Please help fastttt
Each graph shows a linear function. Find an equation for it’s inverse and graph it’s inverse. The first one is done for you.
4. 5.
6. Examine the graphs you drew in problems 4 and 5. How does the dotted like y=x relate to the graphs of f(x) and f^-1(x)?
Answers
The inverse of the functions y = x + 3 and y = 2x - 4 are y = x - 3 and
y = (x + 4)/2 respectively.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, A function y = x + 3 or f(x) = x + 3.
Now, To find the inverse of f(x) we'll solve for 'x' in terms of 'y'.
y = x + 3.
x = y - 3.
y = x - 3.
f⁻¹(x) = x - 3.
Again,
y = 2x - 4.
2x = y + 4.
x = (y + 4)/2.
y = (x + 4)/2.
f⁻¹(x) = (x + 4)/2.
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Related Questions
HELP pls will mark you the brainliest. Show your work.
Answers
Answer:
A
Step-by-step explanation:
The answers you have are in (x, y) form
Looking at first answer, -3 is the x and -1/2 is the y. We plug in the -3 as the x in each equation and hope to get -1/2.
So for (-3, -1/2)
y = 1/2(-3) + 1 = -3/2 + 1 = -1/2
Now the other equation
y = 3/2(-3) + 4 = -9/2 + 4 = -1/2
Since we got -1/2 as both. which is also the Y coordinate, this must be the answer. If it wasn't, we could keep going through the answer choices doing the same method.
Which is the better buy? (18 points)
7-pack of T-shirts for $23.02
8-pack of T-shirts for $26.72
Answers
Answer: 7 Pack
Step-by-step explanation: Divide each price by the number of shirts :)
Cindy is buying necklaces. This table shows how the cost depends on
the number of necklaces purchased.
Necklaces 9 10 11 12
Cost ($) 18 20 22 24
What is the constant of proportionality of this relationship?
(label optional)
Answers
Therefore , the solution of the given problem of unitary method comes out to be $2 for one necklace is constant of proportionality of this relationship.
What is a unitary technique, exactly?After determining the size of a small slice, multiply the quantity by two to complete a task using the unitary technique. The simple expression-based unit variable technique aids in separating a coded item from a given group or collection of groups. 40 pens, for instance, would cost 400 Rs (or $1.01 or 400 pounds). It's possible that one country will have total control over the method employed to do this.
Here,
Given :
Necklaces 9 10 11 12
Cost ($) 18 20 22 24
Cost of one necklace = 18/9 =2
$2 for one necklace.
Therefore , the solution of the given problem of unitary method comes out to be $2 for one necklace is constant of proportionality of this relationship.
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10 in
12 in
10 in
3 in
Answers
Step-by-step explanation:
10in×10in×3in×3in×12in=2172
Discussion: Quadratic Functions
Consider a quadratic function in forms of f(x) = ax^2 + bx + c. How many real zeros can it have? How many complex zeros can it have? How does each case relate to its graph?
To find its zeros you can use two different methods. What are they? When would it be appropriate to use one method over the other?
Answers
1. There are two real zeros, one real zero, or two complex conjugate zeros, depending on the discriminant of the quadratic formula, which is b² - 4ac.
2. This formula gives the two zeros of the quadratic function. You can use the quadratic formula when factoring is not possible or not easy to do.
Quadratic FunctionsA quadratic function in the form of f(x) = ax² + bx + c can have either two real zeros, one real zero, or two complex conjugate zeros, depending on the discriminant of the quadratic formula, which is b² - 4ac.
If the discriminant is positive, meaning b² - 4ac > 0, then the quadratic function has two real zeros, since the quadratic formula gives two distinct real roots. The graph of the function will intersect the x-axis at two distinct points.
If the discriminant is zero, meaning b² - 4ac = 0, then the quadratic function has one real zero with a multiplicity of two, which means the graph will touch the x-axis at one point but not cross it.
If the discriminant is negative, meaning b² - 4ac < 0, then the quadratic function has two complex conjugate zeros. The graph will not intersect the x-axis, but it will have a minimum or maximum point called the vertex.
To find the zeros of a quadratic function, you can use two different methods: factoring and the quadratic formula.
Factoring is an efficient method if the quadratic expression can be factored easily. For example, if the expression is in the form of x² + 5x + 6, it can be factored as (x + 2)(x + 3), and the zeros are x = -2 and x = -3.
The quadratic formula is another method to find the zeros of a quadratic function. This formula can be used for any quadratic expression, regardless of whether it can be factored or not. The quadratic formula is:
x = (-b ± √(b² - 4ac)) / 2a
This formula gives the two zeros of the quadratic function. You can use the quadratic formula when factoring is not possible or not easy to do.
In general, factoring is quicker and simpler when it is possible, but the quadratic formula is always reliable and will give the zeros in any case.
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Mohamed and Zayed are playing DMZ on Warzone 2.0, during 1 match, Mohamed completes 6 more objectives than Zayed. Together they completed 14 objectives. Write and solve and equation to determine how many objectives each of them completed, write only your answer for each in the boxes below.
Answers
Answer:
Mohamed: 8 objectives
Zayed: 6 objectives
Saul makes trail mix with peanuts, raisins, and pretzels. The ratio of cups of raisins to cups of peanuts is 1 to 6. The ratio of cups of pretzels to cups of raisins is 3 to 1. Decide if each statement describing the trail mix is true or false. Choose True or False for each statement.
1.) "Saul uses 6 times as many cups of peanuts as cups
of raisins."
2.) "Saul uses 3 times as many cups of raisins as cups
of pretzels."
3.) "The ratio of cups of peanuts to cups of pretzels is 3 : 6."
4.) "Saul uses 2 times as many cups of peanuts as cups
of pretzels."
Answers
The following statements describing the trail mix;
1.) "Saul uses 6 times as many cups of peanuts as cups of raisins."True
2.) "Saul uses 3 times as many cups of raisins as cups of pretzels."False
3.) "The ratio of cups of peanuts to cups of pretzels is 3 : 6."False
4.) "Saul uses 2 times as many cups of peanuts as cups of pretzels."False
Which statement is true or false?The ratio of cups of raisins to cups of peanuts is 1 to 6.
The ratio of cups of pretzels to cups of raisins is 3 to 1.
Check all that applies;
1.) "Saul uses 6 times as many cups of peanuts as cups of raisins."
True
2.) "Saul uses 3 times as many cups of raisins as cups of pretzels."
False
3.) "The ratio of cups of peanuts to cups of pretzels is 3 : 6."
False
ratio of cups of peanuts to cups of pretzels = 6 : 3
4.) "Saul uses 2 times as many cups of peanuts as cups of pretzels."
False
Hence, the statement can be true if the ratio is correct.
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In a library 3 out of 4 books are nonfiction. of the nonfiction books. 40% are biographies. The Library has a total of 840 books.
Answers
Answer:
so your telling me that you need the answer to a question? how about you answer my queston first. how much wood could a wood chuck chuck if a wood chuck could chuck wood?
Step-by-step explanation:
ANSWER IT RN.
Ed is on a road trip. He has already traveled 211 miles and is driving at a rate of 63 miles per hour. Which equation could be used to find how many hours, x, Ed has left in his road trip if he is traveling 638 total miles?
Answers
Therefore , the solution of the given problem of linear equation comes out to be 683 = 211 + 63x option c is correct.
A linear equation is precisely what?A straightforward regression curve is created using the equation y=mx+b. The y-intercept is m, and the slope is B. The previous sentence is usually referred regarded as a "mathematical formula integrating multiple variables," even though y or y are different parts. Only two variables are present in bivariate linear equations. There are no known solutions to application issues involving linear equations. Y=mx+b.
Here,
Distance already traveled by Ed 211 miles
Also, Ed is driving at a rate of 63 miles per hour.
Distance Speed × Time
Distance traveled by Ed in x hours = 63x
Total distance traveled by Ed= 211 + 63x
Also, total distance traveled by Ed is 638 miles.
Therefore,
=> 683 = 211 + 63x
or
x =7.49
Thus , option c is correct.
Therefore , the solution of the given problem of linear equation comes out to be 683 = 211 + 63x option c is correct.
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The complete question is "Ed is on a road trip. He has already traveled 211 miles and is driving at a rate of 63 miles per hour. Which equation could be used to find how many hours, x, Ed has left in his road trip if he is traveling 638 total miles? A. 211x + 638 = 63 B. 211x + 63 = 638 C. 63x + 211 = 638 D. 63x + 638 = 211"
England and Scotland both produce scones and sweaters. Suppose that an English worker can produce 40 scones per hour or 1 sweater per hour. Suppose that a Scottish worker can produce 20 scones per hour or 2 sweaters per hour. _____________ workers have an absolute advantage in producing scones, _______________ workers have an absolute advantage in producing sweaters.
Answers
English workers have an absolute advantage in producing scones, Scottish workers have an absolute advantage in producing sweaters.
How to get workers with absolute advantage?English workers have an absolute advantage in producing scones as they can produce 40 scones per hour,
while Scottish workers can only produce 20 scones per hour. On the other hand, Scottish workers have an absolute advantage in producing sweaters as they can produce 2 sweaters per hour, while English workers can only produce 1 sweater per hour.
Absolute advantage refers to the ability of a country or individual to produce a good or service more efficiently than another country or individual.
This means that the country or individual with the absolute advantage is able to produce the same good or service with fewer resources or in less time. In this case, each country has an absolute advantage in producing one of the goods, scones or sweaters.
Thus,English workers have an absolute advantage in producing scones, Scottish workers have an absolute advantage in producing sweaters.
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pls help plssssss
it would really help
Answers
The size of the angle YZX is 19.7 degrees.
How to find the angles of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, let's find the angle YZX in the right triangle as follows:
Hence using trigonometric ratios,
sin ∠Z = opposite / hypotenuse
sin ∠Z = 7.5 / 22.3
sin ∠Z = 0.33632286995
∠Z = sin⁻¹ 0.33632286995
∠Z = 19.6530010139
Therefore,
∠YZX = 19.7 degrees.
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A company's weekly profit in pesos is determined by the function P(×)=ײ( × + 100 ) ( × + 300 ) where × represent the number of branches it operates. How much profit does the company make in a week if it operates 10 branches
Answers
P(10) = 10^2(10 + 100)(10 + 300) = 10^2 * 110 * 310
= 10,000 * 110 * 310
= 3,310,000 pesos
So, the company makes 3,310,000 pesos in a week if it operates 10 branches
HELP pls will mark you the brainliest
Answers
The equation for the total cost is y = 2x + 20
How to write an equation for the total cost?Since we are to multiply the number of kites by 2 and add 20 to get the cost at Windy kites.
The table can be filled as follows:
Kite purchased Tota cost
4 (2*4) + 20 = 28
7 (2*7) + 20 = 34
10 (2*10) + 20 = 30
The equation for the total cost can be written as:
y = 2x + 20
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Please help me with this ?
The supplement of an angle is 36 less than the supplement of the complement of the
angle. What is the measure of the angle? Show your work as clearly as you can!
Answers
The measure of the angle is 54 degrees.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Let the measure of the angle "x".
The complement of the angle is 90 - x.
The supplement of the complement is 180 - (90 - x) = 90 + x.
The supplement of the angle is 36 less than the supplement of the complement of the angle, so 90 + x - 36 = x.
90 + x - 36 = x
54 = x
So the measure of the angle is 54 degrees.
Hence, the measure of the angle is 54 degrees.
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A circle has central angle 144° and its arc length is 4 units. the radius of the circle is?
Answers
The radius of the circle is 20/π units or approximately 6.37 units.
To find the radius of the circle given its central angle and arc length, we can use the formula:
arc length = radius * central angle
In this case, we have:
arc length = 4 units
central angle = 144°
Plugging these values into the formula, we get:
4 units = radius * 144°
To solve for the radius, we need to convert the angle from degrees to radians, as the formula requires the angle to be in radians.
1 radian = 180°/π
So, 144° = (144/180) * π radians
Simplifying, we have:
144° = (4/5) * π radians
Now we can rewrite the formula using radians:
4 units = radius * (4/5) * π radians
Solving for the radius, we divide both sides of the equation by (4/5) * π:
radius = (4 units) / ((4/5) * π)
Simplifying further, we can multiply the numerator and denominator by 5 to cancel out the fraction:
radius = (20 units) / π
Thus, the radius of the circle is 20/π units or approximately 6.37 units.
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Please help I have a learning disailty and this is due today.
To find the area of a triangle you use the formula A = 1/2
bh where b stands for the base and h is the height.
Find the area of the triangle drawn below.
The area of the triangle is inches squared _____________________
Answers
The area of the triangle is 12 inches squared.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
From the figure,
Base = 8 in
Height = 3 in
Now,
Area = 1/2 x base x height
Area = 1/2 x 8 x 3
Area = 12 in²
Thus,
12 inches squared is the area of the triangle.
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if a researcher is very confident that changes in the independent variable caused changes in the dependent variable, the study is said to have
Answers
The independent variable caused changes in the dependent variable, then the Pearson’s Correlation Coefficient must be close to either +1 or -1
In order to determine if changes in an independent variable cause changes in a dependent variable, the researcher must use a measure of correlation. The most commonly used measure of correlation is Pearson’s Correlation Coefficient (r). This coefficient measures the strength and direction of the linear relationship between two variables. It can range from -1 to +1 and can be calculated using the formula r = (Σxy) / (√Σx2 * √Σy2).
The value of r indicates the strength of the relationship between two variables. A value of 0 indicates no correlation, a value of 1 indicates a perfect positive correlation, and a value of -1 indicates a perfect negative correlation. The closer the coefficient is to +1 or -1, the more confident the researcher can be that changes in the independent variable caused changes in the dependent variable. If the researcher is very confident that changes in the independent variable caused changes in the dependent variable, then the Pearson’s Correlation Coefficient must be close to either +1 or -1.
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compete question:
What is Pearson's Correlation Coefficient and how is it used to measure the strength of the relationship between two variables?
help me. the problem is in the pic
Answers
The anchor dropped at a rate of -1.8 meters per second.
The time it took to reach the water's surface is given as follows:
30 seconds.
What is the relation between velocity, distance and time?The relation between velocity, distance and time states that the velocity is obtained by the quotient of the distance by the time, as follows:
v = d/t.
In which the parameters are given as follows:
v is the velocity.d is the distance.t is the time.The anchor fell 63 meters in 35 seconds, hence the velocity is given as follows:
v = -63/35
v = -1.8 meters per second. (negative means that it is a drop).
The time needed to fall down 54 meters an reach the water's surface is given as follows:
1.8 = 54/t
t = 54/1.8
t = 30 seconds.
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on day 0, there are 500 barteria in a dish. the number of bacteria doubles every day after that. how many bacteria(y) are there after x days?
Answers
The number of bacteria that represents y at the end of x days will be [tex]y=(500)(2)^{x}[/tex]
As per the given data on the day 0, there are 500 bacteria in a dish.
The number of bacteria that doubles every day after that.
Here we have to determine that how many bacteria which represent y are there after x number of days.
Therefore, the number of bacteria after every day will form a geometric progression (G.P) with the first term as a = 500 and the common ratio as r = 2
Therefore [tex]\mathrm{a}_3=\mathrm{ar}^2=(500)(2)^2=2000[/tex]
Therefore, the number of bacteria at the end of 2nd day will be 480
[tex]$a_5=a^4=(500)(2)^4=8000[/tex]
And [tex]$\mathrm{a}_{\mathrm{n}+1}=\mathrm{ar}^{\mathrm{n}}[/tex]
[tex]$\mathrm{a}_{\mathrm{n}+1}[/tex] represents y and n represents x
[tex]y=(500)(2)^{\mathrm{x}}[/tex]
Thus the number of bacteria at the end of x days will be [tex](500)(2)^{x}$=y[/tex]
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two histograms share a horizontal axis indicating the range of the data in the two samples. the first histogram is entirely to the left of the second. which statements are true?
Answers
The two statements that are true are that the two histograms have different ranges of data and different distributions of data.
The first statement that is true is that the two histograms have different ranges of data. To calculate the difference in range, you can use the formula Range = Maximum - Minimum, where Maximum is the largest value in the sample, and Minimum is the smallest value in the sample. This means that if the maximum value of the first histogram is, say, 10 and the minimum value of the second histogram is 15, the difference in range between the two histograms is 5. The second statement that is true is that the two histograms have different distributions of data. This can be determined by looking at the shape of the histograms. For example, if the first histogram is clustered around a certain range of values, while the second histogram is more evenly distributed, this would indicate two different distributions.
So, in summary, the two statements that are true are that the two histograms have different ranges of data and different distributions of data.
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Nolan is following his family's macaroni and cheese recipe. The recipe calls for 6 cups of shredded
cheese and 4 tablespoons of milk. He wants to make a smaller batch, so he uses only 3 cups of
shredded cheese.
How much milk does Nolan need for this smaller batch?
tablespoons
Answers
Answer:2 tablespoons of milk
Step-by-step explanation:
If nolan divides 6 by 2 he gets 3 cups of shredded cheese and to get the same results he would have to divide the milk portion too. 4/2 is 2 so he would need 2 tablespoons of milk.
What is the volume of this cylinder?
Use ≈ 3.14 and round your answer to the nearest hundredth.
Answers
substitution, pls help!
Answers
By using the substitution method, the solution to the given system of equations include the following:
x = -9.
y = 36.
How to solve this system of equations?In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:
y = -2x + 18 .......equation 1.
y = -4x .......equation 2.
By using the substitution method to substitute equation 1 into equation 2, we have the following:
-2x + 18 = -4x
By re-arranging and collecting like terms, we have the following:
-4x + 2x = 18
-2x = 18
x = -18/2
x = -9
For the value of y, we have the following:
y = -4x
y = -4(-9)
y = 36.
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Find the probability of taking out the king from a well shuffled pack of 52 cards
Answers
Answer:
1/13
Step-by-step explanation:
There are 52 cards in a deck, there are 4 suits and a king in each suit.
That makes 4 kings in a deck of cards.
P(king) = number of kings/ total cards
= 4/52 = 1/13
Answer:
1/13
Step-by-step explanation:
in 52 cards there was 4king
so ＝4/52
simplify ＝1/13
suppose that for budget planning purposes the city in exercise 12 needs a better estimate of the mean daily income from parking fees. a) someone suggests that the city use its data to create a 95% confidence interval instead of the 90% interval first created. how would this interval be better for the city?
Answers
A 95% confidence interval is wider than a 90% confidence interval and so provides a better estimate of the population mean.
A confidence interval represents the range of values within which the population mean is estimated to lie with a certain degree of confidence. The wider the interval, the more certain we can be that the population mean lies within it. In other words, a 95% confidence interval provides a better estimate of the population mean than a 90% interval because it is wider and therefore more likely to contain the true population mean.
This increased accuracy is particularly important for the city in their budget planning as it allows them to make more informed decisions based on a more reliable estimate of their expected daily income from parking fees.
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What is 22.3 × 1.8 ?
Answers
Answer:
40.14
Step-by-step explanation:
Answer: 40.14
Step-by-step explanation:
40.14
Graph the first four terms in the sequence 12, 6, 3, 1
Answers
According to the information, the correct way to graph this sequence is by putting the numbers 1, 2, 3, 4 as x coordinates... Then the coordinates would be (1,12), (2,6), (3,3 ) and (4,1).
How to graph the sequence?To graph the sequence we must establish an additional coordinate for each of the values. In this case we can put the value of 1, 2, 3, 4...
According to the above, the coordinates would be as follows:
(1,12)(2,6)(3,3)(4.1)Additionally, this graph would be a geometric sequence because it expresses values that are decreasing and is not a constant.
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eeeeeeeeeeeeeeeee3eeeeee
Answers
Answer:
23e+3
Step-by-step explanation:
Answer:
Step-by-step explanation:
7 1/4 rounded to nearest 1/4 hour
Answers
The required round of 7 /14 to the nearest 1/4 is itself 7 1/4.
What is rounding of values?The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.
Here,
7 1/4 rounded to the nearest 1/4 hour is 7 1/4. Rounding to the nearest 1/4 hour means finding the closest 1/4 hour mark, which in this case is 7 1/4 itself.
Thus, the required round of 7 /14 to nearest 1/4 is itself 7 1/4.
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6. the sun of the digits of a certain two digit number is 6. if the original number is subtracted from the number formed by interchanging the digits, the result is 36. find the original number
Answers
let the unit place digit be x and tens place digit be y, therefore, the original number is 15.
then the two-digit number will be 10y + x
and the number formed by interchanging the unit place and tens place digits will be 10x + y
according to the first condition given in the qs i.e, the sum of two digits in the number is 6 that is
x + y = 6
Also given that, if the original number is subtracted from the number formed by interchanging the digits, the result is 36.
i.e 10y +x - 10x -y = 36
9(y-x) = 36
y-x = 36/9
y-x = 4 and x+y = 6
solving both the above equations we will get ,
x= 1 and y = 5
since original number is 10y + x = 10(1) + 5
therefore, the original number is 15.
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