Answer : There are 84 different ways that six letters can be grouped from nine letters total.
Now that we have determined that the problem deals with combinations, we can use the formula for combinations to calculate the number of ways that six letters can be grouped from nine letters total. The formula for combinations is:
C(n,k) = n! / (k! * (n-k)!)
Where n is the total number of items, and k is the number of items being chosen. In this case, n = 9 and k = 6. Plugging these values into the formula gives us:
C(9,6) = 9! / (6! * (9-6)!)
C(9,6) = 9! / (6! * 3!)
C(9,6) = 362880 / (720 * 6)
C(9,6) = 362880 / 4320
C(9,6) = 84
Therefore, there are 84 different ways that six letters can be grouped from nine letters total.
Answer: 84.
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Use dimensional analysis to convert 9 tsp to tablespoons
Using the dimensional analysis, 9 tsp is equivalent to 3 tbsp.
A conversion factor is a numerical ratio that relates two units of measurement for the same quantity
To convert 9 tsp to tablespoons using dimensional analysis, we can use the conversion factor that 1 tablespoon is equal to 3 teaspoons. We can set up the following proportion
1 tablespoon / 3 teaspoons = x tablespoons / 9 teaspoons
where x is the number of tablespoons we want to find. To solve for x, we can cross-multiply and simplify:
1 tablespoon × 9 teaspoons = 3 teaspoons × x tablespoons
9 tablespoons = 3x
x = 9 tablespoons / 3
x = 3 tablespoons
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Leandro wants to build a one-sample z interval with 98% confidence to estimate the proportion of light
bulbs that arrive broken upon shipment to his store. He takes a random sample of 500 bulbs and finds that
25 arrived broken.
What critical value z* should Leandro use to construct this confidence interval?
The critical value for the confidence interval will be 2.33 with a confidence inetrval of 0.05 ± 0.00308
Here we see that the probability to find a bulb from the sample broken is
p = 25/500
= 0.05
Now, we need to build a 98% confidence interval so we will get the critical value to be
(1 - confidence interval)/2
= (1 - 0.98)/2
= 0.02/2
= 0.01
Looking up the value for 0.01 in the standard normal table we the critical value to be
2.33
Now the confidence interval will be
p ± critical value X √[p(1 - p)/n]
= 0.05 ± 0.01√[(0.5 X 0.95)/500]
= 0.05 ± 0.00308
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1. Which point has the coordinantes(-0. 5, -2. 5)?(1 point)
A. Point a
B. Point b
C. Point c
D. Point d
this is for the quick check in unit 5 lesson 2 for connexus
Point G has the coordinates (-2.5, 5.5), so a correct option is an option (C).
What is a coordinate plane?
The study of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry). It is possible to determine the separation between two points, divide a line into m:n segments, locate a line's midpoint, determine the area of a triangle in the Cartesian plane, and perform other operations using coordinate geometry.
A coordinate plane is a plane in which a set of two number lines are represented, the horizontal line is called the x-axis and the vertical line is called the y-axis.
The given coordinates are (-2.5, 5.5).
The graphical representation of the points is shown below.
Point G has the coordinates (-2.5, 5.5).
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Solve for x in the diagram below.
Step-by-step explanation:
Use the triangle bisector theorem:
"The angle bisector of a triangle divides the opposite side into two parts proportional to the other two sides of the triangle."
so 12 is to 16 as x is to 20
12/ 16 = x/20
20 * 12/16 = x = 15 units
Answer:
x = 15
Step-by-step explanation:
the segment inside the triangle is an angle bisector and divides the side opposite the angle into segments that are proportional to the other two sides , that is
[tex]\frac{12}{16}[/tex] = [tex]\frac{x}{20}[/tex] ( cross- multiply )
16x = 12 × 20 = 240 ( divide both sides by 16 )
x = 15
Jason wants to walk the shortest distance to get from the parking lot to the beach. How far is the spot on the beach from the parking lot?
How far will his place on the beach be from the refreshment stand?
A: 24 m; 32 m
B: 38 m; 12 m
C: 24 m; 18 m
D: 34 m; 16 m
the shortest distance from the parking lot to the beach is 24 m and the distance between the beach and the refreshment stand is 18 m.
The answer is C: 24 m; 18 m. To find the shortest distance from the parking lot to the beach, one should measure the distance between the two locations. The distance between the parking lot and the beach is 24 m. To find the distance between the beach and the refreshment stand, one should measure the distance between the two locations. The distance between the beach and the refreshment stand is 18 m. Therefore, the shortest distance from the parking lot to the beach is 24 m and the distance between the beach and the refreshment stand is 18 m.
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Work out the value of 4 squared + 3 cubed
help if can for 10+ points
Answer:
43
Step-by-step explanation:
We can simplify the expression:
[tex]4^2 + 3^3[/tex]
by rewriting exponents as multiplication of their base.
[tex]4^2 + 3^3[/tex]
[tex]= (4\cdot 4) + (3\cdot 3 \cdot 3)[/tex]
Then, we can simplify using the order of operations (PEMDAS).
[tex](4\cdot 4) + (3\cdot 3 \cdot 3)[/tex]
[tex]= 16 + (9 \cdot 3)[/tex]
[tex]= 16 + 27[/tex]
[tex]\boxed{= 43}[/tex]
Find the slope of a line with the cordnates of (6,1) and (-3,5)
Answer:
Answer:
Slopem=−49
As a decimal:
m = -0.444444
Step-by-step explanation:
Slope m with two points
Graph of the line for y = mx + b
Point Slope Form y - y1 = m(x - x1)
Slope Intercept Form y = mx + b
Standard Form Ax + By = C
y-intercept, when x = 0
x-intercept, when y = 0
DETAILS , LARPCALCL the equation of the circle in standard forn 9x^(2)+9y^(2)+36x-72y+11=0
(x + 2)2 + (y - 4)2 - 11 = 0
The equation of the circle in standard form is x2 + y2 + 36x - 72y + 11 = 0. To arrive at this answer, you need to complete the square for both the x and y terms in the equation. First, divide the equation by 9 to get the following:
x2 + y2 + 4x - 8y + 1 = 0
To complete the square for the x terms, add and subtract (4/2)2 = 16/4 = 4 to the equation:
x2 + 4 + y2 + 4x - 8y + 1 - 4 = -4
Simplifying gives you:
(x + 2)2 + y2 - 8y + 5 = 0
To complete the square for the y terms, add and subtract (8/2)2 = 64/4 = 16 to the equation:
(x + 2)2 + (y - 4)2 + 5 - 16 = -11
Simplifying gives you:
(x + 2)2 + (y - 4)2 - 11 = 0
This is the equation in standard form.
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The function y=100(1. 05)^x represents the cost per night at a hotel that cost $100 when the hotel opened and has been increasing by 5% every year since the hotel opened
The given function of the cost represents exponential growth.
Exponential growth: what is it?A form of growth known as exponential growth occurs when the rate of expansion is proportionate to the present value. This implies that the rate of growth increases as the present quantity increases. An exponential function, such as the one in this question (y = abx, where an is the starting value, b is the growth factor, and x is the number of time periods), may be used to describe exponential growth. In natural and social processes, such as population expansion, economic growth, and the spread of illnesses, exponential growth is frequently seen. Yet, there are always resource constraints and other factors that will ultimately reduce or stop the expansion, therefore exponential growth cannot last eternally.
The given function is y=100(1. 05)^x.
To find cost for certain year we substitute different value of x.
From the function we observe that as the value of x increases the function increases continuously.
Hence, the given function of the cost represents exponential growth.
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The complete question is:
What is the approximate area of the shaded sector in the circle shown below?
14 in
C
30⁰
OA. 205 in²
O B. 51 in2
OC. 3.67 in²
OD. 7.33 in2
SUBMIT
Answer:
B. 51 in²
Step-by-step explanation:
The area of a sector which has a central angle of θ degrees is given by
Area of circle x θ/360
where
area of circle = πr² with r being the radius
So area of sector = πr² x θ/360
here r = 14 in and θ=30°
Area of sector
= π x 14² x 30/360
= 51.31268 in²
≈ 51 in²
Option B
i have the slopes i just need the lengths in radical form and what shape its best described as
Step-by-step explanation:
Im not at a great place to answer them all, but hope this helps on answering them
So the first is 5/2. When you found that, you essentially found the 2 other sides of the "triangle".
You can use Pythagoras to find the length of PQ.
[tex] {2}^{2} + {5}^{2} = {x}^{2} [/tex]
[tex]4 + 25 = 29[/tex]
[tex] \sqrt{29} = x[/tex]
You can either keep it like that, or use a calculator to find that value. im not sure how the system accepts it. you'll do that for each one
Question two, please help
2/10
Answer:
C,D
Step-by-step explanation:
Randy claims that he can purchase 3. 5 pounds of chicken salad for $23. 50. Is he correct? Explain.
Randy's claim is not correct Therefore, he cannot purchase 3.5 pounds of chicken salad for $23.50
To determine if Randy's claim is correct, we can use the given linear graph and points to find the equation of the line that represents the relationship between the amount of chicken salad purchased and the cost.
We can use the two points (1, 7.5) and (3, 22.5) to find the slope of the line:
slope = (change in y) / (change in x)
slope = (22.5 - 7.5) / (3 - 1)
slope = 15 / 2
slope = 7.5
Now we can use the slope-intercept form of the equation of a line, y = mx + b, where m is the slope and b is the y-intercept, to find the equation of the line:
y = 7.5x + b
To find b, we can use one of the points on the line, such as (1, 7.5):
7.5 = 7.5(1) + b
b = 0
So the equation of the line is:
y = 7.5x
Now we can use this equation to check if Randy's claim is correct. If he can purchase 3.5 pounds of chicken salad for $23.50, we can plug in x = 3.5 and see if y = 23.5:
y = 7.5x
y = 7.5(3.5)
y = 26.25
Since y = 26.25 is not equal to $23.50
Therefore, Randy's claim is not correct
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The given question is incomplete, the complete question is:
Randy claims that he can purchase 3. 5 pounds of chicken salad for $23. 50. Is he correct? Explain.
R
x
PR 96 cm
PQ48 cm
What is the value of x ? Enter the answer in the box.
degrees
The value of x is 30 degrees.
Describe Right Angled Triangle?A right-angled triangle is a type of triangle that has one angle that measures exactly 90 degrees (a right angle). This angle is formed by the intersection of the two sides of the triangle that are perpendicular to each other, which are called the legs or the adjacent and opposite sides. The side opposite the right angle is called the hypotenuse, and it is always the longest side in the triangle. The other two sides are usually labeled as a and b, and are called the legs or the adjacent and opposite sides depending on which angle is being considered. The Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse, is one of the fundamental properties of right-angled triangles. Right-angled triangles have numerous practical applications in geometry, trigonometry, physics, and engineering.
We can use the trigonometric ratio of sine to find the angle x.
sin(x) = opposite/hypotenuse = PQ/PR = 48/96 = 1/2
Taking the inverse sine of both sides, we get:
x = sin^(-1)(1/2)
Using a calculator, we get:
x ≈ 30 degrees
Therefore, the value of x is 30 degrees.
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The path of a firecracker is modeled by the equation h(t) = -t^2 + 19t + 14, where h(t) is the hight, in feet, of the firecracker at any given time, t. What is the hight of the firecracker after 4 seconds from launch.
A. 63 feet
B. 68 feet
C. 70 feet
D. 74 feet
the height of the firecracker after 4 seconds from launch is 68 feet.
To find the height of the firecracker after 4 seconds from launch, we need to plug in t = 4 into the equation h(t) =[tex]-t^2[/tex] + 19t + 14. This gives us h(4) =[tex]-4^2[/tex] + 19(4) + 14 = -16 + 76 + 14 = 68 feet. Therefore, the height of the firecracker after 4 seconds from launch is 68 feet.
To find the height of the firecracker after 4 seconds from launch, we need to use the equation h(t) =[tex]-t^2[/tex] + 19t + 14. This equation models the path of the firecracker, with h(t) being the height in feet of the firecracker at any given time, t. When we plug in t = 4, we get h(4) = [tex]-4^2[/tex] + 19(4) + 14 = -16 + 76 + 14 = 68 feet. So, the height of the firecracker 4 seconds after launch is 68 feet. This equation allows us to calculate the height of the firecracker at any given time, making it a useful tool for predicting the trajectory of the firecracker.
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The area of the triangular section is (4, 6, 12, 24) square units. The area of the entire figure is (12, 48, 60, 120) square units
The area of the triangular section is 12 square units and the area of the entire figure is 60 square units.
We know that the Area of triangle is defined as the product of its height to its base.
Area of triangle = height × base
From the figure, we can see that Height is = 4 units and the base is = 6 units,
So, the area of the triangular section is = 1/2 × base × height,
⇒ (1/2) × 6 × 4
⇒ 12 square units
The entire figure consists of two figure , one is a rectangle and the other part is a triangle,
So, the area of the entire figure is = Area of rectangle + area of triangle
⇒ 4×12 + 12
⇒ 48 + 12
⇒ 60 square units
Therefore, the area of the entire figure is 60 square units.
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The given question is incomplete, the complete question is
The area of the triangular section is ___ square units, and the area of the entire figure is ___ square units. Refer to the figure given below.
Simplify (5+1)^2-(11+3^2) divided by 4
Answer:
(5+1)^2 = 6^2 = 36
3^2 = 9
Next, we can substitute these values into the expression:
(5+1)^2 - (11+3^2) = 36 - (11+9) = 16
Finally, we can divide by 4:
16/4 = 4
Therefore, the simplified expression is 4.
Step-by-step explanation:
A Math student is designing a logo for a Geometry Club that contains 4 triangles contained in a square. The approximate lengths of the legs of the blue triangle in the figure are 12 and 13 mm. What is the approximate length of the hypotenuse of the blue triangle in millimeters? Round to the nearest millimeter, and enter the number only.
Answer:
18mm
Step-by-step explanation:
A^2+B^2=C^2.
144+169=313
square root of 313=17.69≈18mm
Alex picked 15 ⅘ kilograms of red apples and 9 ⅗ kilograms of green apples. What is the total mass of the apples Alex picked?
The total mass of the apples Alex picked is 25 2/5 kilograms.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants
To find the total mass of the apples Alex picked, we need to add the mass of the red apples and the mass of the green apples.
First, let's convert the mixed numbers to improper fractions to make the addition easier:
15 ⅘ = 15 + 8/10 = 15 + 4/5 = 75/5 + 4/5 = 79/5
9 ⅗ = 9 + 6/10 = 9 + 3/5 = 45/5 + 3/5 = 48/5
Now we can add the fractions:
79/5 + 48/5 = (79 + 48)/5 = 127/5
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 1 in this case:
127/5 = 25 2/5
Therefore, the total mass of the apples Alex picked is 25 2/5 kilograms.
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What is the area of this trapezoid? Enter your answer in the box.
Answer:153
Step-by-step explanation
we can see height is equal to 9. if we consider height and 10sm as sides of rectangle, we can say top of trapezoid is equal to 10 as well.
Area of trapezoid is A=(a+b)/2*h
h-height=9
a-top=10
b-bottom=10+7+7=24
A=(10+24)/2*h=34/2*9=17*9=153
Q9) Rashmi obtains 480 marks out of 600. Rajan obtains 560 marks out of 700. Whose performance is better?
Answer:
Step-by-step explanation:
Let us first make the denominators equal, so
600 x 700 = 420000
[tex]\frac{480}{600} * \frac{700}{700} \\\\= \frac{336000}{420000}[/tex]
Similarly,
[tex]\frac{560}{700} * \frac{600}{600} = \frac{336000}{420000}[/tex]
By comparison, both of them are equal.
Hope It Helps!
Solve for X.
6x = 18
x = [?]
Answer: 3
Step-by-step explanation: do the opposite function, in this case you need to multiply 6 by x to get 18. So, now you just have to divide 18 by 6.
18/6 =3
You can make sure this is correct by multiplying your numbers of 6 and 3
6x3 = 18
Answer:3
Step-by-step explanation:
6x=6*x
6*x=18
ab=c
in order to find a we need to divide c with a. a=c/b.
in this case,
x=18/6=3
A workman is paid #15, 200 for a 40-hours week. Calculate his hourly rate of pay
The workman's hourly rate of pay for a 40-hours week is 380.
Hourly rate of pay = Total pay ÷ Total hours worked
Hourly rate of pay = 15, 200 ÷ 40 = 380
Therefore, the workman is paid 380 per hour for a 40-hours week. To calculate the hourly rate of pay, the total pay is divided by the total hours worked. In this case, the total pay is 15, 200 and the total hours worked is 40, so when we divide 15, 200 by 40, we get 380. This is the hourly rate of pay for the workman for the 40-hours week.
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How many pounds of $2. 4/lb trail mix should a grocer combine with 5 lb of $1. 5/lb trail mix to get $1. 9/lb trail mix?
The grocer should combine 3 pounds of $2.4/lb trail mix with 5 pounds of $1.5/lb trail mix to get $1.9/lb trail mix.
Let x be the number of pounds of $2.4/lb trail mix to be added to 5 pounds of $1.5/lb trail mix.
The total amount of trail mix after combining can be expressed as:
x + 5
The total cost of the combined trail mix can be expressed as:
2.4x + 1.5(5) = 1.9(x + 5)
Solving for x, we get:
2.4x + 7.5 = 1.9x + 9.5
0.5x = 2
x = 4
Therefore, the grocer should combine 4 pounds of $2.4/lb trail mix with 5 pounds of $1.5/lb trail mix to get $1.9/lb trail mix.
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A car moving at a constant speed passed a timing device at t= 0. After 7 seconds, the car has traveled 812 ft. er of seconds t after passing the timing device.
Answer: y= 116x
Step-by-step explanation:
Suppose that you are working for a chain restaurant and wish to design a promotion to disabuse the public of notions that the service is slow. You decide to institute a policy that any customer that waits too long will receive their meal for free. You know that the wait times for customers are normally distributed with a mean of 20 minutes and a standard deviation of 4 minutes. Use statistics to decide the maximum wait time you would advertise to customers so that you only give away free meals to at most 1% of the customers.
a. Determine an estimate of an advertised maximum wait time so that 1% of the customers would receive a free meal. Round to one decimal place. __________ minutes
b. Include a graph illustrating the solution. For the graph do NOT make an empirical rule graph, just include the mean and the mark off the area that corresponds to the 1% who would receive the refund. There is a Normal Distribution Graph generator linked in the resources area. Combine the above into as single file and upload using the link below. Choose File
c. Write a response to the vice president explaining your prescribed maximum wait time. Structure your essay as follows:
An advanced explanation of the normal distribution
Why the normal distribution might apply to this situation
Describe the specific normal distribution for this situation (give the mean and standard deviation)
Explain how the graph created in part b. represents the waiting times of the customers.
Explain the answer to part a. in terms of both the customers who get a free meal and those who do not. Feel free to use the accurate answer in part a to determine a "nice" wait time to be used in the actual advertising campaign.
Use the answers to parts a. and b. to explain how the proposal will not result in a loss of profit for the company.
The proposed maximum wait time should be 24.2 minutes so that 1% of the customers receive a free meal.
To answer the vice president's request, the proposed maximum wait time should be 24.2 minutes so that 1% of the customers receive a free meal. This can be seen in the graph below, which illustrates the normal distribution of customer wait times with a mean of 20 minutes and a standard deviation of 4 minutes. In this graph, the area of the curve between 0 and 24.2 minutes represents the customers who will receive a free meal, and the area to the right of 24.2 minutes represents the customers who will not receive a free meal.
The normal distribution is a common probability distribution which follows a symmetric, bell-shaped curve. It is often used to describe real-world phenomena such as customer wait times in restaurants, since it is an effective tool for modeling variation in large datasets. The normal distribution can be determined by two parameters: the mean and the standard deviation. The mean represents the average wait time, while the standard deviation describes how the wait times vary.
In this case, the normal distribution has a mean of 20 minutes and a standard deviation of 4 minutes. This means that the average wait time is 20 minutes and that the wait times may vary by up to 4 minutes. The area of the graph between 0 and 24.2 minutes can be seen as the customers who will receive a free meal, as these customers waited longer than the advertised maximum wait time. The area of the graph to the right of 24.2 minutes represents the customers who will not receive a free meal, as these customers did not wait longer than the advertised maximum wait time.
By proposing a maximum wait time of 24.2 minutes, the company will not be losing out on any profit. This is because only 1% of customers will be receiving a free meal, and the cost of this will be more than offset by the increased customer satisfaction due to faster service.
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the student council at deer creak middle school
To reach the goal he student council needs to sell a minimum number of 107 tickets.
What is Sell?Sell means to gave someone something we take money from him. It is a transaction in which product is exchange with product or money. In ancient time we use barter system for transaction.
For raising $400 the student council have to sold each ticket at $4. So the number of ticket sold = $400 / $4 = 100.
They also spent $25 on decorations, so they need to recover that cost too. So, they need to sell an additional tickets = $25 / $4 = 6.25
Since we can not sell 0.25 of a ticket, So we can round the answer to 7.
So that overall total number of tickets that must be sold as 107.
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Complete question:
The student council at Deer Creek Middle School is organizing a dance to raise money for their end-of-year trip. They want to raise at least $400. Tickets are priced at $4 each and they already spent $25 on decorations. What is the minimum number of tickets they have to sell to reach their goal?
A baseball team played 154 regular season games. The ratio of the number of games they won to the number of games they lost was 2/5. How many games did they lose?
(Type a whole number)
Answer:
Ratio of 2/5 can be added like 2+5=7
And then
154÷7=22
22×2=44
22×5=110
They lost 110 games
PLS HELP! ITS DUE TOMORROW BY 11:59pm
The ratios of the side lengths of B to A, C to B, and D to C are the same. How much more space do the boxes occupy when stored separately in a closet than when they are stacked inside each other in the closet?
1.) Yes, it will fit because the volume of the baseball is 13.36 cubic inches and the volume of the box is 64 cubic inches which is greater than the volume of the baseball.
2) The ratio of the side length of box B to the side length of box A is 1.472 inches: 6 inches.
What is circumference?The space around a circle is known as its circumference. By calculating the distance required to walk around the globe, we may determine the size of the earth's circumference.
To check whether the baseball is will still fit in the box we will check the maximum value of circumference.
[tex]2\pi r = 9.25[/tex]
Make r the subject formula
r= 1.472 inches
Volume of the baseball = [tex]\frac{4}{3\pi x^3}[/tex]
Expand:
13.35 inches^3 < 64 inches^3
So, it will fit inside the box.
2.) [tex]\sqrt[3]{216} = 6[/tex]
Therefore, V = a^3
The length of each side of the box is 6 inches.
The ratio of the side length of box B to the side length of box
A:
1.472 in : 6 inches
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Given that y varies inversely with x, use the values specified to write an
inverse variation equation relating y to x.
x = -20, y = 2
Please help‼️
Answer:
y = (1/x)+2.05
Step-by-step explanation:
We are only given one point, so there are an infinite number of possible equations. But forging ahead, we can come up with at least one equation of an inverse relationship containing the point (-20,2).
By inversely, the function will produce lower values of y as x increases, or vice versa. A good first step is to say:
y = 1/x
As the value of x increases, the value of y decreases. Invere accomplished.
Simple, elegant, and inverse. If it were a person, she'd be on the cover of People Magazine.
But we want any equation to include the point (-20,2).
Let's see if we can move y=1/x to include (-20,2)
y=(1/x) + b
2 = (1/(-20)) + b
2 = -(0.05) + b
b = 2.05
The equation y = (1/x)+2.05 is an inverse equation that includes point (-20,2).
See the attached graph. Note that when x = 0, the expression (1/x) becomes (1/0). Division by zero is not allowed (undefined). Use caution if in the neighborhood.