Find a formula for RN for the function f(x) = (5x)² on [-1, 5] in terms of N.

Could you please show the work? I was able to get the area but can't exactly figure out what they want for the formula.

Compute the area under the graph as a limit.

lim RN=1050

Find A Formula For RN For The Function F(x) = (5x) On [-1, 5] In Terms Of N.Could You Please Show The

Answers

Answer 1

Therefore , R(N) = 100 + 400 (N+1)(2N+1) + 800 x N2 N3 and area are the formulas for R(N) for the function f(x) = (5x)2 on [1, 5] and the function f(x) = (5x)2 in terms of N. R(N) = 767(approx) (approx).

What is function?

Each x value in the domain has one but only one y value range, according to the rule of a function. Definition. If there is only one and only one value of x variable such that f(x) = y, then the function is one-to-one.

Here,

In the given question, we have to find a formula for R(N) for the function f(x) =(5x)^2 on [1, 5] in terms of N.

The given function is f(x)=(5x)^2 on [1, 5].

Ax = (5-1)/N

Ax = 4/N

X = 1+iAx

X = 1+i4/N

f(x) = 25X^2

f(x) = 25(1+i4/N)^2

f(x) = 25(1+i8/N+16/N^2 i^{2})

R(N) = 1ƒ(X) Ax

Now putting the value of f(x) and Ax

R(N)==1 [25 (1+ &i + 16i2)]

R(N) = 1001 (1 +Ni + 16i2)

N100 (1+i+12)N

100 (N += i +122)+16 N(N+1)(2N+1)(+1)(2N+1)

R(N)=100 (N + √2/ N(N+1) x 100

R(N) =2/6× N + 100 × 5 × N(N+1) + 100 x 2

[tex]\lim_{n \to \infty}[/tex] R(N) = 100 + 400 + 800/3

[tex]\lim_{n \to \infty}[/tex] R(N) = 766.67

[tex]\lim_{n \to \infty}[/tex] R(N) = 767(approx)

Therefore , the solution of the given problem of function comes out to be [tex]\lim_{n \to \infty}[/tex] R(N) = 767(approx).

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Related Questions

Find the sum of the first 12 terms of the geometric series
2 + 4 + 8 +...

Answers

In the geometric series 2, 4, 6, 8, 10, 12,..., 24 is the 12th term. Each number in this series is separated by a factor of two.

How can the sum of the initial terms in a geometric series be determined?

the total of a geometric sequence's terms. Sn=a1(1rn)1r, r1 denotes the sum of the first n terms in a geometric series. an infinite geometric series whose total is provided by the expression S=a11r and where |r|1.

What is a geometric series term?

A geometric sequence is a set of numbers that follows a pattern in which the next term is determined by multiplying the previous one by a factor known as the common ratio, r.

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Select ALL composite numbers with their correct prime factors(I need help)

Answers

Answer:

The answer would be the second and fourth options.

Step-by-step explanation:

This can be solved by using a calculator, the prime factor method, etc. Good luck on your math journey!

You give tours on the Great Lakes and talk about points of interest. A lighthouse typically has 2 beacons that rotate together but not necessarily facing opposite directions. In that way, it can be a shorter time between the first and second flashes than between the second flash and the third flash
(when the first beacon comes around for the second time). One way of identifying which lighthouse you are looking at is to find the ratio of the short time between flashes to the long time between flashes. If the beacons are set 120 degrees apart along the rotation, ash shown below, what is this ratio?

Answers

The required ratio is 1:2.

What is ratio?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

Given that, A lighthouse typically has 2 beacons that rotate together but not necessarily facing opposite directions, it can be a shorter time between the first and second flashes than between the second flash and the third flash,  One way of identifying which lighthouse you are looking at is to find the ratio of the short time between flashes to the long time between flashes. The beacons are set 120 degrees apart along the rotation

If the second beacon is 120° after the first, then the first is 360° -120° = 240° after the second.

Therefore, the ratio of the times between beacons is =

120° : 240° = 1 : 2

Hence, the ratio is 1 : 2

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the inaugural attendance of an annual film festival is 20,000. The attendance y increases by 5% each year
1. about how many people will attend the festival in the fifth year?

Answers

Answer:

24,241 people

Step-by-step explanation:

To determine the attendance at the festival in the fifth year, we need to calculate the cumulative increase in attendance over five years.

1st year: 20,000

2nd year: 20,000 * 1.05 = 21,000 (5% increase from the first year)

3rd year: 21,000 * 1.05 = 22,050 (5% increase from the second year)

4th year: 22,050 * 1.05 = 23,127.50 (5% increase from the third year)

5th year: 23,127.50 * 1.05 = 24,241.38 (5% increase from the fourth year)

So, in the fifth year the festival will be attended by approximately 24,241 people.

The Board of Education (DOE) claims that the average salary of substitute teachers in school
district in Nassau County, NY, is about $175 per day. A random sample of 6 school districts is
selected, and the daily salaries (in dollars) are collected into calculation with sample mean is $80
and sample standard deviation is 6.3. Calculate at α = .05 significance level whether the true
mean greater than $175.
Please explain step by step and as clear as possible

Answers

The null hypothesis is rejected.

The mean is not greater than $175.

What is the hypothesis?

An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.

Given:

Sample size (n) = 6

Sample mean ([tex]\bar x[/tex]) = $80

Sample standard deviation(s)=6.3

Significance level(α)=0.05

We have to test the claim that the true mean greater than $175.

The null and alternative hypotheses:

H₀ : μ = 175

H₁ : μ > 175

Here, Population Standard deviation is unknown and sample size is less than 30.

So we will use t- distribution.

Test Statistic t,

t   = ([tex]\bar x[/tex] - μ) / {s/√n}

t  =  (80−175) / (6.3 /√6)

t   =  (80−175) / (6.3 / 2.45)

t  = − 95 / 2.57196423

t = −36.937

degree of freedom (df) = n−1

                                     = 6−1

                                     = 5

p-value at  t = −36.937, df = 5 and α = 0.05

Absolute value of −36.937 = 36.937

Notice that 36.937 does not show up in the table, but it does fall between the two values 31.821 and 63.657.

So, p-value = 1

Since, p-value > α

That means, we fail to reject the null hypothesis (H₀).

Therefore, the true mean is not greater than $175.

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Estthe product silve using an area model and the standard algorithm 1.7x55=

Answers

The expression 1.7 x 5.5  can be an area model of the rectangle where the length is 1.7 and the width is 5.5

What is a rectangle?

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

The expression 1.7 x 55 is an area model.

Area of rectangle = length x width

Now,

Length = 1.7

Width = 55

Area = 1.7 x 5.5

Thus,

The expression 1.7 x 5.5 can be an area model.

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the average number of wins for a team is 7.6 for the season with a standard deviation of 1.3. What is the probability that the team will win more the 9 games this season?

Answers

The probability that the team will win more than 9 games this season, given the average number of wins for the team, is 4 %

How to find the probability ?

The Z-score formula is:

Z = (x - mean) / standard deviation

Where x is the number of wins we're interested in (9), mean is the average number of wins (7.6), and standard deviation is the standard deviation of the number of wins (1.3)

Z = (9 - 7.6) / 1.3

= 2.3 / 1.3

= 1.77

This means that 9 wins is 1.77 standard deviations above the mean. The result is the probability of a team winning more than 9 games this season, which is around 0.04 or 4% from the standard normal distribution table.

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Manuel will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $60 and costs an additional $0.60 per mile driven
The second plan has no initial fee but costs $0.80 per mile driven.
For what amount of driving do the two plans cost the
same?
miles
What is the cost when the two plans cost the same?
3

Answers

From the given values and conditions, We need to form a equations and equate both sides to solve for the miles, The answer is 300 miles.

What is a equation?

An equation is a statement of equality between two expressions. It typically includes numbers and mathematical operations such as addition, subtraction, multiplication, and division. For example, the equation 2x + 3 = 7 is a statement that the value of the expression 2x + 3 is equal to the value of 7. Equations can also include variables, which represent unknown values that can be solved for.

What is unitary method?

The unitary method is a method used in mathematics to solve problems involving units of measurement. It involves expressing the units of measurement as a fraction or multiple of a single unit and then using this fraction or multiple to solve the problem. The method is particularly useful in solving problems involving conversions between different units of measurement. The unitary method is particularly useful in solving word problems where the conversion of units is required. It involves expressing the given information in terms of a single unit and then using that information to find the unknown quantity.

x= miles

60+0.6x=0.8x

0.8x-0.6x=60

0.2x=60

x=60/0.2

=300 miles

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1 18. You have a --cup 4 1 measuring cup and a --cup measuring 2 cup. What are two ways you can 3 measure 2 cups of water? - 4​

Answers

Use another measurement cup

summarize how you can find the slope of a parallel line.

Answers

The slopes of parallel lines are equal and the formula for the slope of parallel lines is m1 = m2. The parallel lines are equally inclined with respect to the positive x-axis and hence the slope of parallel lines are equal.

Summary of slope of parallel lines:

Parallel lines have equal slopes. The parallel lines are equally inclined with regard to the positive x-axis, and this is taken into account when calculating a line's slope.

If one line has a slope of m1, another line has a slope of m2, and both lines are parallel, then we get m1 = m2.

The coefficients for "x" and "y" in the equations that depict parallel lines are identical.

Ax + by + c2 = 0 is the line that is parallel to ax + by + c1 = 0. Observation reveals that the x and y coefficients in both equations are equivalent.

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The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on the interval -5 < x < -4?

Under the < is a _ thing

Answers

Answer: “Rate of change” just means “slope”. All of calculus is just ways to find the slope for curves. Find y at -5 and at -4 and calculate the slope.

Step-by-step explanation:

Find X and Y - 20 POINTS

Answers

Check the picture below.

The Barker family just left the local pet store with Lucky, their new family dog. The pet store owner told the Barker family that for the next 6 months, Lucky would grow at an average rate of 9 pounds per month. Currently, Lucky is 2 months old and weighs 3 pounds. Age, in months 2 3 4 5 6 7 8 Weight, in pounds 3 at 2 months old Part A: Complete the given table that represents Lucky's current weight, in pounds, as a function of his age, in months. Part B: Graph the data in the table from Part A. Be sure to label the graph and all data points. Part C: Create a linear model that represents the Lucky's current weight, in pounds, as a function of his age, in months. Part D: If Lucky continues to grow at the rate of 9 pounds per month beyond the expected six months, how much will Lucky weigh by the time he is one year old?

Answers

The table is given below.

The graph is given below.

The linear model that represents lucky's current weight in pounds as a function of his age in months is

f(x) = 9x - 15.

Lucky's weight in one year is 93 pounds.

What is a function?

function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Lucky current age and weight = 2 months and 3 pounds.

The growth rate of lucky per month = 9 pounds.

Table of age and weight of lucky.

Age (months)        Weight (pounds)

2                              3

3                              12

4                              21

5                              30

6                              39

7                              48

8                              57

Now,

The coordinates on the graph from the table are:

(2, 3), (3, 12), (4, 21), (5, 30), (6, 39), (7, 48), and (8, 57).

The graph of the table is given below.

Now,

The function for the weight of the lucky in x months.

f(x) = mx + c

m = 9

(2, 3) = (x, f(x))

So,

3 = 9 x 2 + c

c = 3 - 18

c = -15

So,

f(x) = 9x - 15

Where x is the number of months.

Now,

The weight of lucky in one year i.e 12 months.

This means,

x = 12 months

f(12) = 9 x 12 - 15 = 108 - 15 = 93

Thus,

The table is given above.

The graph is given below.

The function for lucky weight in x months is f(x) = 9x - 15.

The weight of lucky in one year is 93 pounds.

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6x2x(x−3) x (x−3)10(x+2)

Answers

The product of given numbers is 60x³(x−3)²(x+2)

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra,

Multiply the numbers:

6x²x(x−3) * (x−3)10(x+2)

Multiply 6 and 10

60x²x(x−3) (x−3)(x+2)

Multiply x terms

60x³(x−3) (x−3)(x+2)

Multiply (x-3) terms

60x³(x−3)²(x+2)

So, the product of given numbers is 60x³(x−3)²(x+2)

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17v = 62 (exponential equations with logarithms, solve)

Answers

Therefore v = log(62) / log(17) is the solution for v, the unknown variable in the equation.

Define log(Logarithm).

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be increased in order to obtain a number x is the logarithm of x to the base b.  For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3.

What is a function?

A function in mathematics is an expression, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). Each element of X receives precisely 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.

To solve this exponential equation, we can use the logarithms property that is log(a^b) = b*log(a).

Given the equation 17v = 62, we can take the logarithm base 17 of both sides:

log(17^v) = log(62)

v*log(17) = log(62)

Dividing both sides by log(17) gives us:

v = log(62) / log(17)

This is the solution for v, the unknown variable in the equation.

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Simplify the following expression: 3(5 – 12) + 4 ÷ 2
A. -19
B. 19
C. -23
D. -8.5

I think it's either A or B

Answers

3(5 - 12) + 4 ÷ 2 = - 19

A must be the answer

find the first term in geometric sequence if the 11th term is -160 and the ratio is -1/3​

Answers

Answer:

  -9447840

Step-by-step explanation:

You want the first term of a geometric sequence whose 11th term is -160 and whose common ratio is -1/3.

N-th term

The n-th term of a geometric sequence is ...

  an = a1·r^(n-1)

where a1 is the first term and r is the common ratio.

Using the given values, we have ...

  -160 = a1·(-1/3)^(11 -1)

  a1 = (-160)·(-3)^10 = -9447840

The first term is -9447840.

pls help I have a hundred points for someone who answers

Answers

957÷3=319 this divide answer i hope help you

What is the slope of the line through (2, -1) and (-2, -3)?

Answers

The slope of the line is 1/2
The slope would be..1/2!!

pls help last test of semester half my grade please complete entire table i give brainliest

Answers

y=6(-4)-1
y=-24-1
y=-25

y=6(0)-1
y=0-1
y=-1

y=6(6)-1
y=36-1
y=35

Solve the following equation for aa. Be sure to take into account whether a letter is capitalized or not.
2n= a(d+g)

Answers

The solution to the equation is given as [tex]a = \frac{2n}{(d + g)}[/tex]

How to solve for a in the equation

The equation is given as 2n= a(d+g), we are to make a the subject of the equation

in order to have a stand on its own we would have to divide the two sides of the equation by d + g

hence we would have:

[tex]\frac{2n}{(d + g)} =\frac{a(d+g)}{(d+g)}[/tex]

this would cancel out on the right hand side such that we would have:

[tex]\frac{2n}{(d + g)} =a[/tex]

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Find y.
7.54
6.76
18.55
29.83

Answers

The length of y in the triangle is 18.55 units.

How to find the side of a triangle?

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. The side y of the triangle can be found using sine law.

Therefore,

a / sin A = b / sin B = c / sin C

Applying the sine law,

y / sin 106 = 15 / sin 51

cross multiply

y sin 51° = 15 sin 106°

divide both sides by sin 51°

y sin 51° / sin 51° = 15 sin 106° / sin 51°

y = 15 sin 106° / sin 51°

Therefore,

y = 15 × 0.96126169593 / 0.77714596145

y = 14.4189254391 / 0.77714596145

y = 18.5536589719

Hence,

y = 18.55 units

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i need help pls i do not get it

Answers

The perimeter and the area of the fountain is calculated to be

94.25 feet and 625.32 square feet respectively

How to find the perimeter and the area of the fountain

The perimeter of the fountain consisting of two semicircles and a quarter circle is

= perimeter of semicircle * 2 + perimeter of circle * 1/4

= π d + 2 π r * 1/4

for semicircle, diameter, d = 20 ft

for circle, radius r, = 20 ft

substituting the values

= 20π + 2 * π * 20 * 1/4

= 20π + 10π

= 30π

= 94.25 feet

Area of the fountain

= area of semicircle * 2 + area of circle * 1/4

area of semicircle * 2 = area of circle of radius 10 ft

for semicircle, radius, r = 10 ft

for circle, radius r, = 20 ft

= π 10² + π 20² * 1/4

= 100π + 100π

= 200π

= 625.32 square feet

The area of the fountain is 625.32 square feet

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You are a post person and deliver 40 letters an hour. You start at 6:45 and have 100 to deliver before your break. What time is your break?

Answers

Answer:

9:15

Step-by-step explanation:

Time needed to deliver 100 letters: 100 : 40 = 2,5 hours = 2:30min
Your break: 6:45 + 2:30 = 9:15

Customary American Units of Capacity
1 cup = 8 ounces
1 pint = 2 cups or 16 ounces
1 quart = 2 pints, 4 cups, or 32 ounces
1 gallon = 4 quarts, 8 pints, 16 cups, or 128 ounces


9 cups = ___ pints ____ cups

Answers

20.945649350649 c = 9 dry pt, Four pints equal nine cups. The metric system uses the litre and millilitre as the units of capacity. By dividing by 11000, we may convert millilitres into litres.

What is the US customary unit for capacity?

In the United States, ounces, cups, pints, quarts, and gallons are the commonly used measurement units for capacity or volume. Cups, pints, quarts, and gallons are some of the volume or capacity measuring units used in the United States. 8 fluid ounces are the equivalent of 1 cup. There are 2 cups in a pint. 1 quart equals 2 pints.

The solution is clear cut and simple to remember when dealing with liquids. Eight fluid ounces make up one cup, which is the unit of measurement for liquids. Every liquid has this property. The solution is clear cut and simple to remember when dealing with liquids. Eight fluid ounces make up one cup, which is the unit of measurement for liquids. For all liquids, this is true. 4 pints are equal to 9 cups.

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d^2a/db^2 +a = 4b+10sin(b)

Answers

The given equation is a second order differential equation

What is a differential equation?

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.

Isaac Newton listed three kinds of differential equations given -

[tex]${\displaystyle {\begin{aligned}{\frac {dy}{dx}}&=f(x)\\[4pt]{\frac {dy}{dx}}&=f(x,y)\\[4pt]x_{1}{\frac {\partial y}{\partial x_{1}}}&+x_{2}{\frac {\partial y}{\partial x_{2}}}=y\end{aligned}}}[/tex]

Given is a differential equation as follows -

d²a/db² + a = 4b + 10sin(b)

The given equation is -

d²a/db² + a = 4b + 10sin(b)

Let y = a and x = b, then we can write -

d²y/dx² + y = 4x + 10sin(x)

A second order differential equation is one that expresses the second derivative of the dependent variable as a function of the variable and its first derivative. It is of the form -

d²y/dx² + P(x) dy/dx + Q(x) y = f(x)

For the equation given -

d²y/dx² + y = 4x + 10sin(x)

On comparing, we get -

P(x) = 0

Q(x) = 1

f(x) = {4x + 10sin(x)}

Therefore, the given equation is a second order differential equation.

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what is an equation of the line that is parallel to y = - 5 x + 6 and passes through the point (-4,-1)

Answers

The equation of the line that is parallel to the line y = - 5x + c and passes through (-4, -1) will be y = - 5x - 21.

What is the equation of a parallel line?

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.

The equation of the line is given below.

y = - 5x + 6

The equation of the line that is parallel to the line y = - 5x + 6 is written as,

y = - 5x + c

The equation passes through (-4, -1), then we have

- 1 = - 5 (-4) + c

- 1 = 20 + c

- 21 = c

The equation of the line that is parallel to the line y = - 5x + c and passes through (-4, -1) will be y = - 5x - 21.

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Please help asap!

A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.

spinner divided evenly into eight sections with three colored blue, one colored orange, two colored purple, and two colored yellow

Determine P(not orange) if the spinner is spun once.

25%
12.5%
87.5%
37.5%

(no links)

Answers

Answer:

7/8 = 87.5%

Step-by-step explanation:

You have only one of eight (1/8) evenly divided sections that is orange. The rest is not orange (1 - 1/8 = 7/8).

Therefore, spinning once will yield 7/8 odds of not landing on orange, or 0.875 or 87.5%.

The probability of not getting orange is 87.5%. The correct option is C.

What is probability?

Probability is a number that indicates the likelihood of an event occurring. Probability is defined as the ratio of favourable outcomes to all outcomes.

Probability = Number of favourable outcomes / Number of samples

Given that a spinner with repeated colours numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.

You only have one of eight (1/8) evenly divided orange sections.

The rest is not orange,

P = (1 - 1/8

P =  7/8

P = 87.5%

Therefore, spinning once will yield 7/8 odds of not landing on orange or 0.875 or 87.5%.

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($75,000 - $80,000) x (1 - .21)

Answers

Answer:

-3,950

Step-by-step explanation:

First -5,000(1-0.21)

Then multiply -5,000 x 0.79 = -3,950

Which graph represents the solution to the following inequality? 3x - 2y ≥ 6

Answers

Answer:

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

For:

x

=

0

(

3

0

)

+

2

y

=

6

0

+

2

y

=

6

2

y

=

6

2

y

2

=

6

2

y

=

3

or

(

0

,

3

)

For:

y

=

0

3

x

+

(

2

0

)

=

6

3

x

+

0

=

6

3

x

=

6

3

x

3

=

6

e

d

)

(

3

)

x

=

2

or

(

2

,

0

)

We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.

graph{(x^2+(y-3)^2-0.125)((x-2)^2+ y^2-0.125)(3x+2y-6)=0 [-20, 20, -10, 10]}

Now, we can shade the left side of the line. And we need to make the boundary line a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(3x+2y-6) < 0 [-20, 20, -10, 10]}

Step-by-step explanation:

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