Answers
In order to find the inverse of a function, the first step is "replace f(x) with y".
Then, the second step is "swap x and y".
The third step is "solve for y".
And finally, the fourth step is "change y to f^-1(x)".
For example, let's find the inverse function of f(x) = 2x:
[tex]\begin{gathered} f(x)=2x \\ y=2x \\ x=2y \\ y=\frac{x}{2} \\ f^{-1}(x)=\frac{x}{2} \end{gathered}[/tex]Related Questions
What is the range of the following relation?{(-3, 3), (1, 1), (0, -2), (1, -4), (5, -1)}
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What is the range of the following relation?
{(-3, 3), (1, 1), (0, -2), (1, -4), (5, -1)}
The range is
[tex]\lbrace3,1,-2,-4,-1\rbrace[/tex]The graph of y=√x is reflected over the y-axis and then translated down 2 units to form f(x). Which is the graph off(x)?$ 10-10-88 10 x
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We must apply some transformations to the function:
[tex]y=g(x)=\sqrt[3]{x}.[/tex](1) A reflection across the y-axis is given by the transformation:
[tex]g(x)\rightarrow h(x)=g(-x)=\sqrt[3]{-x}=-\sqrt[3]{x}.[/tex](2) A translation down 2 units is given by the transformation:
[tex]h(x)\rightarrow f(x)=h(x)-2=-\sqrt[3]{x}-2.[/tex]Plotting the function f(x), we get the following graph:
Answerwrite -6/11×3/4 in lowest terms.-6/136/139/22-9/22
Answers
In order to multiply two fractions we just multiply each side of the fraction:
Then, in this case:
[tex]-\frac{6}{11}\cdot\frac{3}{4}=\frac{-6\cdot3}{11\cdot4}=\frac{-18}{44}[/tex]Since 18 and 44 are pair numbers, but can be divided by 2, then we divide both:
[tex]-\frac{18}{44}=-\frac{9}{22}[/tex]Answer: D -9/22
(6x+31-9=0
3X+34-320
Answers
Answer:
X= - 154/3
Step-by-step explanation:
A gardener has a bag of flower seeds. Half of the seeds are roses, one fourth are gardenias,
and one fourth are irises.
a. P(gardenias)
b. P(not gardenias)
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The numbers of students in the 9 schools in a district are given below. (NOTE THAT THESE ARE ALL ALREADY IN ORDER FROM LEST TO GREATEST)
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Given:
The data is:
240,256, 307, 310, 325, 333, 359, 363, 378
Required:
If the number 378 changes to 261 then
(a) What happens to the median
(b) What happens to the mean
Explanation:
(a)The number of terms = 9
Median = 5th term
Median = 325
if the term 378 changed to 261 then the data will be:
240,256, 261 307, 310, 325, 333, 359, 363
Median = 310
Thus the median is decreasing.
Decreased value = 325 - 310 = 15
(b) Mean is given by the formula:
[tex]mean=\frac{sum\text{ of observation}}{Total\text{ number of observation}}[/tex][tex]\begin{gathered} mean\text{ = }\frac{240+256+307+310+325+333+359+363+378}{9} \\ mean\text{ =}\frac{2871}{9} \\ mean\text{ =319} \end{gathered}[/tex]if the term 378 changed to 261 then
[tex]\begin{gathered} mean=\text{ }\frac{240+256+307+310+325+333+359+363+261}{9} \\ mean=\text{ }\frac{2754}{9} \\ mean=\text{ 306} \end{gathered}[/tex]Thus the mean is decreasing.
Decreased value = 319 - 306 = 13
Final answer:
(a) median is decreased by 15
(b) mean is decreased by 13
A car rental company charges $15 per day and $0.55 per kilometer to rent a car. What is the total bill if a car is rented for 4 days and is driven 146 kilometers?
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the total bill is $140.30
Use the diagram below to find x x = 34x = 32x = 30x = 28
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Given the following question:
Given the image below, identify the value of x. 9 2x - 19 M
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You have the the length of segment NK is 23.
Furthermore, you have that segment NK is the sum of the following segments:
NK = NM + ML + LK
Each of the previous segments are given by the following algebraic expressions:
NM = x - 6
ML = 9
LK = 2x - 19
You sum the previous expression, by taking into account that the result is 23. Then you solve for x, just as follow:
NM + ML + LK = NK
(x - 6) + (9) + (2x - 19) = 23 eliminate parenthesis
x - 6 + 9 + 2x - 19 = 23 simplify similar terms
x + 2x - 6 - 19 + 9 = 23
3x - 16 = 23 add 16 both sides
3x = 23 + 16
3x = 39 divide by 3 both sides
x = 39/3
x = 13
Hence, the solution for x is x = 13
ahmed want to make a triangle, he has rods that measure 9 inch and 15 inches. the rods cannot be cut. which is the length of a rod he could use to complete the triangle?
Answers
The length of the rod that he could use to complete the triangle is 12 inches. This is solved based on the principle of Pythagorean Triples.
What are the Principles of Pythagorean Triples?Pythagorean triples are a collection of three positive numbers that fit into the Pythagorean theorem formula, which is written as a² + b² = c², where a, b, and c are positive integers. In this case, 'c' is the 'hypotenuse,' or the triangle's longest side, while 'a' and 'b' are the other two legs of the right-angled triangle.
Pythagorean triples are denoted as (a,b, c). The most well-known Pythagorean triple example is (3, 4, 5). We can see that the numbers 3, 4, and 5 meet the equation a² + b² = c².
To prove that the length of the rod that should be used to complete the triangle is 12. Let's subject the values to the Principles of Pythagorean Triples.
Given:
9,
let's assume that 15 is the longest side.
Thus,
If we are correct,
9² + 12² should equal 15²
9² = 81
12² = 144
15² = 225
81 + 144 =225
Hence the length of the rod that must be used to complete the triangle is 12 inches.
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Prove that the following four points will form a rectangle when connected in orderby showing the diagonals are congruent. Show all work.AIO. -3). B(-4.0). C(2. 8). D(6. 5)
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SOLUTION
For the four points to form a rectangle, the length of the diagonals will be equal.
This means that we have to find the distance between the point BD and AC. If
BD = AC, then the four points would form a rectangle.
[tex]\begin{gathered} Dis\tan ce\text{ betw}ee\text{n points B and D, that is BD} \\ \text{Distance betw}ee\text{n two points = }\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ BD=\text{ }\sqrt[]{(6-(-4)^2+(5-0)^2} \\ BD=\sqrt[]{10^2+5^2} \\ BD=\sqrt[]{125} \\ BD=\text{ 5}\sqrt[]{5} \end{gathered}[/tex]Now let's find AC
[tex]\begin{gathered} AC=\text{ }\sqrt[]{(2-0)^2+(8-(-3)^2} \\ AC=\sqrt[]{2^2+11^2} \\ AC=\sqrt[]{4+121} \\ AC=\sqrt[]{125} \\ AC=5\sqrt[]{5} \end{gathered}[/tex]So, since BD = AC, the four points A, B, C and D would form a rectangle.
A T-shirt company has determined that the profit it makes from a new T-shirt design can be modeled by the quadratic equation below:y = -100(x - 9)(x - 17)Where x represents the price of a T-shirt in dollars and y represents the company profit in dollars.According to this model, how much should the T-shirt company charge if they want to maximize their profit.Round your answer to the nearest penny.
Answers
Given data:
The expression for the profit function is y=-100(x-9)(x-17).
Differentiate teh above expressionn and equate to zero, in order to maimize the profit function.
[tex]\begin{gathered} \frac{dy}{dx}=0 \\ -100\frac{d}{dx}(x-9)(x-17)=0 \\ -100(x-9)\frac{d(x-17)_{}}{dx}-100(x-17)\frac{d(x-9)}{dx}=0 \\ -100(x-9)-100(x-7)=0 \\ -100(x-9+x-7)=0 \\ 2x=16 \\ x=8 \end{gathered}[/tex]Thus, 8 T-shirts must be sold in order to maximmize tthe profit.
The weight of 8 eggs is 496 grams. Identify the constant of proportionality of total weight to number of eggs.
Group of answer choices
60
56
62
58
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What is the first point you would graph the function 3x+1/2y=2
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First, let's clear y to get the slope-intercept form:
[tex]\begin{gathered} 3x+\frac{1}{2}y=2 \\ \\ \rightarrow6x+y=4 \\ \Rightarrow y=-6x+4 \end{gathered}[/tex]This way, we can conclude that the y-intercept is 4. This is the first point we have to graph:
[tex](0,4)[/tex]Can you someone solve for x
-2x + -3 = 1x
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Answer: x = -3/2
Step-by-step explanation:
Equation:
x -2x + -3 = 1x
Combine Like Terms:
x - 2x + -3 = 1x
-x - 3 = 1x
+x +x
[tex]-3 = 2x[/tex]
[tex]\frac{-3}{2} = \frac{2x}{2}[/tex]
-3/2 = x
The ages of the people on the bus are 24, 38, 47, 29, 51, 44, 40, 31, 36, and 43. If a bus passenger is selected at random, what is the probability that he or she is younger than 30?
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We want to know the probability of a passenger to be younger than 30.
There are 10 persons on the bus and out of those, just 2 are younger than 30.
Denote by E the event: "obtaining a person younger than 30 when its selected at random from the bus". Then,
[tex]P(E)=\frac{\text{number of persons younger than 30}}{\text{total persons on the bus}}=\frac{2}{10}=\frac{1}{5}=0.2[/tex]This means that the probability of a passenger to be younger than 30 is 0.2.
which integer could represent the fact that the water level of a pool decreases by 4 feet
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-4
1) In this question, there's not much information so let's think of a rule
2) We can sketch this out:
We could even write a function that describes this, which "W" stands for Water Level and "t":
3) So if the level of water is decreasing by 4 feet each and every water level from now on is negative.
Please help with math problem FAST
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The percent error in his calculation is 13.04%
How to find percent error?He calculated the object will take 2.3 seconds to fall on the ground.
It takes 2.5 seconds for the object to fall.
Therefore, the percent error can be calculated as follows:
percent error = | theoretical value - experimental value | / theoretical value × 100
Therefore,
percent error = |2.3 - 2.5| / 2.3 × 100
percent error = 0.3 / 2.3 × 100
percent error = 0.3 × 100 / 2.3
percent error = 30 / 2.3
percent error = 13.0434782609
Therefore,
percent error = 13.04 %
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can i get some help on this one?
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Answer:
[tex](x+9)^2=-4[/tex]Step by step explanation:
Completing the square is where we take a quadratic equation like this:
[tex]\begin{gathered} ax^2+bx+c=0 \\ \text{ and turn it into this:} \\ a(x+d)^2+e=0 \end{gathered}[/tex]Where d and e can be represented by the following expressions:
[tex]\begin{gathered} d=\frac{b}{2a} \\ e=c-\frac{b^2}{4a} \end{gathered}[/tex]Since we have the following equation:
[tex]\begin{gathered} x^2+18x+74=-11 \\ x^2+18x+85=0 \end{gathered}[/tex]So, for a=1, b=18 and c=85.
Find d and e:
[tex]\begin{gathered} d=\frac{18}{2}=9 \\ e=85-\frac{18^2}{4}=4 \end{gathered}[/tex]Then, the result for completing the square would be:
[tex]\begin{gathered} (x+9)^2+4=0 \\ (x+9)^2=-4 \end{gathered}[/tex]you have 20oz of egg noodles. You need 5oz to make one of chicken noodle soup how many service can you make
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Okay. You have 20 oz of egg noodles.
You need 5 oz to make one of chicken noodle soup,
Then I can make 20 / 5 = 4 services
For 4.5 lb,
I6 ounces = 1 pound.
4. 5 x 16 ounces = 4.5 lb= 72 ounces
Then, we have 8 oz per serving.
Then we can have 72/8 = 9 services.
4.5 x 16 / 8 = 72/8 =9 servings
Okay. 2 tbsp = 1 serving
18 tbsp = (18 x 1) / 2 = 9 servings
Find the equation of the line that passes through the two points (2, -1) and (5, 5). Write your answer in standard form.
Answers
Explanation
Given the points two points (2, -1) and (5, 5) we can find the equation of a line using the point-slope formula.
[tex]\begin{gathered} y_-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ Where\text{ x}_1,y_1=2,-1 \\ x_2,y_2=5,5 \end{gathered}[/tex]Therefore, we will have;
[tex]\begin{gathered} y-(-1)=\frac{5-(-1)}{5-2}(x-2) \\ y+1=\frac{6}{3}(x-2) \\ y+1=2(x-2) \\ y+1=2x-4 \\ 2x-y=1+4 \\ 2x-y=5 \\ \end{gathered}[/tex]Answer: 2x-y=5
A new road is being constructed parallelto the train tracks through point V. An equation of the line representing thetrain tracks is y = 2x.Find an equation of the linerepresenting the new road.
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the equation of the line representing the new road will be 2 x - y + 7 = 0.
The line is:
y = 2 x.
The slope of the line is:
m = 2
Now, the point V is:
V = (- 2, 3)
Since the train track is parallel to the line, its slope will be:
m' = 2 ( slope of parallel lines are equal)
So, the equation of the new road line will be:
y - y₁ = m (x - x₁)
y - 3 = 2 ( x + 2)
y - 3 = 2 x + 4
2x - y + 7 = 0
Therefore, the equation of the line representing the new road will be 2 x - y + 7 = 0.
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the ratio of the measures of three angles of a triangle is 3:6:1. Find the measurements of each angle
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Gabe, you are doing great. Now you need to solve for x:
3x + 6x + x = 180
10x = 180
dividing by 10 at both sides:
10x/10 = 180/10
x = 18 That is the answer you have.
Finally, you need to multiply the ratio for the value of x, you just calculated:
Side 1 = 3 * 18
Side 2 = 6 * 18
Side 3 = 1 * 18
If p and q vary inversely and p is 19 when q is 16, determine q when p is equal to 8.
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The value of q solving with variation method is 38
How to calculate the value of q ?Variation van be described as the relationship between a set of variable. We will be applying inverse variation to solve the question
The value of q can be calculated by using variation method
p= k/q
The first step is to calculate the constant k
19= k/16
cross multiply both sides
k= 19 × 16
k= 304
Since the value of k is 304, then the value of q can be calculated as follows
p = k/q
8= 304/q
cross multiply both sides
8q= 304
q= 304/8
q= 38
Hence the value of q when the value of p is 8 is 38
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3. Use the slope and y-intercept to complete thetable of values with solutions that includeonly integers. (1 point total)y=2x-3=xу
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given the equation:
y = 5/4x - 3
to complete the table for the values of x and y using intergers
fristly,
when x = -4
y = 5/4(-4) - 3
y = -5 - 3
y = -8
when x = 0
y = 5/4(0) - 3
y = 0 - 3
y = -3
when = 4
y = 5/4(4) - 3
y = 5 - 3
y = 2
when x = 8
y = 5/4(8) - 3
y = 5(2) - 3
y = 10 - 3
y = 7
so completing the table:
y = 5/4x - 3
x y
-4 -8
0 -3
4 2
8 7
You are dealt one card from a standard 52-card deck. Find the probability of being dealt a 9 and an 8
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The probability to being a 9 and an 8 from a standard 52 - card deck
will be;
⇒ 2 / 13
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
The total number of cards = 52
Number of a 9 dealt = 4
Number of a 8 dealt = 4
Now,
Total number of cards = 52
And, Number of dealt a 9 and an 8 card = 4 + 4
= 8
Since, Probability = Number of dealt a 9 or 8 / Total number of cards
Thus, The probability of being dealt a 9 and an 8 will be;
= 8 / 52
= 2 / 13
Therefore, The probability to being a 9 and an 8 from a standard 52 - card deck will be;
⇒ 2 / 13
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find the volume of a conebase diameter of 10 ydheight 6 ydsuse the value 3.14 for pie
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Given
The formula
[tex]\begin{gathered} \text{The volume of a cone =}\frac{1}{3}\pi r^2h \\ \\ \pi=3.14 \\ r=5 \\ h=6 \end{gathered}[/tex][tex]\begin{gathered} \text{The volume of a cone =}\frac{1}{3}\pi r^2h \\ \text{The volume of a cone =}\frac{1}{3}\times3.14\times5^2\times6 \\ \\ \text{The volume of a cone =}\frac{1}{3}\times3.14\times25^{}\times6 \\ \\ \text{The volume of a cone =}\frac{1}{3}\times3.14\times150 \\ \\ \text{The volume of a cone =}3.14\times50 \\ \\ \text{The volume of a cone =}157yd^3 \end{gathered}[/tex]The final answer
[tex]\text{The volume of a cone =}157yd^3[/tex]Hi, can you help me to solve this exercise, please!!
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Based on the statement, we can deduce that cot(θ) must be negative as θ is in the fourth quadrant.
We have to find the ratio between the adjacent leg and the opposite leg knowing that the ratio between the hypotenuse and the opposite leg is -(√638)/22.
Using the pythagorean theorem for this purpose, we have:
[tex]\begin{gathered} (\sqrt[]{638})^2=22^2+a^2\text{ (Given that the sum of the squares of the legs must be equal to the square of } \\ \text{ the hypotenuse)} \end{gathered}[/tex][tex]\begin{gathered} 638=484+a^2\text{ (Raising the numbers to the power of 2)} \\ 154=a^2(\text{ Subtracting 484 from both sides of the equation)} \\ \sqrt[]{154}=a\text{ (Taking the square root of both sides)} \end{gathered}[/tex][tex]\begin{gathered} \text{ The ratio between the adjacent leg and the opposite leg would be: } \\ \frac{\sqrt[]{154}}{22} \end{gathered}[/tex]Given that cot(θ) must be negative the answer would be:
[tex]\cot \mleft(\theta\mright)=-\frac{\sqrt[]{154}}{22}[/tex]I need some help on number 4...Also, was my answer right for number 5, I believe it is..
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In order to find the solution of this system of equations, we need to find the ordered pair that is a solution to both equations.
To do so, let's use the value of x from every option and calculate the corresponding value of the functions:
[tex]\begin{gathered} x=0\colon \\ f(0)=\sqrt[]{0+4}=2 \\ g(0)=0-4=-4 \\ \\ x=1.6\colon \\ f(1.6)=\sqrt[]{3.2+4}=2.68 \\ g(1.6)=1.6^3-4=0 \\ \\ x=-1.3\colon \\ f(-1.3)=\sqrt[]{-2.6+4}=1.18 \\ g(-1.3)=(-1.3)^3-4=-6.2 \\ \\ x=1.9\colon \\ f(1.9)=\sqrt[]{3.8+4}=2.8 \\ g(1.9)=(1.9)^3-4=2.8 \end{gathered}[/tex]So the correct option is the fourth one.
Gravel is being dumped from a conveyor belt at a rate of 40 ft/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast (in ft/min) is the height of the pile increasing when the pile is 5 ft high?
(Round your answer to two decimal places.)
The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm/s) when the diameter is 40 mm? (Round your answer to two decimal places.)
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The formula Wh = Rs + Q, where Q stands for total energy losses experienced upon impact, can be used to represent any of the five fundamental types of dynamic pile drive formulas now in use.
Calculate dynamic pile ?
Fixed Formula
Maximum load a pile or set of piles (group pile) can support (Qu)
Depending on the soil's properties
Qu=Qp+Qs
Maximum failure load
Qp is the pile's point resistance.
Qs is the shaft resistance caused by rubbing between the pile and the dirt.
Load (Q) (Q)
Qp
QsQs.
Given diameter
height = h = ft(say)
radius = r =h/2
volume =v =1/3πr²h =1/3π(h/2)²h
=1/3π(h²/4)(h)
=1/12πh³
dv/dt = 1/12π(3h²dh/dt)
dv/dt = π/4 h² dh/dt
here dv/df =40ft³ and h =5ft
40 = π/4 (5² dh/dl
=40*4/100π
= 160/100π
=8/5π
So, the height is increasing at the rate of (8/5π) ft/min.
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