The probability that at least two of the balls have the same number is 27.40%
What is probability?Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.
Probability requested is equivalent to:
P(at least 2 have same number) = 1 - P(no 2 have the same number)
P(no 2 have same number) = No. of ways to succeed / No. of possible outcomes
No. of ways to succeed = 90P8
No. of possible outcomes = 90^8
No. of ways to succeed =
nPr = n! / (n-r)!
90P8 = 90! / (90-8)!
90P8 = 90! / (82)!
90P8 = 90*89*88*87*86*85*84*83*82! / [(82)!
90P8 = 90*89*88*87*86*85*84*83
90P8 = 3.13x10^15
P(no 2 have same number) = 3.13x10^15 / 90^8
P(no 2 have same number) = 0.73
P(at least 2 have same number) = 1 - P(no 2 have the same number)
P(at least 2 have same number) = 1 - 0.73
P(at least 2 have same number) = 0.2740 = 27.40%
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The air temperature of a mountain drops by 2 ℃ for every 500 m of elevation. If the air temperature is 26 ℃ at the base of the mountain, at what elevation will the air temperature be 16 ℃ ?
At the height of 2500 m, the temperature will be T = 16 ℃.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that air temperature of a mountain drops by 2 ℃ for every 500 m of elevation. If the air temperature is 26 ℃ at the base of the mountain, at what elevation will the air temperature be 16 ℃.
2 ℃ for every 500 m of elevation.
Then, for 1 m of elevation, it will change by (2/500) or (1/250) ℃
We can write the function as -
T{x} = 26 - {x/250}
Now, for T = 16 ℃, we can write -
26 - {x/250} = 16
26 - 16 = x/250
10 = x/250
x = 2500 m
Therefore, at the height of 2500 m, the temperature will be T = 16 ℃.
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please help thank you :)
Answer:
Without exponents: a * a * a * a * a
Fill in the blank: [tex]a^5[/tex]
Step-by-step explanation:
We have to use exponent rules:
[tex]x^y * x^y = x^{y+y} \\= x^{2y}[/tex]
So for this problem, we can apply that rule here:
[tex]a^3 * a^2 = a^{3+2}[/tex]
= [tex]a^5[/tex]
^ This will be the answer to the second question.
Now, to find the equation without exponents, we can use the information we have from above. We need to use this rule: [tex]x^2 = x * x[/tex]
Since our equation is [tex]a^5[/tex], we can rewrite it as a * a * a * a * a.
Find x for the picture
Answer:
x = 20
Step-by-step explanation:
Because these are alternate interior angles, 2x+20 and 3x are equivalent to each other. Therefore, we can set up this equation:
2x+20 = 3x
Now, we can solve this equation and find x:
20 = 3x-2x
x = 20
These provided angle measures (3x and 2x + 20) are a pair of alternate interior angles because they satisfy the following required conditions:
The two angles must lie on the inside of the parallel lines.The two angles must lie on the opposite sides of the transversal.Since the two angles ARE alternate interior angles, they are EQUAL! Therefore, we can equate the two angles and solve for the variable (x).
{2x + 20 is equal to 3x} ⇒ 2x + 20 = 3x
Process in solving the linear equation:The key step in solving the linear equation is to ISOLATE the variable completely by removing the coefficient until you have 1 as the coefficient.
There are 4 possible ways to isolate the variable:
If you have a negative integer/variable as the coefficient, you can divide the negative integer/variable on both sides of the equation. If you have a positive integer/variable as the coefficient, you can divide the positive integer/variable on both sides of the equation. If your variable is added by a positive integer/variable, you can subtract the same integer/variable on both sides of the equation. If your variable is added by a negative integer/variable, you can add the same number/variable on both sides of the equation.Once your variable is completely isolated, simplify (if possible) on the other side of the equation. If the opposite side of the variable is simplified, you can conclude your solution for the linear equation.
Solving the Linear equationNow, let us solve the equation using the above step by step processes.
⇒ 2x + 20 = 3x (Given equation)Isolating the variable from the constant(s) on the R.H.S:
⇒ 2x + 20 - 2x = 3x - 2xSimplify both sides of the equation:
⇒ 20 = xTherefore, the solution to the linear equation (x) is 20.
__________________________________________________________
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What expressions are equivalent to 6g - 18h?
Choose 2 answers
A: (g - 3) x 6
B: 2 x (3g - 18h)
C: 3(2g - 6h)
D: (-g - 3h)(-6)
E: -2 x (-3g + 9h)
The expression that is equivalent is options D. (-g - 3h)(-6) and E. -2(-3g + 9h)
What is factorization?Factorization is a process in which a given term is reduced to its lowest form by comparing common divisible number, or alphabet.
Considering the given expressions, that one that will be equivalent to 6g - 18h can be determined by;
i. 6g - 18h
factor out 6 to have;
6g - 18h = (g - 3h)6
= (-g - 3h)(-6)
ii. 6g - 18h
The common divisor is 2, so that;
6g - 18h = 2(3g - 9h)
minus sign can be factor out
2(3g - 9h) = -2(-3g + 9h)
So that on expansion, the initial expression in the question can be gotten.
Therefore, the expression that are equivalent are (-g - 3h)(-6) and -2(-3g + 9h)
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escribe two different ways to find the slope of a function and two different ways to find the y-intercept of a function
Order of operations with fractions and exponents
Evaluate the expression.
Do not round your answer.
2
3²
Stuck? Review related articles/videos or use a hint.
Report a problem
Step-by-step explanation:
you did not provide an expression. only fragments, I suspect.
I can give you the basic rules.
always remember the order of operations :
1. brackets
2. exponents
3. multiplications and divisions
4. additions and subtractions
a fraction is a division.
e.g. 2/3 = 2 divided by 3
e.g. (a/b)⁵ = a⁵/b⁵
(a×b)⁵ = a⁵×b⁵
e.g. a^-b = 1/(a^b)
e.g. a^(c/b) =
[tex] \sqrt[b]{ {a}^{c} } [/tex]
I think that is all about exponents and fractions.
Han and Leia plan on renting a 1050SQFT apartment. In order to do this, they
have the following fees: $150 application desposit, $15 credit report, Security
deposit equal to 1 month's rent, Last AND first month's rent, Broker's fee that
is 12% of the yearly rent. If 1 month's rent is $1350, howmuch should Brian
and Jamie plan on spending when they sign their lease?
The amount that Brian and Jamie have to plan on spending should be: $4859.
How to solve for the amount that should be spentThe security deposit is equal to 1 month's rent, which is $1350.
The first and last month's rent is also $1350, so that's a total of $2700 for the first and last month's rent and the security deposit.
The broker's fee is 12% of the yearly rent, which is $1350 x 12 = $16,200.
12% of $16,200 is $1944.
So in total, they will have to pay $150 application deposit + $15 credit report + $2700 + $1944 = $4859.
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Can someone help with this
y = 4x is the only function that represents the proportionality.
What is proportionality?the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given there are Few functions, we need to find which of the given function is proportional:
Since, We know that only the linear functions that pass through the origin are proportional.
So only function that provides the value of y at x = 0 is 0 will shoe properties of proportionality
Therefore, only function that is proportional is y = 4x.
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To predict the performance of her first period class on their next quiz, á teacher randomly selects eight students from the class and takes the mean of their scorés on the last quiz. Is this sample representative of the class's performance on the quiz? Explain your reasoning.
It's important to note that even if the sample is random, there's still a chance that the sample may not be representative of the population, this is known as sampling error.
What does reason mean?
The fundamental act of thinking about anything logically and sensibly is best described as reasoning.
It depends on how the teacher choose the class members. Because every student had an equal chance of being chosen, the sample, if the students were chosen at random, is likely to be indicative of the class' performance on the quiz. However, the sample would not be indicative of the class's performance on the quiz if the teacher arbitrarily chose the students, for instance, by selecting only the best or the worst performers.
In general, if a sample is large enough and random, it is thought to be representative of the population. The likelihood that the sample is representative of the population rises with greater sample sizes. Since only 8 students were chosen in this instance, it's possible that the results don't accurately reflect how the entire class did on the quiz.
The term "sampling error" refers to the possibility that a sample, even one drawn at random, may not be representative of the population as a whole.
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Divide. Write the quotient in lowest terms. 5\dfrac{2}{3} \div 4 =5 3 2 ÷4=5, start fraction, 2, divided by, 3, end fraction, divided by, 4, equals
The quotient for the given division of fractions [tex]5\dfrac{2}{3} \div 4[/tex] is 17/12.
We are given the equation - [tex]5\dfrac{2}{3} \div 4[/tex]
First we will convert the mixed fraction 5\dfrac{2}{3} in to improper fraction as follows -
[tex]5\dfrac{2}{3}[/tex] [tex]= \frac{3*5+2}{3}[/tex]
[tex]5\dfrac{2}{3}[/tex] [tex]= \frac{17}{3}[/tex]
Now we will divide the fraction as follows -
[tex]5\dfrac{2}{3} \div 4[/tex]
= 17/3 ÷ 4
taking the reciprocal of 4 and changing the divide sign into multiplication we get,
= 17/3 x 1/4
= 17*1 / 3*4
= 17/12
Hence, the quotient for the given division of fractions is 17/12.
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selena would like to learn a new language. to gauge how common it is for people to know more than one language, she asks 10 of her friends how many languages they speak. she compiles the responses in the table below. languages spoken 2 1 1 1 2 3 1 2 1 1 use a calculator to create a relative frequency distribution for the data. what is the relative frequency of her friends who speak more than one language?
The relative frequency of Selena's friends who speak more than one language is 3/16 or 0.1875
To create a relative frequency distribution, we first need to find the total number of responses by summing up the number of languages spoken by Selena's friends. In this case, the total number of responses is 2 + 1 + 1 + 1 + 2 + 3 + 1 + 2 + 1 + 1 = 16.
Next, we need to find the relative frequency for each category, which is the number of responses in that category divided by the total number of responses. To find the relative frequency of her friends who speak more than one language, we need to add up the number of responses in categories 2, 3, and above.
In this case, the number of responses in category 2 is 2, the number of responses in category 3 is 1, and there are no responses above 3.
So the relative frequency would be (2+1)/16 = 3/16 or 0.1875
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Consider the quadratic function y = mx².
When a > 0, the graph
When a < 0, the graph
When a > 0, the graph opens upward
When a < 0, the graph opens downward
How to complete the statementsFrom the question, we have the following parameters that can be used in our computation:
The quadratic function y = mx²
The variable represents the leading coefficient
i.e. a = m
As a general rule:
Equations with negative leading coefficients open downwards, while other open upwards
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judes water balloon is empty but filling up at a rate of 5 ml per second. Ian's water balloon contains 45ml of water of water and is losing 10 mL of water per second.
Write an equation to represent y, the amount of water in each balloon based on x, the number of seconds.
Jude:
Ian:
Answer:
Jude: y = 5x
Ian: y = 45 - 10x
Step-by-step explanation:
Jude:
y = 5x
Ian:
y = 45 - 10x
let , and be arithmetic progressions. if and , then what is ? let , and be arithmetic progressions. if and , then what is ?
An arithmetic progression (AP) is a sequence of numbers such that the difference between any two consecutive terms is always the same.
This common difference is called the common ratio of the arithmetic progression. The general form of an arithmetic progression is a, a + d, a + 2d, ..., where a is the first term and d is a common difference.
The nth term of an arithmetic progression can be found by using the formula: a_n = a + (n-1)d, where a is the first term, d is a common difference, and n is the position of the term in the progression.
If a, b, and c are in arithmetic progression, then the common difference is (b-a) = (c-b).
If d, e, and f are also in arithmetic progression, then the common difference is (e-d) = (f-e).
If a, d are the same and b, e are the same, then c = f.
so the common difference between both progressions is the same, and c = f
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let , and be arithmetic progressions. if and , then what is ? let , and be arithmetic progressions. if and , then what is the common difference
Question What is the radical form of each of the given expressions? Drag the answer into the box to match each expression. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
The radical form for each expression is given as follows:
[tex]5^{\frac{2}{3}} = \sqrt[3]{5^2}[/tex][tex]5^{\frac{1}{2}} = \sqrt{5}[/tex][tex]3^{\frac{2}{5}} = \sqrt[5]{3^2}[/tex][tex]3^{\frac{5}{2}} = \sqrt{3^5}[/tex]How to obtain the radical form of each expression?The general format of the exponential expression is given as follows:
[tex]a^{\frac{n}{m}}[/tex]
To obtain the radical form, we have that:
a is the radicand.n is the exponent.m is the root.Hence the radical form of the exponential expression is given as follows:
[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]
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Determine which integers in the set S:{−40, −10, 20, 40} will make the inequality one fifth times the difference of m and five is less than or equal to one tenth times the difference of m and twenty false
Answer: The inequality one fifth times the difference of m and five is less than or equal to one tenth times the difference of m and twenty can be rewritten as:
(1/5)(m-5) <= (1/10)(m-20)
To find the integers in the set S that will make this inequality false, we need to find the values of m that do not satisfy it. We can start by simplifying the inequality:
(1/5)(m-5) <= (1/10)(m-20)
(1/5)m - (1/5)5 <= (1/10)m - (1/10)20
(1/5)m <= (1/10)m - (1/10)20 + (1/5)5
(1/5)m <= (1/10)m - 2 + (1/5)5
(4/5)m <= (1/5)5 - 2
m <= -5
So, the integers in the set S that do not satisfy the inequality are 20 and 40. These integers will make the inequality false.
Step-by-step explanation:
PLEASE HELPPPPPPPP.
The value of x would be √2.
What is the 45-45-90 triangle?
A 45-45-90 triangle is a special type of right triangle where the angles measure 45 degrees, 45 degrees, and 90 degrees. The sides of the triangle are in a specific ratio to each other. The hypotenuse, or the longest side of the triangle, is the same length as the other two sides (the legs). This side length is also equal to the square root of 2 times the length of either leg. The legs of the triangle are congruent to each other. This triangle is also known as an "isosceles right triangle".
In the given figure, we can apply a 45-45-90 triangle,
side opposite to 45 = 1/√2 * Hypotenuse
x = 1/√2 * 2
x = √2
Hence, the value of x would be √2.
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2. The function f is defined as f(x) = - 4x³ - 4x². What is f(-4)
A. -320
B. -192
C. 16
D. 192
E. 320
Find the values of x and y.
Answer:
x = 7 , y = 4
Step-by-step explanation:
the triangle on the right has 3 congruent angles and is therefore equilateral with 3 congruent sides, so
3x - 5 = 5y - 4 → (1)
the triangle on the left has 2 congruent angles and is therefore isosceles with the 2 legs being congruent, so
3x - 5 = y + 12 → (2)
we have 2 equations with 3x - 5 on the left side so equate the right sides
5y - 4 = y + 12 ( subtract y from both sides )
4y - 4 = 12 ( add 4 to both sides )
4y = 16 ( divide both sides by 4 )
y = 4
Then
5y - 4 = 5(4) - 4 = 20 - 4 = 16 , so
3x - 5 = 16 ( add 5 to both sides )
3x = 21 ( divide both sides by 3 )
x = 7
(3x + 12 + 2x³ + x²)/(x + 2)
Answer: If your simplifying it's: 2x (power of 3) + x (power of 2) + 3x + 12x +2. Dividing would be 2x (power of 2) − 3x + 9 − 6/x+2. Have a nice day ;)
Please Help!
I don't understand how to work out this question.
∠XBC is 55 degrees because it is corresponding to ∠AXY..
The angle ∠BXC is 70 degrees
How to find angles in parallel lines?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, same interior angles, vertically opposite angles etc.
Therefore, XY and BD are parallel lines.
XB = XC
ΔXBC is an isosceles triangle.
Therefore, ∠XBC is 55 degrees because it is a corresponding angle to ∠AXY.
Let's find ∠BXC.
Therefore, the base angles of an isosceles triangle are congruent.
Hence,
∠XBC = ∠BCX = 55 degrees
Therefore,
55 + 55 + ∠BXC = 180
110 + ∠BXC = 180
∠BXC = 180 - 110
∠BXC = 70 degrees
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An iron rod of length 10.38 ft is bent to form a circle. What is the radius of the circle?
The radius of circle for the given length of rod is found as 1.65 ft
Define the term perimeter of the circle?The border or entire arc length of a circle's perimeter is known as its perimeter. A circle's circumference is the term used to describe its edge.The radius of circle serves as one of the three variables in the perimeter of such a circle formula, along with two constants. The formula for calculating a circle's circumference or perimeter is as follows:Perimeter of circle = 2 π r
In which,
r = radius of the circleπ = 3.14When the length of the rod is bent to form the circle.
Length of rod = Perimeter of circle
10.38 = 2 π r
r = 10.38 / 2 π
r = 1.65
Thus, the radius of the circle for the given length of rod is found as 1.65 ft.
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Fran swims at 2. 2 mph in still water. The Lazy River flows at a speed of 0. 6 so how long will it take her to go 2. 4 mi upstream and 2. 4 mi downstream?
If Fran swims at 2.2 mph in still water and Lazy River flows at a speed of 0.6 mph , the the time required by Fran to go 2.4 mi upstream is 1.5 hours and 2.4 mi downstream is 0.857 hours .
the speed of Fran in still water (rate) = 2.2 mph ;
the sped of the river (current) is = 0.6 mph ;
The time taken by Fran to swim 2.4 miles upstream and 2.4 miles downstream can be calculated by formula :
⇒ time = distance/(rate + current) ;
the distance to be covered is = 2.4 miles ;
For the time taken by Fran to swim upstream , the speed of current is subtracted from the Speed of Fran ;
So , time = 2.4/(2.2-0.6) = 2.4/1.6 = 1.5 hours
For the time taken by Fran to swim downstream, the speed of current is added to the Speed of Fran ;
So , time = 2.4/(2.2 mph + 0.6) = 2.4/2.8 = 0.857 hours
Therefore , by Fran it will take 1.5 hours to travel 2.4 miles upstream and 0.857 hours to travel downstream .
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35 less than a number m is -72
The required simplified value of the m is given as -37. as of the given information.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
According to the question, we have variable m, and 35 less than m is -72
m - 35 = -72
Add 35 on both sides
m = -72 + 35
m = -37
Thus, the required simplified value of the m is given as -37.
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The perimeter of the floor in an office building is 127. 5 feet. What is the perimeter of the floor in the office building in yards?
The perimeter of the floor of the office building which was given as 127.5 feet is equal to 42.5 yards.
Perimeter of the floor in an office building is equal to 127.5 feet.
Convert perimeter of the floor of the given office building in feet into yards:
Number of feet in one yard = 3 feet
3 feet = 1 yard
⇒ 1 feet = ( 1 / 3 ) yard
⇒ 127.5 feet = ( 127.5 ) × ( 1 / 3 ) yards
⇒127.5 feet = ( 127.5 / 3 ) yards
⇒127.5 feet = ( 42.5 ) yards
Therefore, the perimeter of the floor of the given office building is equal to 42.5 yards.
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For a set of data, r = 0.27. Which is true about the correlation of the variables?
• The variables have a strong positive correlation.
• The variables have a weak negative correlation.
The variables have no correlation.
O The variables have a weak positive correlation.
The sign of r is positive and there is a positive and weak correlation.
What is Statistics ?
In statistics, association is any statistical relationship, whether causal or not, between two random variables or bivariate data. One is independent and other is dependent variable.
In the broadest sense correlation is any statistical association, though in common usage it most often refers to how close two variables are to having a linear relationship with each other.
Examples are exercise and sickness are negatively correlated.
Study hours and marks are positively correlated
When correlation is nearer -1 or +1 there is a strong correlation. When correlation is nearer to 0 than to 1 or -1 we say that there is a negative correlation.
Hence, The sign of r is positive and there is a positive and weak correlation.
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What are the domain and range of f(x) =7?
Answer:
C
Step-by-step explanation:
tara can develop 2 rolls of film in about 18 minutes. at this rate, how long will it take her to develop 8 rolls of film?
1 hour and 12 minutes is the time that will it take her to develop 8 rolls of film.
According to the question,
Tara develops 2 rolls of film in about 18 minutes.
Tara develops 1 roll of film in about = (18 ÷2) minutes
= 9 minutes (using division)
Tara develops 8 rolls of film in about = ( 8 × 9) minutes
= 72 minutes
we know that, 1 hour = 60minutes
Tara can develop 8 rolls of film in about = (72 ÷ 60)
= 1 hour 12 minutes
So, Tara can develop 8 rolls of film in about 1 hour and 12 minutes.
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26. In the diagram below, what must be the
measure of the angle marked x?
39
62
Please help
The angle denoted by the letter x is an inscribed angle created by the intersection of the chords AC and BD, as can be seen.
What is meant by angle?Corner, whether it be a protruding element or a section of an enclosed space. the pattern created by two lines that diverge from the same point.
a measurement of an angle or the degree of rotation necessary to parallelize or align two angled lines or planes.
An angle in planar geometry is a form created by two rays or lines that have a common termination. The English word "angle" derives from the Latin word "angelus," which means "corner."
The vertex, which serves as the joint terminus of two rays, and the two rays are known to as the sides of an angle and an angle, respectively.
Our goal is to determine the size of the angle denoted by the x:
We may use the chord theorem formula because we can see that the angle denoted with x is an inscribed angle created by the intersection of the chords AC and BD.
x = BC + AD / 2
By replace BC with 39 and AD with 62, we get:
x = 39 + 62/2
x=50.5°
Therefore, measure of the angle marked x=50.5°
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The inverse of a relationship can be found by
switching the coordinates in each ordered pair. Complete the table for three
input and output values of y = x + 3 and its inverse. Then use the table to
write an equation of the inverse of y = x + 3.
y=x+3
Input (x)
Output (y)
Inverse of y=x+3
Input (x)
Output (y)
The equation of the inverse of y = x + 3 is y = x - 3.
What is inverse relationship?The theory used in this question is the concept of inverse relationships. In mathematics, an inverse relationship is a relationship where two variables are related in such a way that when one variable increases, the other decreases.
In this case, the relationship between x and y is represented by the equation y = x + 3.
To find the inverse of this equation, we need to switch the coordinates in each ordered pair, which is done by subtracting 3 from the output (y) for each ordered pair.
This gives us the equation y = x - 3, which is the inverse of y = x + 3.
y=x+3
Input (x) Output (y)
3 6
-1 2
5 8
Inverse of y=x+3
Input (x) Output (y)
6 3
2 -1
8 5
The equation of the inverse of y = x + 3 is y = x - 3.
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