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Based on the calculations on these invertible functions, f⁻¹(f(6.022)) is equal to 6.022 and f⁻¹(-10) + f(-6) is equal to -16.
What is an invertible function?An invertible function refers to a type of function that is obtained by reversing the operation of a given function (f(x)).
In Mathematics, a function and its inverse function has the following property f⁻¹(f(x)) = x. By applying this property, we have:
f⁻¹(f(6.022)) = 6.022.
From the table, we have:
f⁻¹(-10) = -6
f(-6) = -10
Therefore, f⁻¹(-10) + f(-6) is given by:
f⁻¹(-10) + f(-6) = -6 - 10
f⁻¹(-10) + f(-6) = -16.
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Related Questions
PLEASE HELP ASAP
:) thank you
Answers
Answer:
(16, 0) should be right.
Step-by-step explanation:
Well, I used to do the math, but after using Acellus a while, I found Symbolab.
It's suuuper handy with Algebra. I highly recommend.
How I found this intercept was enter:
intercept -2x+8y=-32
and bam it lists you all intercepts!
To determine whether a graph of a relation is also a function, Shayla declares that the y-axis is a vertical line and counts the number of times that the graph intersects the y-axis. If the graph has exactly one y-intercept, Shayla concludes that the graph shows a function. In all other cases, she declares that it is not a function.
Is Shayla applying the vertical line test correctly?
No, because the y-axis is a horizontal line.
No, because using the y-axis tests only whether x = 0 is mapped to multiple values.
Yes, because multiple y-intercepts represent multiple x-values being mapped to y = 0.
Yes, because the y-axis represents all vertical lines of the x-values.
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Answer: Choice B
No, because using the y-axis tests only whether x = 0 is mapped to multiple values.
===================================================
Further Explanation:
Shayla stating that the y axis being used to conduct a vertical line test is part of the process. But she needs to move the vertical line around and not have it fixed in place.
If it is possible to have a vertical line (on the y axis or not) pass through more than one point on the curve, then we don't have a function. It is said the curve fails the vertical line test.
Otherwise, the graph passes the vertical line test and we have a function.
The graphs of f(x) and g(x) are shown below: graph of function f of x open upward and has its vertex at negative 7, 0. Graph of function g of x opens upward and has its vertex at negative 7, negative 2. If f(x) = (x + 7)2, which of the following is g(x) based on the translation? (5 points) a g(x) = (x + 9)2 b g(x) = (x + 5)2 c g(x) = (x + 7)2 + 2 d g(x) = (x + 7)2 − 2
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The equation of the function is g(x)=(x+7)² -2 , Option D is the correct answer.
What is a Function ?A function is a mathematical statement that defines relation between two variables.
The f(x) = (x+7)²
The equation for g(x) is ?
graph of function f of x open upward and has its vertex at (-7,0).
Graph of function g of x opens upward and has its vertex at (-7,2).
g(x) is formed by the translation of the function f(x) such that it's vertex is (-7,-2)
Therefore the equation of the function is
g(x)=(x+7)² -2
Therefore , the translation is a shift of the function f(x) 2 units down
Option D is the correct answer.
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Solve for x. Round to the nearest tenth, if necessary
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[tex]\tan 61^{\circ}=\frac{59}{x}\\\\x=\frac{59}{\tan 61^{\circ}} \approx \boxed{32.7}[/tex]
6543549 ² × 4³ ÷8
it also states to simplify to the simplest form
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The simplification form of the provided expression 6543549 ² × 4³ ÷8 is 3.4254×10¹⁴
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have a mathematical expression:
= 6543549² × 4³ ÷ 8
Using BODMAS
= 6543549² × 8
= 3.4254×10¹⁴
Thus, the simplification form of the provided expression 6543549 ² × 4³ ÷8 is 3.4254×10¹⁴
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1.Simplify using suitable properties
(i) 13−51+2
Answers
Answer:
This is my answer:
Step-by-step explanation:
hey! Solving linear equations with integers! i don’t think it should be that hard since it’s practice, I just need some help with a bit more problems! :’)
1) -3 ( 3 - x ) = 2x + 5
2) -6 - 9p = + 3p
3) -5 (-4 - a ) = 3a + 8
4) s - 6 = -5s
that should be it! Ty
Answers
Solution 1 :-
>> -3 (3 - x) = 2x + 5
>> -3 × (3 - x) = 2x + 5
>> -9 + 3x = 2x + 5
>> 3x - 2x = 9 + 5
>> x = 14
Solution 2 :-
>> -6 - 9p = 3p
>> -9p - 3p = 6
>> -12p = 6
>> p = -1/2
Solution 3 :-
>> -5 (-4 - a) = 3a + 8
>> -5 × (-4 - a) = 3a + 8
>> 20 + 5a = 3a + 8
>> 5a - 3a = 8 - 20
>> 2a = -12
>> a = -12 / 2
>> a = -6
Solution 4 :-
>> s - 6 = -5s
>> s + 5s = 6
>> 6s = 6
>> s = 6 / 6
>> s = 1
Answer:
1) x = 14
2) p = - [tex]\frac{1}{2}[/tex] (- 1/2)
3) a = -6
4) s = 1
work shown in image :)
hope this helps!!
easy problem for you guys to solve
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In the ΔIJH, the value of the cosec (I) is [tex]1\frac{9}{56}[/tex].
Given ΔIJH the length of the hypotenuse is 65, the length of the base is 33, and the length of the opposite side is 56.
We have to find the value of the cosec (I).
A function of an arc or angle that is most easily represented in terms of the ratios of pairs of sides of a right-angled triangle, such as the sine, cosine, tangent, cotangent, secant, or cosecant.
We know cosec (I) = hypotenuse / opposite side
Substitute the values
cosec (I) = 65/56
= [tex]1\frac{9}{56}[/tex]
Hence the value of cosec (I) is [tex]1\frac{9}{56}[/tex].
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If k(x) = 5x – 6, which expression is equivalent to (k + k)(4)?
5(4 + 4) – 6
5(5(4) – 6) – 6
54 – 6 + 54 – 6
5(4) – 6 + 5(4) – 6
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What is the measurable quantity given by its formula with the appropriate units
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Answer:
Where is the formula
Step-by-step explanation:
What is equivalent? A B C OR D
please help
Answers
Answer:
[tex]8^{\frac{x}{3} }[/tex]
Step-by-step explanation:
Simplify
21x^6 y^5
14x^2y^9
Answers
Answer:
[tex]\frac{3x^{4} }{2y^{4} }[/tex]
Step-by-step explanation:
Factor out 7 from top and bottom :
[tex]\frac{7(3x^6y^5)}{7(2x^2y^9)}[/tex]
Divide top and bottom by 7 :
[tex]\frac{3x^6y^5}{2x^2y^9}[/tex]
Simplify :
[tex]\frac{x^6}{x^4}=x^{2}[/tex]
Simplify :
[tex]\frac{y^5}{y^9} = y^{-4} = \frac{1}{y^{4} }[/tex]
Collect everything together :
[tex]\frac{3x^{4} }{2y^{4} }[/tex]
Hope this helped and have a good day
A car travels a distance of 210 m in a time of 6 seconds. Calculate the time in seconds for the car to travel a distance of 1928 m.
Answers
Answer:
It will take 55.08 seconds.
Step-by-step explanation:
6 seconds = 210m
1 second = (210÷6)
= 35m
1928m ÷ 35m
=55.08 seconds
Answer = it will take 55.08 seconds to travel 1928m
which graph best represents -8x+2y=18
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See the graph in the image.
tch and his brother, Terry, went on a hiking expedition. Starting at sea level, the brothers climbed to a scenic cliff located 6.6 kilometers above them. From there, they descended 1.3 kilometers in one hour. Mitch discovered that he had left behind some essential supplies on the cliff. So, the brothers decide to head back up. They climbed 0.8 kilometer within the next hour. At this point, Mitch and Terry were
away from the scenic cliff.
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Mitch and Terry were 0.5 km away from the scenic cliff
What is Sea Level ?Sea level is the base for calculating the depth and the elevation of Earth
It is given that
Total Height of the scenic Cliff = 6.6km
After 1 hour the brothers are at = 6.6 - 1.3 km = 5.3 km from the sea level.
They climb back 0.8 km in the next hour so they will be
5.3 +.8 = 6.1 km from the sea level
6.6 - 6.1 = 0.5 km
Therefore the brothers are 0.5 km away from the scenic cliff
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The sides of a square bedroom measure 3.5 yards. if carpet costs $16 per square yard, how much will it cost to cover the floor?if one side of a square notebook measures 20 cm, what is the area of the front cover of the notebook?
Answers
Answer:
£196 and 400cm
Step-by-step explanation:
3.5^2 = 12.25 will give the whole floor
12.25 × 16 = 196
20^2= 400cm is the front cover of the book
Javier is comparing costs of two cars. Car A costs $130 per month for insurance and $0.10 per mile to run. Car B costs $108 per month for insurance and $0.15 per mile to run. He defines x as the number of miles driven each month and y as the total cost to run the car. Which set of equations can be used to find the number of miles Javier would need to drive to make the costs equal?
0.10 x = 130. 0.15 y = 108
y = 0.10 x + 130. y = 0.15 x + 108
0.10 x = 108. 0.15 y = 130
y = 0.15 x + 130. y = 0.10 x + 108
Answers
Answer:
y = 0.10 x + 130. y = 0.15 x + 108
Step-by-step explanation:
0.10 and 0.15 are the slope in the equation y = mx + b since it requires an input (number of miles) to spit out an output (number of miles*0.10 = price) and the x intercept is 130 and 108 creating the equation y = 0.10 x + 130. y = 0.15 x + 108.
help me please grade 5 math fast as possible please
Answers
Answer:
21/4
Step-by-step explanation:
Answer:
[tex]\frac{42}{8}[/tex]
Step-by-step explanation:
• First multiply the numerators:
6 x 7 = 42
• Then multiply the denominators:
(6 doesn't have a denominator, which is the same as having a denominator of 1)
1 x 8 = 8
∴ The answer is [tex]\frac{42}{8}[/tex] .
What is the missing number below in the solution to 968 divided by 10
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Answer: 484/5
Step-by-step explanation:
For this word problem, it seems confusing with the wording but the equation would just be:
968÷10=x
solving for x, we get 484/5.
Which is a valid prediction about the continuous
function f(x)?
Of(x) ≥ 0 over the interval [5, ∞).
Of(x) ≤0 over the interval [-1, %).
Of(x) > 0 over the interval (-∞, 1).
Of(x) < 0 over the interval (-∞. –1).
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33333333333333333333333333333333333
4. What is the slope of the line that passes through the points (2, 7) and (6, 21)? Answer may be in decimal
point. Someone please please help I would really appreciate it
Answers
Answer:
About 3.5
Step-by-step explanation:
To get slope, you essentially need to find the rise (the y values) over run (the x values). You'll most likely see the formula for slope written like this:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
Thankfully, you have the values you need to solve the problem!
x1 = 2
x2 = 6
y1 = 7
y2 = 21
So plugging these numbers in, we get:
[tex] \frac{(21) - (7)}{(6) - (2)} \\ \\ \frac{14}{4} \\ \\ 3.5 [/tex]
[EDIT: I misread 6 as 5. Answer has been updated!]
Explanation:
To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.
To convert a fraction to a decimal, we'll just divide the numerator...by the denominator. In our example, we'll divide 1 by 4. 1 divided by 4 equals 0. To keep dividing, we'll add a decimal point and a zero after the 1
24. Factorise completely the expression: 7x-21+ 2xy - 6y
Answers
Answer:
below
Step-by-step explanation:
7(x-3)+2(xy-3y)
I'm positive it's the correct answer
PLS HELP
What is the relationship between \blueD{\angle a}∠astart color #11accd, angle, a, end color #11accd and \greenD{\angle b}∠bstart color #1fab54, angle, b, end color #1fab54?
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Two angles whose sum is 180° are called supplementary angles. The correct option is C.
What are supplementary angles?Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
In the given Image, ∠a and ∠b are supplementary angles to each other. Therefore, the correct option is C.
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Select all the correct answers.
The diagram shows the construction of two tangent lines to a circle from a point outside the circle.
A circle with a center O. Two tangents, JP and KP are drawn from the same external point P. A horizontal line is drawn from P to O. A vertical line is drawn through the tangent and intersects the horizontal line at M. A line connects JM.
From the diagram, which three statements are true?
- line segment MJ≅ Line segment MP
-∡OJP≅∡OML
-∡OJM≅∡JMO
- line segment OM≅line segment MP
- line segment OJ≅line segment MJ
- line segment LM≅line segment MP
Answers
1) line segment MJ≅ Line segment MP
2) ∡OJP≅∡OML
3) line segment OM≅line segment MP
The below mentioned statements are true according to the figure , Option A, B and D is the correct answer.
What are Tangents ?A line that intersects the curve at a single point at 90 degree is called a tangent.
In the given figure it can be seen that the
∡OJP≅∡OML (right angle)line segment OM≅line segment MP (as M is bisecting the line OP)line segment MJ≅ Line segment MPTherefore , Option A , B and D is the correct answer
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can someone please help me(20 points and I will give brainliest!!!)
Answers
Answer:
a)(0,k)
b)(0,-k)
Step-by-step explanation:
Finding the vertex: Using calculusGiven:
[tex] \begin{cases} y = a {x}^{2} + k \\ y = a {x}^{2} - k \end{cases}[/tex]
Taking the derivative of y's yields
[tex] \begin{cases} y '= \dfrac{d}{dx} a {x}^{2} + k \\ \\ y '= \dfrac{d}{dx} a {x}^{2} - k \end{cases} \\ \implies\begin{cases} y '= 2a x\\ \\ y '=2ax\end{cases} [/tex]
Now set y' to 0 and solve for x:
[tex] \implies\begin{cases} 2a x = 0\\ \\ 2ax = 0\end{cases} \\ \implies\begin{cases} x= 0\\ \\ x= 0\end{cases} [/tex]
plug in the value of x into the original equation thus
[tex] \begin{cases} y = a ({0}^{2}) + k \\ y = a ({0}^{2} )- k \end{cases}\\ \implies \begin{cases} y = k \\ y= - k \end{cases} [/tex]
Hence,
a. vertex (0,k)b. vertex (0,-k)What type of relationship is expressed below?
5x = 2x 9
O equation
O function
O inequality
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Answer:
The answer will be equation
Determine the equation of the line with slope -2 that passes through the point M(-1, -3).
Answers
Answer:
Given:
Let, the slope of the line passing through the point ( m) = -2
The line passing through the point M(-1,-3)= (x1 , y1)
The equation of the line passing through the point M(-1,-3) is
y-y1 = m (x-x1)
or, y-(-3) = -2 (x-(-1))
or, y+3 = -2 (x+1)
or, y+3 = -2x-2
or, 2x+y = -2-3
Hence, 2x+y =-5 is the required equation.
(a) is the correct answer .
(a) By what least number must 27 be divided to make it perfect square
Answers
Answer:
3
Step-by-step explanation:
When you divide 27 by 3 it will give you 9 and the square root of 9 gives you a perfect answer indicating that 3 is the least number that must be divided into 27
Answer:
[tex]\fbox {3}[/tex]
Step-by-step explanation:
First, prime factorize 27 :
⇒ 27 = 3 × 3 × 3
If 27 was divided by 3, it would give 3 × 3, which would give 9, a perfect square.
HELP PLEASE IM BEGGING PLEASEEE I NEED IT NOWWW
Answers
cylindrical-shaped aquarium is to be filled with water for the newly bought salt water fishes. How much salt water is needed if the aquarium has a 2 ft radius of its base and a height of 3 ft?
Volume = πr²h
V = (3.14) (2)² (3)
V = (3.14) (4) (3)
V = 37.68 ft³
37.68 ft³ of salt water is needed to fill the cylindrical aquarium.
Mr. Lee is buying a spherical water tank for his tomato plantation. How much water could be stored if the water tank has a radius of 2 meters?
Volume = (4/3) πr³
V = (4/3) (3.14) (2)³
V = (4/3) (3.14) (8)
V = (4/3) (25.12)
V = 33.493 m³
Mr. Lee can store 33.493 m³ of water in the spherical tank.
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Match the following reasons with the statements to complete the following proof.
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In order to proof that ∠ ABC + m ∠DBE = 180° the correct proof is given as follows:
m ∠CBD - m ∠DBE - Given ∠ABC, ∠CBD are supplementary - Given by the definition of supplementary angels. m ∠ABC + m ∠CBD = 180° - this is is also based on exterior sides in opposite raysm ∠ABC + m ∠DBE = 180° because of the substituted angles.QEDWhat is a supplementary angle?Supplementary angles comprise of angles that are on a straight line and which must add up to 180°
It is right to state therefore, that ∠ABC, ∠CBD are supplementary angels.
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