Dr. Benton just got his PhD, and he wants to print copies of his thesis in hardcover book format. He could use Middletown Printing, paying a setup fee of $39 and $3 for every book printed. Alternately, he could go through Oxford University, paying an up-front fee of $35 and $5 per book. It turns out that, given the number of books Dr. Benton wants to print, the two options cost the same amount. How many books is that? What is the amount?​

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

First off, let's write the line in point-slope form:

  [tex]\rm \hookrightarrow (y-y_0)=m(x-x_0)[/tex]

Let's calculate the slope:

 [tex]\rm \hookrightarrow Slope = \frac{y_2-y_1}{x_2-x_1}[/tex]

                 [tex]\rm \hookrightarrow slope = \frac{-3--6}{2--2} =\frac{3}{4}[/tex]

Now that we found the slope, let's put it into the point-slope form

  ⇒ we need (x₀, y₀) ⇒ let's use (2,-3)

     [tex](y-(-3))=\frac{3}{4} (x-2)\\y+3=\frac{3}{4} (x-2)[/tex]

The equation, however, could also be put into 'slope-intercept form'

     ⇒ gotten by isolating the 'y' variable to the left

          [tex]y = \frac{3}{4}x-\frac{9}{2}[/tex]  

Answer:[tex]y = \frac{3}{4}x-\frac{9}{2}[/tex] or [tex]y+3=\frac{3}{4} (x-2)[/tex]

   *Either equations work, put the one that you are the most familiar with

Hope that helps!

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Answer:

Step-by-step explanation:

The reflection of the triangle DEFG will be given in the figure.

A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.

Reflection does not change the size and shape of the geometry.

The image of the figure under reflections in line m and then line t.

The reflection of the triangle DEF will be given in the figure.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{What is the formula for finding slope?}[/tex]

[tex]\mathbf{\dfrac{y_2 - y_1}{x_2 - x_1} = slope}[/tex]

[tex]\huge\textbf{Often people understand it better by:}[/tex]

[tex]\mathbf{\dfrac{rise}{run} = slope}[/tex]

[tex]\huge\textbf{Answering the given question:}[/tex]

[tex]\mathbf{y_2 \rightarrow 4}\\\\\mathbf{y_1 \rightarrow 7}\\\\\mathbf{x_2\rightarrow 0}\\\\\mathbf{x_1 \rightarrow -1}[/tex]

[tex]\huge\textbf{Now, that we have that information out}\\\huge\textbf{the way, we can answer the question.}[/tex]

[tex]\huge\textbf{Solving for the answer:}[/tex]

[tex]\mathbf{\dfrac{4 - 7}{0 - (-1)} = slope}[/tex]

[tex]\mathbf{\rightarrow \dfrac{4 - 7}{0 + 1} = slope}[/tex]

[tex]\mathbf{\rightarrow \dfrac{-3}{1} = slope}[/tex]

[tex]\mathbf{-3\div 1 = slope}[/tex]

[tex]\mathbf{\rightarrow -3 = slope}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\textsf{S}\frak{lope \rightarrow -3}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

When two variables are being examined, and one variable moves one way and the other variable moves in the opposite direction, this is called an inverse relation.

Correlation is a statistical degree (expressed as various) that describes the size and path of a courting among or extra variables. A correlation between variables, however, does now not robotically suggest that the trade in a single variable is the purpose of the alternate inside the values of the opposite variable.

A positive correlation is clear while variables move within an equal course. An inverse correlation is clear whilst variables circulate inside the opposite route.

A negative correlation is a relationship among variables that pass in contrary instructions. In other phrases, while variable A increases, variable B decreases. A poor correlation is likewise known as an inverse correlation.

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When two variables are being examined, and one variable moves one way and the other variable moves in the opposite direction, this is called a(n): Inverse Relationship.

Consumption is subject to diminishing marginal utility. -A lower price increases the purchasing power of a buyer's income, enabling a buyer to purchase more of a product.

The law of supply and demand is a keystone of modern economics. According to this theory, the price of goods is inversely related to the quantity offered. This makes sense for many goods, since the more costly it becomes, fewer people will be able to afford them and demand will subsequently drop.

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Answer:

[tex]x= \dfrac{3-2x}{4-3x}[/tex]

Step-by-step explanation:

Given:

[tex]x=\dfrac{1}{2-\dfrac{1}{2-\dfrac{1}{2-x}}}}[/tex]

Simplify:

[tex]\begin{aligned}2-\dfrac{1}{2-x} & =\dfrac{2(2-x)-1}{2-x}\\\\ & =\dfrac{3-2x}{2-x}\end{alilgned}[/tex]

Therefore:

[tex]x=\dfrac{1}{2-\dfrac{1}{\dfrac{3-2x}{2-x}}}[/tex]

Simplify:

[tex]\begin{aligned}2-\dfrac{1}{\dfrac{3-2x}{2-x}} & =2-\dfrac{2-x}{3-2x}\\\\ & =\dfrac{2(3-2x)-(2-x)}{3-2x}\\\\ & = \dfrac{6-4x-2+x}{3-2x}\\\\ & = \dfrac{4-3x}{3-2x}\end{aligned}[/tex]

Therefore:

[tex]x & =\dfrac{1}{\dfrac{4-3x}{3-2x}}[/tex]

[tex]\textsf{Apply the fraction rule}: \quad \dfrac{1}{\frac{b}{c}}=\dfrac{c}{b}[/tex]

[tex]\implies x& = \dfrac{3-2x}{4-3x}[/tex]

Answer:

hope it will help you to

hope it will help you

It would be y = ex - 4

As a suggestion, I would recommend using the desmos calculator online. It's an entirely free graphing calculator and helps with questions like this. I hope that helps!

Answer:

x=5/6 but since you gave options in terms of y: -8y=6

Step-by-step explanation:

When you add equations together to solve for a systems of equations, it because you want to cancel out one of the values, and in this case it's the 6x, since the 6x + (-6x) = 0

Now all you need to do is add the -12 and 4y and you get -8y which is going to be the left side of the equation

Now add the -8 and 14 and you get 6 which is going to be the right side of the equation. This gives you the equation:

-8y = 6

Divide both sides by -8

y =  -0.75

Now plug this into either original equation but in this case I'll just use the -6x+4y=-8

Plug in -0.75 as y

-6x+4(-0.75) = -8

-6x-3=-8

-6x=-5

Divide both sides by -6

x=5/6

The width that must meet a right angle is 14.87 cm

The given parameters are:

The width is calculated using the following Pythagoras theorem.

Width^2 = Diagonal^2 - Length^2

So, we have:

Width^2 = 18.2^2 - 10.5^2

Evaluate

Width^2 = 220.99

Take the square root of both sides

Width = 14.87

Hence, the width that must meet a right angle is 14.87 cm

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The predicted value of Y must be between 0 and 1.

A linear probability model (LPM) is a regression model where the outcome variable is a binary variable, and one or more explanatory variables are used to predict the outcome. Explanatory variables can themselves be binary, or continuous.

Suppose, that the linear probability model yields a predicted value of Y that is equal to 1.3.

This is nonsensical because

The predicted value of Y must be between 0 and 1.

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The value of x will be equal to 6 units.

Trigonometry is the branch of mathematics that set up a relationship between the sides and angle of the right-angle triangles.

Given that:-

Given that the radius of the circle is 9 which is SO= 9 and SG = 9.

Now the value of x will be calculated by using the Pythagorean theorem.

H² = P ² + B ²

OG² = 12² + 9 ²

OG = √225

OG = 15

Since, OG = OH + HG

HG = OG - OH

x  = 15 - 9

x = 6 units

Therefore the value of x will be equal to 6 units.

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9 and -4
7 and -2
5 and 0

Each and every pair has a total of 5.

Answer:

9 and-4

7 and -2

5 and 0

Step-by-step explanation:

When ya subtract 4 from 9 you get 5

the same applies to the rest.

The probability that both of them have landed 5 is 1/7.

Two fair dice have been tossed,

The total of their top faces is found to be divisible by 5,

Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence, which is expressed as a number between 1 and 0.

The probability that both of them have landed 5 is

E={(x,y)|x+y=5 or x+y=10, 1≤x,y≤6},

F={(5,5)}.

P(F|E)= 1/7.

Hence, The probability that both of them have landed 5 is 1/7.

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5400

4500 multiplied by 1.2

Answer:

The original price would be $5,625

Step-by-step explanation:

The formula to finding out the original price is -

OP = SP/1 - P

- OP = Original Price

- SP = Sale Price

- P = Percent Discount

Now just put in the respected values and you'll get -

OP = 4500/1 - 0.20

Now solve :D

OP = 4500/1 - 0.20

= 4500/0.8

= 5625

So the original price is $5,625

Hope this helped! :D

Answer:

x = 77/100

Step-by-step explanation:

When you solve this equation: 1.68+ 12x = 10.92

The answer is x = 77/100

The cost of each bottle of juice will be $0.77.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Adrian brought snacks for his team's practice. He bought a bag of apples for $1.68 and a 12-pack of juice bottles. The total cost before tax was $10.92.

From the given data the expression will be formed as below:-

1.68+ 12x = 10.92

12x = 10.92 - 1.68

12x = 9.24

x =9.24 / 12

x = $0.77

Therefore, the cost of each bottle of juice will be $0.77.

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The correct theorem or definition that justifies the given statement for the diagram is; Definition of a Right angle Triangle

We are given that;

∠MRS ≅ ∠MRO

Now, what that means is that ∠MRS is congruent to ∠MRO. Thus, to understand this concept of equality or congruence, we can prove it since  from the given image, we see that;

m∠MRS = m∠MRO = 90°

Since they are both right angles then we can say that the correct theorem is the definition of a right angle triangle.

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The set of equation that is known to have 5 and 0 as solutions is A and B.

From the graph that we have here in this question, we are supposed to identify the equations that have this point.

We can do this by tracing the lines in order to locate 5 and 0 on the grid.

When we trace the bine that has 5 and 0, We would find out that it is traceable to A and B.

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The area of the wetland that will be covered in purple loosestrife 7 years from now is modeled by this expression 500(1.2)^7

The exponential expression to calculate the area covered by purple loosestrife seven years from now will be:

= 500 × 1.2^7

After evaluating the expression, the model predicts that approximately 1,792 acres of the wetland will be covered in purple loosestrife 7 years from now.

This is not a valid prediction because the total area of the wetland is only 1,240 acres. Therefore, a constraint on the model is that the value of the expression 500(1.2)^t must be less than or equal to 1,240.

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Answer:

[tex] - \frac{2}{3} [/tex]

Step-by-step explanation:

Given (6x18)(3x+2) = 0

[tex]108(3x + 2) = 0 \\ 324x + 216 = 0 \\ 324x = - 216 \\ x = \frac{ - 216}{324} \\ = - \frac{2}{3} [/tex]

Answer:

a = -5/3

Step-by-step explanation:

3/a × -4 = 20

3a × -4/-4 = 20/-4

3a = -5

a = -5/3

Check:

3/(-5/3) × - 4 = 20

-5 × - 4 = 20

Answer:

None of them are correct i believe

Step-by-step explanation:

its sideways lol

Answer:

N=[tex]\sqrt{61}[/tex]

Step-by-step explanation:

We have the first point as (2,4), and the second point as (-3,-2). This means that [tex]x_1=2, y_1=4,x_2=-3,y_2=-2.[/tex] Using the distance formula, we get [tex]\sqrt{(2-(-3))^2+(4-(-2))^2} \\\sqrt{(2+3)^2+(4+2)^2}\\\sqrt{25+36}=\sqrt{61}[/tex]

Answer:

[tex]\sqrt{61}[/tex]

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

this is the anser on e2020

Answer:

Y = 5x + 25

Step-by-step explanation:

$25 is the constant, meaning regardless of the time he spends, he will not pay more or less.

However, he pays 5 dollars for every hours (x) = 5x

The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is (1, 7)

The solution to the linear and quadratic equation is as follows:

For the linear, a solution is 1 and 7.

This is because when x = 1, f(x) = 7

For the quadratic equation, 1 and 7 also works.

2x² + x + 4

2(1)² + 1 + 4

2 + 1 + 4 = 7

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Work Shown:

16% of x = 17

0.16x = 17

x = 17/(0.16)

x = 106.25

The z score for the number 7 is -0.92.

The standard deviation is 4.32

X is the score that is 7 given.

We have to calculate the z score for doing so we need the mean also.

Mean is obtained by dividing the sum of numbers / total frequency.

Mean = Summation of numbers / total numbers

= 5, 7, 9, 11, 13, 15, 17 / 7

= 77/7

= 11

Formula of z-score, Z= x - mean /S.D.

x is the number that is 7.

S D is the standard deviation.

Z= 7-11 / 4.32

= -4/4.32

Z score = -0.92

In data, the standard deviation is a degree of the quantity of version or dispersion of a fixed of values. A low fashionable deviation suggests that the values have a tendency to be near the suggest of the set, while a high widespread deviation shows that the values are spread out over a much broader range.

Standard deviation is vital because it is able to assist users check chance. Bear in mind a funding option with a median annual return of 10% in line with the year. However, this average changed into derived from the past three-year returns of 50%, -15%, and -5%. with the aid of calculating the same old deviation and understanding your low likelihood of really averaging 10% in any single given 12 months, you're better armed to make knowledgeable decisions and apprehend underlying risk.

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In a binomial​ experiment to say that each trial is independent of the other​ trials means that the outcome of one trial does not affect the other trial.

An experiment with a set number of independent trials and just two results is referred to as a binomial experiment.

To say that in a binomial experiment, each trial is independent of the other trials means that the outcome of one trial does not affect the other trials.

This means that whatever we get in the first trial, does not affect the outcome of the second or any other trial.

For example, in the tossing of a coin 10 times, the outcome of the first trial doesn't affect any of the other nine trials.

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