(x+1)
3x^2+3x+8x+8
=3x^2+11x+8

Both methods are efficient, it all depends with the users preference

Final answer:

To simplify (3x+8)(x+1), we can use the FOIL method, the Distributive Property, or a multiplication table, all leading to the same simplified expression: 3x² + 11x + 8. The FOIL method is typically the most efficient for binomials.

Explanation:

The question asks to simplify the expression (3x+8)(x+1) using a table, the Distributive Property, and the FOIL method and to determine which method is most efficient.

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last and represents a quick way to multiply two binomials:

First: Multiply the first terms in each binomial (3x×x = 3x²).

Outer: Multiply the outer terms (3x×1 = 3x).

Inner: Multiply the inner terms (8×x = 8x).

Last: Multiply the last terms in each binomial (8×1 = 8).

Adding these products together, we get 3x² + 3x + 8x + 8, which simplifies to 3x² + 11x + 8.

Using the Distributive Property

This involves expanding the expression by multiplying each term in the first polynomial by each term in the second: (3x+8)(x) + (3x+8)(1), which also simplifies to 3x² + 11x + 8.

Using a Table

Create a table where you list each term of the first polynomial in the first row and the terms of the second polynomial in the first column, and then fill in the table with the products of the intersecting terms. The sum of these products will also yield 3x² + 11x + 8.

While all three methods will give the correct answer, the FOIL method is generally seen as the most efficient for this particular problem, as it provides a straightforward, step-by-step process that is easy to follow and remember for multiplying two binomials.

Use multiplying by 1 to find an expression equivalent to 3/14 with a denominator of 14 y.

Answers

as a matter of simplification, same/same = 1.

now, "same" could be anything whatsoever, you name it, a whole polynomial, a whole anything whatsoever.

[tex]\bf \cfrac{\sqrt{2}}{\sqrt{2}}=\cfrac{\sqrt{3}}{\sqrt{3}}=\cfrac{100000000}{100000000}=\cfrac{eggs}{eggs}=\cfrac{miles}{miles}=\cfrac{\frac{\quad \sqrt{3}}{\sqrt[5]{17}}\quad }{\frac{\sqrt{3}}{\sqrt[5]{17}}}=\cfrac{whatever}{whatever}=1[/tex]

now, that said, let us use 1 in this case then ... hmmmm we simply need a "y" in the denominator, so we simply multiply the denominator AND numerator by "y", y/y  = 1 btw.

[tex]\bf \cfrac{3}{14}\cdot \cfrac{y}{y}\implies \cfrac{3y}{14y}[/tex]

Lupe has 14 stickers that she wants to give to 2 friends. She wants each friend to have the same number of stickers. Select the three statements that describe how Lupe should give the stickers to her friends. Each friend gets 14÷2 stickers. Each friend gets 2 of the 14 stickers. Each friend gets 142 stickers. Each friend gets 7 of the 14 stickers.

Answers

Each friend gets 7 of the 14 stickers. They will get 7 because their are 2 Friends and she has 14 stickers to make sure they get an even amount you can dived 14 by 2 and you will get your answer

Answer:

The correct options are 1, 3 and 4.

Step-by-step explanation:

It is given that Lupe has 14 stickers that she wants to give to 2 friends.

Total number of stickers Lupe has is 14.

The number of friends is 2.

She wants each friend to have the same number of stickers. It means each friend will get half of 14.

The number stickers Lupe should give to her friends is 14 divided by 2.

[tex]\text{Number of stickers}=14\div 2[/tex]

Write this value in fraction form.

[tex]\text{Number of stickers}=\frac{14}{2}[/tex]

[tex]\text{Number of stickers}=7[/tex]

It means the correct statements are

1. Each friend gets 14÷2 stickers.

3. Each friend gets (14)/2 stickers.

4. Each friend gets 7 of the 14 stickers.

Hence correct options are 1, 3 and 4.

Centennial park is evaluating the capacity of the park and have determined that 15 people can comfortably stand in a section that is 5ft by 8ft , the park has dimensions that are 400yds by 200 yds estimate the number of people who can fit in the park

Answers

If you multiply all those numbers you will get 5.76e9 yds

We have been given that 15 people can comfortably stand in a section that is 5ft by 8ft .

Hence, the area of this section is given by

[tex]A=5\times 8\\ A=40 ft^2[/tex]

Hence, we can say that 15 people can comfortably stand in an area 40 square feet.

Now, we know that 1 yard is equal to 3 feet.

Hence, the area of the section 400yds by 200 yds is equal to

[tex]400\times 3 \times 200 \times 3\\ =720000 ft^2[/tex]

Now, in 40ft^2, 15 people can stand comfortably.

Hence, in 720000 ft^2, number of people can stand comfortably is

[tex]\frac{15}{40} \times 720000\\ \\ =270000[/tex]

Therefore, 270000 people can stand in the park of dimension 400 yds by 200 yds

how many ounces of 30% hydrochloric acid solution and 80% hydrochloric acid solution must be mixed to get 10 oz of 50% hydrochloric acid solution

Answers

I like to use a little X diagram to work mixture problems. The constituents are listed on the left, the mix value in the middle, and the differences are listed on the right along the lines of the X.

This diagram tells you the constituents 80% and 30% solution are in the proportion 20:30 or 2:3 or 4:6 to make the mix having 50% hydrochloric acid. Note that the numbers 4 and 6 add to 10, the number of ounces of solution we want.

4 ounces of 80% solution must be mixed with 6 ounces of 30% solution to make 10 ounces of 50% solution.

-5n+22>=-73
[tex] - 5n + 22 \geqslant - 73 = [/tex]

Answers

First, subtract both sides by 22
(note: I know it's greater than or equal to, but I'm just going to use > for the sake of time)
-9n > -95
Divide both sides by -9 (This will flip the sign):
n < -95/9
n [tex] \leq [/tex] -10 5/9
(I'm not sure if you wanted a mixed fraction or not, so...)

What is the surface area of a cylinder with a radius of 5 ft and a height of 2 ft?

Answers

[tex]\bf \textit{total surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\ -----\\ r=5\\ h=2 \end{cases}\implies SA=2\pi (5)(2+5) \\\\\\ SA=10\pi (7)\implies SA=70\pi [/tex]

Answer:

Its B.

Have a great day! OwO

The rate of the number of bags mishandled by the airlines fell to 4.77 bags per 1000 passengers in 2011. At this​ rate,
estimate how many bags would be mishandled for 1650 passengers.

Answers

7.8705 bags, 4.77 divided by 1000 is 0.00477 per passenger, so multiplied by 1650 is 7.8705 per every 1650 passengers. Is this really college mathematics?!?!

plz help me
it sounds confusing

Answers

Given that m = -3,

[tex]2700 \times 3^m = 2700 \times 3^{-3}= \dfrac{2700}{3^3} = \dfrac{2700}{27} = 100[/tex]
2,700 × 3^m

m = -3

3^-3 = 1/27

1/27 × 2,700 = 2,700/27

2,700/27 simplified = 100

Answer = 100

Hope this helped☺☺

Josh is hiking Glacier National Park. He has now hiked a total of 1 7 km 17 km17, space, k, m and is 2 km 2 km2, space, k, m short of being 1 2 2 1 ​ start fraction, 1, divided by, 2, end fraction of the way done with his hike. Write an equation to determine the total length in kilometers ( h ) (h)left parenthesis, h, right parenthesis of Josh's hike.

Answers

17 + 2 = 19 km is 1/2 of the total length, that is, 

19 = (1/2)h

(1/2)h = 19 multiply both sides by 2

h = 2*19

h = 38 km

The total length in kilometers is 38 km.

hello can you please help me posted picture of question

Answers

The answer is C. (-2,-7)

you just have to find the solution to Y.
Vertex of a parabola exists at:

[tex]( \frac{-b}{2a},y( \frac{-b}{2a})) [/tex]

b = coefficient of x term = 8
a = coefficient of squared term = 2

So,

[tex] \frac{-b}{2a}= \frac{-8}{4}=-2 [/tex]

and

[tex]y(-2)=2(-2)^{2}+8(-2)+1=-7 [/tex]

Therefore, the vertex occurs at (-2, -7)

So, the correct answer is option C

Mrs. Daly's reading classes were surveyed about their reading preferences. the data is summarized in the table below.



given that a student is in 9th grade, what is the probability that they like to read non-fiction novels, based on this data?

Answers

0.60...don't know how I got this but it's right trust me

Answer:

0.60

Step-by-step explanation:

A cat and a dog have a race. The cat’s strides are 30% shorter than the dog’s but it makes 30% more strides than the dog. Which of them will win the race?

Answers

The cat travels 0.7 times as far as the dog on each stride, but it takes 1.3 times as many strides in a given time interval. Hence the cat's distance relative to the dog's is 0.7*1.3 = 0.91. This is less distance than the 1 unit the dog covers in the same time.

The dog will win the race.

the answer would be 90% because when you multiply 30% x 30% =90% its the same as 3 x 3 = 9

I WILL MARK BRAINLIEST PLEASE HURRY

Answers

Consider, pls, this explanation + solution:
according to the given equation the centre of this circle is in the poit (6;7) and its radius =4 units.
Using this data, it is possible to define right choice: D.

answer: graph D.

Explain why the equation (x-4)^2-10=15 has two solutions. Then solve the equation to find the solutions.
Please show all your work! (30 points)

Answers

Hello there,
Let's solve it first so that we can understand whats going on in the equation

(x-4)²-10=15
add 10 to both sides
(x-4)²=25
square root both sides

(Okay, so here is where the problem can have 2 solutions. Because the square root of 25 could be (5*5) or it could be (-5*-5). If it's positive five then...

x-4=5
add 4 to both sides
x=9

if it's negative 5 then...

x-4=-5
add 4 to both sides
x=-1

So the answer could be x=-1 or x=9.

It has two solutions because there are two possibilities for the answer to the square root of 25.

I hope this help, and if you have any more questions, please feel free to ask me.
Have a nice day!

pleae help thanks a bunch

Answers

Hello!

You use the Pythagorean theorem to solve this

[tex] a^{2} + b^{2} = c^{2} [/tex]

Put in the values it tells you to

[tex]a^{2} + 4.4^{2} = 5.5^{2} [/tex]

Square the numbers

[tex]a^{2} + 19.36 = 30.25[/tex]

Subtract 19.36 from both sides

[tex] a^{2} = 10.89[/tex]

Take the square root of both sides

a = 3.3

The answer is 3.3

Hope this helps!

After being rearranged and simplified, which two of the following equations could be solved using the quadratic formula?

Answers

Polynomial equations that can be solved with the quadratic formula have the following properties, assuming all like terms have been simplified.
1. degree = 2 (i.e. the highest power equals exactly two)
2. the linear term (e.g. 4x, or -5x...) and constant term (e.g. 5, -30, pi, etc.) may or may not be present.

Now let's simplify and examine the given equations, and see if each can be solved with the quadratic formula:
A.
[tex]5x^3+2x-4=2x^2[/tex]
[tex]5x^3+-2x^2+2x-4=0[/tex]
The degree (highest power) is three, so it is not "exactly two". NO.

B.
[tex]5x^2-3x+10=2x^2+21[/tex]
[tex]3x^2-3x-11=0[/tex]
The degree (highest power) is two, so it is "exactly two". YES.

C.
[tex]5x^2-3x+10=5x^2[/tex]
[tex]0x^2-3x+10=0[/tex]
[tex]-3x+10=0[/tex]
The degree (highest power) is one, so it is not "exactly two". NO.

D.
[tex]x^2-6x-7=2[/tex]
[tex]x^2-6x-9=0[/tex]
The degree (highest power) is two, so it is "exactly two". YES.

Note that it is very important to simplify the equations before checking the degree.

If you need further explanations, please feel free to post in comments.

Answer:

The Answer will Be B and D

Step-by-step explanation:

5,895÷36
show all your work

Answers

5895/36 = 163 3/4 = 163.75

____
The calculator is certainly faster.

hey can you please help me posted picture of question

Answers

To solve the problem shown in the figure above you must keep on mind the following information:

 1. The figure shows a parabola whose vertex is (0,0).

 2. The x² indicates that the red parabola shown in the figure is vertical 

 3. and the sign - indicates that the red parabola opens down.

 Therefore, you can conclude that the red parabola has the equation f(x)=-x²

 So, the answer is B.
If we observe the graph of F(x) and G(x), F(x) can be obtained by shifting the graph of G(x) 4 units down.

Shifting 4 units down means subtracting 4 from the function value.

So, G(x) = 4 - x²

Thus,

F(x) =  G(x) - 4 
F(x) = 4 - x² - 4 = - x²

Therefore, the correct answer is option B

how many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of 30% alcohol solution

Answers

The problem asks you to find how many gallons of 20% solution and 50% solution, respectively, are needed to create a 12 gallon solution that is 30% alcohol.

 

To solve this, set up the following equation using the given values: that you have some quantity of a 20% solution, a quantity of a 50% solution, and that you need to have 12 gallons of a 30% solution. We will use a variable, x, together with the "goal" quantity of 12 gallons to solve this problem with only one unknown, even though we really have two unknowns (the quantity of 20% solution and that of the 50% solution).

 

Remember that when writing out percentages, a 20% solution is also a 0.2 solution, and a 50% solution is a 0.5 solution.

 

Let x = an unknown quantity of the 20% (or 0.2) solution. We therefore have 0.2x, since we have x gallons of the 20% solution. (Remember that "of" is a key word that denotes multiplication).

Therefore, 12 - x is the other unknown and is multiplied by the 0.5 (50%) solution, since we have this quantity of the 50% solution. Really, we could say that we have 0.5y (if we want to introduce another variable; however, it is much simpler to put the other quantity in terms of x, which is easy to do, since we know that the two unknown quantities must amount to 12 gallons). Now, we must multiply our second unknown, 12 - x, by 0.5. This gives us 0.5(12 - x). 

 

Our two unknown quantities, 0.2x and 0.5(12 - x) add up to 12 gallons of a 30% solution. Putting all the words together to form an equation we get:

0.2x + 0.5(12 - x) = 0.3(12)

 

Now we expand the equation (call it distributing out the parentheses).

0.2x + 6 + 0.5x = 3.6

 

Combine like terms:

-0.3x + 6 = 3.6

 

Solve for x:

-0.3x = -2.4

x = 8

 

Plug x = 8 back into the equation to check that this is possible. 

x = 8, and 12 - x = 4

0.2(8) + 0.5(12 - (8)) = 0.3(12)

0.2(8) + 0.5(4) = 0.3(12)

3.6 = 3.6 

Check

Final answer:

To create 9 gallons of a 30% alcohol solution, mix 6 gallons of the 20% alcohol solution with 3 gallons of the 50% alcohol solution by setting up and solving a system of equations based on volumes and concentrations.

Explanation:

To find out how many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of a 30% alcohol solution, we can set up a system of equations based on the volumes and concentrations of the solutions. Let's let x represent the volume of the 20% solution and y represent the volume of the 50% solution.

Since the total volume of the mixture should be 9 gallons, we have our first equation:

x + y = 9

Next, we consider the concentration of alcohol in the final mixture. The amount of pure alcohol from the 20% solution is 0.20x gallons, and from the 50% solution, it is 0.50y gallons. The final mixture has a concentration of 30%, so the total amount of alcohol in the 9 gallons mixture is 0.30 * 9 gallons. This gives us our second equation:

0.20x + 0.50y = 0.30 * 9

Now we have a system of two equations with two variables that can be solved using methods such as substitution or elimination. After solving, we find that x = 6 gallons and y = 3 gallons. Therefore, to obtain 9 gallons of a 30% alcohol solution, you'd need to mix 6 gallons of the 20% alcohol solution with 3 gallons of the 50% alcohol solution.

If a+5=b, then what is the value of (b−a)^4?

Answers

Because b=a+5, we can substitute “a+5” in for “b” in the equation.

(b-a)^4
((a+5)-a)^4

Simplification, as follows:

((a+5)-a)^4
(5)^4 the a’s cancel
625

The value of (b-a)^4 when a+5=b is 625.

PLZ HURRY!!
If a Professional basketball player earns $3 million playing 125 games per year and plays an average of 40 minutes per game, how much does he earn per second of playing time?

Answers

3,000,000/125= 24,000 per game
24,000/40= 600 per minute
600/60= 10 per second
$10 per second.

Which type of triangle is formed by joining the vertices A(-3, 6), B(2, 1), and C(9, 5)?

Answers

We can determine the type of triangle from the length of the sides. The length of the sides can be found using the distance formula.

[tex]AB= \sqrt{ (2+3)^{2} + (1-6)^{2} } =5 \sqrt{2} \\ \\ BC= \sqrt{ (9-2)^{2} + (5-1)^{2} } =\sqrt{65} \\ \\ CA = \sqrt{ (-3-9)^{2} + (6-5)^{2} } = \sqrt{145} \\ \\ [/tex]

None of the side lengths are equal, so the triangle formed by the given vertices is a Scalene Triangle. Moreover, the Pythagorean theorem is also not satisfied with given side lengths, so the triangle is NOT a Right Angled Triangle.

A bookstore costs $90 a day to keep open, and spends $12 for each book it sells. the store charges $18 for each book it sells. If n represents the number of books sold, which equation represents the revenue function for this bookstore?

Answers

Total Cost in a day is [tex]TC= 90 + 12n[/tex]. Profit function is [tex]P=18n[/tex]. And the revenue function is [tex]R = P-TC = 18n-12n-90 = 6n-90[/tex]. In a day, bookstore must sell at least 15 books, because of 6n-90=0, in order to make profit. 

Answer:

[tex]R=6n-90[/tex]

Step-by-step explanation:

Let

R------> the revenue function

n------> the number of books sold per day

we know that

In this problem

[tex]18n[/tex] -----> represent the profit

[tex](12n+90)[/tex] -----> represent the cost

so

The revenue is equal to the profit minus the cost

[tex]R=18n-(12n+90)[/tex]

[tex]R=n(18-12)-90[/tex] ------> equation that represent the revenue function

Simplify

[tex]R=6n-90[/tex]

A suit regularly costs $389.90., Bob buys it on sale for $ 265.00 . How much does he save?

Answers

He saves $124.90 because $389.90 - $265.00 = 124.90 and so that is the difference in the prices which is the answer. 
he saves $124.90 <<<<<<<<<<<<<<
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Write a point-slope equation for the line that has slope 4 and passes through the point (11,7). Do not use parentheses on the y side. Data Set 1 has a mean of 84 and a MAD of 6. Data Set 2 has a mean of 78 and a MAD of 8. What can be concluded about the two distributions? Select each correct answer.A. The distributions are somewhat similar.B. The means-to-MAD ratio is 1.C. The means-to-MAD ratio is 0.75.D. The distributions are similar. The half-life of cobalt-60 is 5.20 yr. how many milligrams of a 2.000-mg sample remains after 6.55 years? participants in one experiment were either frustrated or not frustrated. they then were given what they thought was an opportunity to administer electric shocks to either the person who had frustrated them or a stranger. this experiment was designed to test which part of the frustrationaggression hypothesis? What is the product of the two solutions from the quadratic formula? Which statement about the free enterprise system is true? It allows the citizen to own government property. It exempts the citizen from taxes if that person serves the government. It allows the citizen to share political power with the rest of the population. It allows the citizen to own and operate a private business for profit. It allows the citizen to be part of a one-class system under state control. Which of the following equations will produce the graph shown below? Being a living example of a tobacco-free lifestyle can __________.a. prevent others from trying smokingb. convince friends to stop smokingc. make others around you more healthyd. all of the above please select the best answer from the choices provided. a b c d You have two exponential functions. One function has the formula g(x) = 5 x . The other function has the formula h(x) = 5-x . Which option below gives formula for k(x) = (g - h)(x)?k(x) = 10xk(x) = 5x + 5-xk(x) = 5x - 5-xk(x) = 2(5x) What is the name of the opinion that becomes the official ruling of the Court? A rectangular field is four times as long as it is wide. if the perimeter of the field is 340 yards, what are the field's dimensions In 1492, Portuguese explorers believed they could get to Asia more quickly by Of all rectangles with area 9 which one has the minimum perimeter Jolene frequently gets into fights at school. when asked about her behavior, she says that she just can't help but fight. according to the psychoanalytic theory, jolene likely is being influenced by _____ the atomic mass is important because?a. it tells you the size of the atom b.it tells you the number of electrons Construct the described data set. the entries in the data set cannot all be the same. the median and the mode are the same. what is the definition of median? What is the difference between the most expensive item and least expensive item on the menu, including 6% tax and 15% tip, to the nearest cent? Imported Asset Question options:$4.23$4.36$5.45$5.49You have a $20 bill. You and your friend ordered two roast beef wraps, one soup, one fries, and two coffees. If the tax is 5% and the tip is 15%, what change did you receive back from the $20? Imported Asset Question options:$5.45$1.45$3.38$2.54 1990s alternative rock was known for a particular kind of sound in its guitars, drums and vocals, but a few of the bands diverted from the norm through elaborate arrangements and experiments in the recording studio. among the most well known for this practice is songwriter/vocalists: What are the next three terms in the sequence? -6,5,16,27, ... A.38, 49, 60B.37, 47, 57C.36, 45, 54D.36, 46, 56 A client comes to the emergency department reporting symptoms of the flu. when the health history reveals intravenous drug use and multiple sexual partners, acute retroviral syndrome is suspected. a test for the human immunodeficiency virus (hiv) is performed and acute retroviral syndrome is diagnosed. which clinical responses are associated most commonly with this syndrome