I need to graph y=8x but i dont know how ToT
Answers
Answer:
Search up Demos Graphing Calculator and plug in y=8x like the picture below
Step-by-step explanation:
Hope this helps!
Also Yesssss Deku
Answer:
Check the attachment. (0,0) (8,1)
Step-by-step explanation:
So the formula to solve a line is y=mx+b.
M is the slope and B is the y intercept.
You want to solve for the y intercept first. Since there is nothing after 8x this line has an intercept of 0.
After that you want to solve for the slope which is 8 and it can be rewritten as \(\frac{8}{1}\). Now always remember that for slope it's \(\frac{rise(y)}{run(x)}\)
All you have to do now is plot your points
(0,0) - The intercept
(1,8) - You can find using the slope value.
(Sorry I didn't do a great job explaining it. I hope this helped a bit though)
Related Questions
5
4
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Mark this and return
N
-5-4-3-2-1₁.
24
1+
GAW N
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-3
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1 2 3 4 5 x
What is the range of the function on the graph?
O all the real numbers
O
all the real numbers greater than or equal to 0
all the real numbers greater than or equal to 2
O all the real numbers greater than or equal to -3
Save and Frit
Answers
The range of the function on the graph would be: D. all real numbers greater than or equal to 2
How to calculate the function rangeTo obtain the range, observe the y values whose result can be obtained by the function of x. To obtain this range, we examine the graph and note that the range begins from 2 on the y-axis and extends upwards.
So, if we wish to define our range, we will enter all real numbers that are equal to or greater than 2 as seen in the direction of the graph.
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what is 7 5/6 as im improper fraction?
Answers
7*6/6+5/6
7*6*5/6
Answer:
=47/6
In what quadrant is cosine negative and cotangent negative?
Answers
Answer:
Step-by-step explanation:
cosine is negative in 2nd and 3rd quadrant.
cotangent is negative in 2nd and 4th quadrant.
In the second quadrant, both cosine and cotangent are negative.
What are the signs of each trig function in four quadrants?In the first quadrant all trig functions are positive, In the second quadrant sine and sec are positive in the third quadrant tan and cot are positive, and in the fourth quadrant cos and cosec are positive.
We know there are four quadrants in an XY plane.
We also know that sine is positive on 1st and second quadrants and cosine is positive on the first and fourth quadrants.
tan = (sin/cos).
So, cot = 1/tan = cos/sing.
∴ cotangent is negative if any one of sine and cosine is negative which is in the second and fourth quadrants because in the third quadrant both sine and cosine are negative making cotangent positive.
∴ In the second quadrant cosine and cotangent, both are negative.
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\(\begin{equation}\text { Question: If } \ln (x+y)=4 \times y \text {. Find } \frac{d^{2} y}{d x^{2}} \text { at } x=0 \text {. }\end{equation}\)
Answers
I think you meant to say
\(\ln(x+y) = 4xy\)
and not "4 times y" on the right side (which would lead to a complex value for y when x = 0). Note that when x = 0, the equation reduces to ln(y) = 0, so that y = 1.
Implicitly differentiating both sides with respect to x, taking y = y(x), and solving for dy/dx gives
\(\dfrac{1+\frac{dy}{dx}}{x+y} = 4y + 4x\dfrac{dy}{dx}\)
\(\implies \dfrac{dy}{dx} = \dfrac{4xy+4y^2-1}{1-4x^2-4xy}\)
Note that when x = 0 and y = 1, we have dy/dx = 3.
Differentiate both sides again with respect to x :
\(\dfrac{d^2y}{dx^2} = \dfrac{(1-4x^2-4xy)\left(4y+4x\frac{dy}{dx}+8y\frac{dy}{dx}\right)-(4xy+4y^2-1)\left(-8x-4y-4x\frac{dy}{dx}\right)}{(1-4x^2-4xy)^2}\)
No need to simplify; just plug in x = 0, y = 1, and dy/dx = 3 to get
\(\dfrac{d^2y}{dx^2} \bigg|_{x=0} = \boxed{40}\)
) DeShawn invests $3,044 in a retirement account with a fixed annual interest rate of 3.14% compounded 3 times per year. How long will it take for the account balance to reach $5,341.12?
Answers
Consider the formula,
\(A=P(1+\frac{r}{100})^n\)Here, P is the principal, r is the rate of interest, n is the number of periods, and A is the amount.
According to the problem, the compund interest is to be applied quarterly i.e 3 times per year, so the rate of interest is calculated as,
\(r=\frac{R}{3}=\frac{3.14}{3}=\frac{157}{150}\)Substitute the values and solve for 'n',
\(\begin{gathered} 5341.12=3044(1+\frac{157}{150\times100})^n \\ (1.0105)^n=1.755 \end{gathered}\)Consider the formula,
\(\ln (e^x)=e^{\ln x}=x\)Then the equation becomes,
\(\begin{gathered} \ln (1.0105)^n=\ln (1.755) \\ n\ln (1.0105)=\ln (1.755) \\ n=\frac{\ln (1.755)}{\ln (1.0105)} \\ n=53.85 \\ n\approx54 \end{gathered}\)Thus, the required number of periods in 54.
The corresponding number of years will be 54 by 3 i.e. 18, since the compounding is done 3 time
What is the slope of the line represented by the given table?
X -14 0 7 14 21
y -6 2 6 10 14
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HELP! the student council at woodlands middle school is planning a field trip. they polled randomly selected teachers and students and asked what they want to eat for lunch. the results are shown in the tables below. which of the following statements are true?
Answers
Answer:
c
Step-by-step explanation:
because on the chart is says 19% under burgers for teachers.
Tell me if it is right.
HELP PLEASE ASAP. NO LINKS OR I WILL REPORT
Answers
Answer:
For Question 19 the answer is A (the first answer)
For question 34 the answer is C (the third one) but for that I am not 100% you can search that one up
For question 20 the answer is A (the first answer)
Find the compound interest of N5000 for 2 years at 5% per annum
Answers
For finding the compound Interest first we need to get the amount and then subtract the value of principal from amount
Calculation Begins
Principal = 5000, Rate of Interest = 5%, Time = 2 yrs
\( \looparrowright \sf{A = P(1 + \frac{r}{100} )^{n} } \\ \\ \looparrowright \frak{ {\sf A} = 5000(1 + \frac{5}{100} )^{2} } \\ \\ \looparrowright \frak{ {\sf A} = 5000(1 + \frac{1}{20} )^{2} } \\ \\ \looparrowright \frak{ {\sf A} = 5000( \frac{21}{20})^{2} } \\ \\ \looparrowright \frak{ {\sf A} =5000 \times \frac{441}{400}} \\ \\ \looparrowright \frak{ {\sf A} = 12.5 \times 441} \\ \\\looparrowright \frak{ {\sf A} = 5152.5} \)
Hence the amount is 5152.5
Compound Interest = Amount - Principal
= 5152.5 - 5000 = 152.5
152.5 is the Compound InterestA veterinarian visits an aninal shelter with 147 dogs. 42 are randomly selected for a study. Of tjose selected 14 have a disease. What is the best estimate for the number of dogs that suffer from tge disease? 49, 41,52 or 38?
Answers
Answer:
The answer is 49
Step-by-step explanation:
We can use proportions to estimate the number of dogs in the entire population that have the disease, based on the sample of dogs with the disease.
We know that 42 dogs were selected for the study, and 14 of them had the disease. This means that the proportion of dogs in the sample with the disease is:
14/42 = 0.3333
We can use this proportion to estimate the number of dogs in the entire population that have the disease, by multiplying it by the total number of dogs:
0.3333 * 147 = 49
Therefore, the best estimate for the number of dogs that suffer from the disease is 49.
A sine function has the following key features:
Period =12
Amplitude=4
Midline:y=1
y-intercept: (0, 1)
The function is not a reflection of its parent function over the x-axis.
Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the grapn closest to the first point.
Please show me on a graph how to do this.
Answers
Compared with the parent function y= sin(x), the graph of 4 sin[ (π/6)x ] + 1 will be stretched vertically by a scale factor of 4, translated 1 unit up, and with a shorter distance between the peaks.
What is a function?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between varied quantities and other variables.
Here, we have
1) The parent function is sin(x)
2) sin(x) has:
Middle line: y = 0
Amplitude: 1 because the function goes from 1 unit up to 1 unit down the middle line.
Period: 2π because the sine function repeats every 2π unit.
y-intercept: (0,0) because sin(0) = 0.
Now look at how these changes in the function reflect on the parameters:
A sin (ωx + B) + C:
That function will have:
amplitude A, because the amplitude is scaled by that factor
Period: 2π / ω, because the function is compressed horizontally by that factor.
It will be translated B units to the left
It will be translated C units up.
And you need
Period = 12 => 2π / ω = 12 => ω = π/6
A = 4
Translate the midline from y = 0 to y = 1 => shift the function 1 unit up => C = 1.
Translate the y-intercept from y = 0 to y = 1, which is already accomplished when you translate the function 1 unit up.
So, this is the function searched
y = A sin (ωx + B) + C = 4 sin[ (π/6)x ] + 1
Now you can check the amplitude, the period, the middle line, and the y-intercept of that y = 4 sin[ (π/6)x ] + 1.
Hence, compared with the parent function y= sin(x), the graph of 4 sin[ (π/6)x ] + 1 will be stretched vertically by a scale factor of 4, translated 1 unit up, and with a shorter distance between the peaks.
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Determine if the equation given in slope-intercept form represents the graph. If the equation is correct support your reasoning with why it is correct. If the equation is incorrect, give the correct slope-intercept form equation explaining how you determined it.
Answers
The equation of the line would be y = (4/5)x + 4 which in slope-intercept form represents the graph.
The graph is given in the question.
As per the given line, we take two points (0, 4) and (5, 8)
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = 0, y₁ = 4
x₂ = 5, y₂ = 8
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 4 = (8 - 4)/(5-0 )[x -0]
⇒ y - 4 = (4/5)x
⇒ y = (4/5)x + 4
The given equation of the line y = 4x + 5 is incorrect because its slope is not correct.
So, the equation of the line would be y = (4/5)x + 4.
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The table below shows the scores of a group of students on a 10-point quiz.Test ScoreFrequency31425460728391102The mean score on this test is: The median score on this test is:
Answers
Answer:
The mean: 6.53
The median: 7
Explanation:
To find the mean we average over all the test scores.
The average is defined as
Sum of all data points / total number of data points.
In our case, the data points are the scores.
From the frequency table, we first multiply each score by its frequency. Next, we sum all the numbers in the frequency column. Doing this we get
\(3\times1+4\times2+5\times4+6\times0+7\times2+8\times3+9\times1+10\times2=98\)Next, we sum all the numbers under the frequency table.
\(1+2+4+0+2+3+1+2=15\)Therefore, the average is (rounded to the nearest hundredth)
\(\frac{98}{15}=6.53\)Next, we find the median.
To find the median, we arrange the numbers from least to greatest with their frequencies.
\(3,4,4,5,5,5,5,7,7,8,8,8,9,10,10\)The median is the middle number. In this case, the 8th number to the left is the median of the data set.
Hence, the median of the data set is 7.
To summerise:
The mean: 6.53
The median: 7
Using the logarithm, solve the following equation for x.
6400 = (8) (2^4x)
Answers
Answer:
x = 2.411
Step-by-step explanation:
6400 = (8) (2^(4x))
Divide both sides by 8 to get;
6400/8 = (2^(4x))
800 = (2^(4x))
Using logarithms, we can solve as;
Log 800 = 4xLog 2
4x = Log800/Log2
4x = 2.9031/0.3010
4x = 9.6449
x = 9.6449/4
x ≈ 2.411
The perimeter of a triangle is 42 cm. If two of its sides are 16 cm
and 12 cm. Find its third side
Answers
Answer:
14cm
Step-by-step explanation:
To find the third side of a triangle when given the perimeter and the length of two of its sides, you can use the following formula:
Perimeter = side1 + side2 + side3
Given the perimeter of 42cm and two sides 16cm and 12cm
We can find the third side by subtracting the known sides from the perimeter:
side3 = Perimeter - side1 - side2
so,
side3 = 42 - 16 - 12 = 14cm
Therefore, the third side of the triangle is 14cm.
Step-by-step explanation:
you really need help with that ?
the perimeter means the way of 1 time around the whole shape.
in case of a triangle : going along all 3 sides. in other words - the sum of all 3 sides.
42 = 16 + 12 + third side
third side = 42 - 16 - 12 = 14 cm
Please help worth 10 points
Answers
Answer:
2.5%
Step-by-step explanation:
ahhh has to be 20 characters
I would say 50 percent
7 1/8 - 3 5/8 plz help me on this math
Answers
Answer:
7/2 or 3 1/2
Step-by-step explanation:
Question 2
No calculations are necessary to answer this question.
3/01
3/02
$1.7420 $1.7360
Date
July GBP Futures
Contract Price
O long; long
Based on the closing prices of July GBP Futures Contract over the 3-day period in March 20XX as shown above, you shou
position on 3/01 and a position on 3/02.
O long; short
O short; short
3/03
short; long
$1.7390
Answers
The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.
Quinn tried to solve an equation. 4 3 = q + 1 3 4 3 − 1 3 = q + 1 3 − 1 3 Setting up 2 3 = q Calculating 3 4 3 4 − 3 1 3 2 =q+ 3 1 =q+ 3 1 − 3 1 =q Setting up Calculating Where did Quinn make their first mistake?
Answers
One mistake Quinn made was in setting up the equation.
What is equation?An equation is a mathematical statement that expresses the relationship between two or more quantities, using symbols such as +, -, =, and so on. It can be used to solve problems involving unknowns, such as the number of solutions to an equation or the value of a certain variable. In addition, equations can help to predict future outcomes based on current data.
Quinn set up the equation incorrectly by subtracting 3/2 from both sides instead of subtracting 3/1 from both sides. This caused the equation to become unbalanced, resulting in an incorrect solution. To solve the equation correctly, Quinn should have subtracted 3/1 from both sides to get the correct equation: 2/3 = q.
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she made the mistake of calculating
Step-by-step explanation:
Find the missing dimension for the triangle given the area and one other
dimension.
A =97.5 sq. ft, h = 13 ft, b =?
Answers
Can someone help me please?
Answers
Answer:
64/100 or 0.64 :)
Step-by-step explanation:
It seems that the square has 100 small squares in total. Out of those small squares, 64 are green.
64/100 = 0.64
I need help with this question
Answers
Using word problems and equations, Sarah worked for 10 hours and Penelope worked for 5 hours
What is the number of hours Sarah and Penelope worked?This is a word problem and in order to solve this, we need to translate mathematical statements in form of word problems into mathematical equations.
Let's assume that Sarah worked x hours.
Given that Sarah can iron 30 shirts per hour, the total number of shirts she ironed is 30x.
Since Penelope worked half the hours of Sarah, Penelope worked x/2 hours.
Given that Penelope can iron 35 shirts per hour, the total number of shirts she ironed is 35 * (x/2) = (35/2)x.
The total number of shirts ironed by both Sarah and Penelope is 475 shirts.
So, we can write the equation: 30x + (35/2)x = 475.
To solve this equation, we can simplify it: (60/2)x + (35/2)x = 475, which becomes (95/2)x = 475.
Now, we can solve for x: x = (475 * 2) / 95 = 10.
Therefore, Sarah worked 10 hours and Penelope worked half of that, which is 5 hours.
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find the distance between (-6,0) and (-9,-4)
Answers
Answer:
5 units
Step-by-step explanation:
d=
\( \sqrt{(x2 - x1}^{2} ) + \sqrt{(y2 - y1) {}^{2} } \)
Sally bought 1.4 kilograms of bananas for AED 7.35 $ a kilo. How many kilograms
of apples sold at 10.20 $ per kilogram should you buy so that the kilogram of fruit
costs 8.15 $
Answers
You should buy approximately 1.067 kilograms of apples at $10.20 per kilogram in order to have the kilogram of fruit cost $8.15.
Let's assume that Sally bought x kilograms of apples at $10.20 per kilogram.
The total cost of bananas is given as AED 7.35 per kilogram, and Sally bought 1.4 kilograms of bananas. So, the cost of the bananas is:
Cost of bananas = AED 7.35 * 1.4 = AED 10.29
The total cost of apples is given by the equation:
Cost of apples = $10.20 * x
The total cost of the fruits combined should be AED 8.15 per kilogram. So, the equation becomes:
Total cost of fruits = (Cost of bananas + Cost of apples) / (1.4 + x) = AED 8.15
Substituting the known values, we have:
(10.29 + 10.20 * x) / (1.4 + x) = 8.15
Cross-multiplying and simplifying, we get:
10.29 + 10.20 * x = 8.15 * (1.4 + x)
Expanding the equation, we have:
10.29 + 10.20 * x = 11.41 + 8.15 * x
Rearranging the equation, we get:
10.20 * x - 8.15 * x = 11.41 - 10.29
1.05 * x = 1.12
Dividing both sides by 1.05, we find:
x = 1.12 / 1.05
x ≈ 1.067
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1. Maya's ice cream machine makes 10 cups of ice cream from 0.5 cup of sugar. How many cups of ice cream can be made with 5 cups of sugar?
Answers
Answer:
100
Step-by-step explanation:
Since ten cups of ice cream is made from .5 cups of sugar, lets first find out how many cups of ice cream can be made form one cup of sugar
.5*2=1
10*2=20
Since the ratio of sugar to ice scream is .5/10 if you do anything to the top you need to do it to the bottom
so now you have 1/20
for every one cup of sugar there are 20 cups of icecream
now you need to multiply both top and bottom by five
1*5=5
20*5=100
5/100
You can make 100 cups of ice cream
*don't forget to label your answer with cups of ice cream*
100 cups of ice cream can be made with 5 cups of sugar.
What are comparing quantities?
Comparing quantities is the qualitative relation between two quantities which reflects the relative size of both the quantities.
It is given that,
10 cups of ice cream requires = 0.5 cup of sugar
⇒ 1 cup of sugar = 10/0.5 cups of ice cream
⇒ 1 cup of sugar = 20 cups of ice cream
Hence we see that Maya's ice cream machine makes 20 cups of ice cream from 1 cup of sugar.
Similarly, 5 cups of sugar = 5 x 20 cups of ice cream
⇒ 5 cups of sugar = 100 cups of ice cream
Therefore,100 cups of ice cream can be made with 5 cups of sugar.
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Which describes the pedestrian crossing sign shown?
The sign is a trapezoid because exactly one pair of opposite sides is parallel.
The sign is a parallelogram because both pairs of opposite sides are parallel.
The sign is a kite because both pairs of opposite sides are congruent.
The sign is a parallelogram because at least one pair of opposite sides is parallel
Answers
The sign is a parallelogram because both the pairs of the opposite sides are parallel.
A parallelogram is a quadrilateral with two sets of parallel sides. A parallelogram has opposing sides that are the same length and angles that are the same size. the internal angles on the same side that are in addition to the transversal. The sum of all interior angles is 360 degrees.
Characteristics of a parallelogram:
The contrasting sides are parallel and congruent.Angles that diverge line up.The following angles act as a fallback.If any one of the angles is a right angle, then all the angles will be at right angles.Split in half are the two diagonals.Each diagonal divides the parallelogram into two equal and congruent triangles.A parallelogram's diagonals are equal to the sum of its squares.To learn more about parallelogram visit :
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Answer:
B
Step-by-step explanation:
The data below were obtained from an experiment were participants were given drinks with or without caffeine and then asked to tap their fingers. The data for 20 participants are below. Assume the number of taps per minute is normally distributed. The variance is unknown. Find a 95% CI for μ number of taps. Identify the pivot function used. 246 242 248 245 250 244 252 248 248 247 250 248 246 242 248 244 245 246 250 242
Answers
Answer:
The 95% confidence interval is \(244.26 < \mu < 246.95\)
The pivot function used is
\(t = \frac{\=x - \mu}{ \frac{\sigma}{\sqrt{n} } }\)
Step-by-step explanation:
From the question we are told that
The data given is 246 242 248 245 250 244 252 248 248 247 250 248 246 242 248 244 245 246 250 242
The sample size is \(n= 20\)
Given that the confidence level is 95% then the level of significance is
\(\alpha = (100 - 95)\%\)
\(\alpha = 0.05\)
The degree of freedom is mathematically represented as
\(df = 20 -1\)
\(df = 19\)
From the student t-distribution table the critical value of \(\frac{\alpha }{2}\) is
\(t_{\frac{\alpha }{2} , 19 } = 2.093\)
The mean is mathematically represented as
\(\= x = \frac{\sum x_i}{ n}\)
\(\= x = \frac{246+ 242 +248+245+ 250+ 244+252+ 248 +248 +247+ 250+ 248+ 246+ 242 +248 +244 +245 +246+ 250+ 242}{20}\)\(\= x = 246.6\)
The standard deviation is mathematically represented as
\(\sigma = \sqrt{\frac{\sum (x_i - \= x )^2)}{n} }\)
\(\sigma = \sqrt{\frac{(246- 246.6)^2 +(242- 246.6)^2 +(248- 246.6)^2 + (248- 245)^2+}{20} } \ ..\)
\(\ ...\sqrt{\frac{(250-246.6 )^2+ (244- 246.6)^2+(252- 246.6)^2+ (248- 246.6)^2+ (248- 246.6)^2+}{20} } \ ...\)
\(\ ..\sqrt{\frac{(247- 246.6)^2+ (250- 246.6)^2+ (248-246.6)^2+ (246-246.6)^2+ (242-246.6)^2+ (248-246.6)^2+ (244-246.6)^2+}{20} } \ ...\) \(\sqrt{\frac{ (245-246.6)^2+ (246-246.6)^2+ ( 246-246.6)^2 + ( 250-246.6)^2+ ( 242-246.6)^2 +( 246-246.6)^2+ ( 242-246.6)^2 }{20} }\)\(\sigma = 2.87411\)
The margin of error is mathematically represented as
\(E = t_{\frac{\alpha }{2} , 19} * \frac{\sigma }{\sqrt{n} }\)
\(E = 2.093 * \frac{2.87411 }{\sqrt{20} }\)
\(E = 1.345\)
The 95% confidence interval is mathematically represented as
\(\= x - E < \mu < \= x + E\)
=> \(245.6 - 1.345 < \mu <245.6 + 1.345\)
=> \(244.26 < \mu < 246.95\)
The pivot function used is
\(t = \frac{\=x - \mu}{ \frac{\sigma}{\sqrt{n} } }\)
What is the exact value of sin pi/3?
Answers
The exact value of sin(pi/3) is √3. By definition, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, sin(pi/3) = √3/1 = √3.
The exact value of sin(pi/3) can be determined using trigonometric properties and identities.
First, we know that pi/3 is equivalent to 60 degrees. In a unit circle, the point corresponding to 60 degrees forms an equilateral triangle with the origin and the x-axis. This triangle has side lengths of 1, 1, and √3.
To find the sine of pi/3, we consider the side opposite the angle (pi/3) in the triangle. In this case, the opposite side has a length of √3. The hypotenuse of the triangle is 1, as it is the radius of the unit circle.
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. Suppose a government agency has a monopoly in the provision of internet connections.
The marginal cost of providing internet connections is 1
2
, whereas the inverse demand
function is given by: p = 1
Answers
The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.
In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.
The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.
To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.
Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.
As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.
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Which equation represents a line that has a slope of 1/3 and passes through point (-2, 1)?
y=1/3x-1
Y=1/3x+5/3
Y=1/3x-5/3
Y=1/3x+1
Answers
Considering the definition of a line, the equation of the line that passes through the point (-2, 1) and has a slope of 1/3 is y= 1/3x + 5/3.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Line in this caseIn this case, you know:
The line has a slope of 1/3.The line passes through the point (-2, 1).Substituting the value of the slope m, you get:
y= 1/3x + b
Replacing the value of the point in previous expression, the value of the ordinate to the origin b can be obtained:
1= 1/3× (-2) + b
1= - 2/3 + b
1 + 2/3= b
5/3= b
Finally, the equation of the line is y= 1/3x + 5/3.
Learn more about equation of a line:
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