3.
Write an equation for the inverse function for each one-to-one function.
a. k(x)=58-2
x+10
b. h(x) =
x-3
need some help
Answers
Answer:
a) k(x) = 5x - 2
x = 5(y) - 2
5y = x + 2
y = (x+2)/5
k-¹(x) = (x+2)/5
b) h(x) = (x+10)/(x-3)
x = (y+10)/(y-3)
x(y-3) = y + 10
xy -3x = y + 10
xy - y = 3x + 10
y(x-1) = 3x + 10
y = (3x + 10)/(x-1)
h-¹(x) = (3x+10)/(x-1)
Related Questions
Find the missing dimension of the cone.
Volume = 118π ft3
2/3 ft
h =_ft
Answers
The height of the cone with a volume of 1/18π ft³ is: 1.5 ft.
What is the Volume of a Cone?Volume of a cone = 1/3πr²h, where, h = height of cone, and r = radius of the cone.
Given the following:
Volume = 1/18 π ft³Diameter = 2/3 ftRadius = (2/3)/2 = 1/3 ftHeight (h) = ?Plug in the values into the volume formula:
1/18π = 1/3π(1/3)²h
1/18π = 1/3π(1/9)h
1/18π = (πh)/27
Divide both sides by π
1/18 = h/27
Cross multiply
27 = 18h
27/18 = h
h = 1.5
Therefore, the height of the cone with a volume of 1/18π ft³ is: 1.5 ft.
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A circle has a radius of 5.4 m. what is the exact length of an arc formed by a central angle measuring 60°? enter your answer in the box. express your answer using π . m
Answers
The length of the arc of the circle with a radius of 5.4 m and the central angle measuring 60° is 5.655 meters.
What is the Length of an Arc?The length of an arc is given by the formula,
[tex]\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360}[/tex]
where
θ is the angle, which arc creates at the centre of the circle in degree.
The length of the arc of the circle with a radius of 5.4 m and the central angle measuring 60° can be written as
[tex]\text{Length of the Arc} = 2\pi r \dfrac{\theta}{360}[/tex]
[tex]= 2 \times \pi \times 5.4 \times \dfrac{60}{360}\\\\=5.655\rm\ m[/tex]
Hence, the length of the arc of the circle with a radius of 5.4 m and the central angle measuring 60° is 5.655 meters.
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A swimmer speeds up 1.9 m/s to 3.8 m/s during the last 11.0 seconds of the race. What is the acceleration of the swimmer?
Answers
Initial speed (v) = 1.9m/s
Final speed (u) = 3.8m/s
Time (t) = 11 s
Formula Used :-[tex]v = u + a×t [/tex](a = acceleration)
➾ [tex]a = {\frac{u-v}{t}}[/tex]
Solution:-[tex]a = {\frac{u-v}{t}}[/tex] (putting the value of v, u and t from above)
➾ [tex]a = {\frac{3.8-1.9}{11}}[/tex]
➾ [tex]a = {\frac{1.9}{11}}[/tex]
➾ [tex]a = 0.17 m/s (approx.)[/tex]
Therefore, the acceleration rate = 0.17m/s.
A flower pot is approximately in the shape off a cylinder. The diameter is 10 inches and the height is 6 inches. Find the surface area off the flower pot round to the nearest inch
Answers
The surface area of the cylindrical flower pot to the nearest inch is equal to [tex]346\;in^2[/tex]
Given the following data:
Diameter = 10 inches.
Height = 6 inches.
Radius = [tex]\frac{diameter}{2} =\frac{10}{2}[/tex] = 5 inches.
How to calculate surface area.Mathematically, the surface area (SA) of a cylinder is given by this formula:
[tex]S.A = 2\pi rh + 2\pi r^2[/tex]
Where:
h is the height.r is the radius.Substituting the given parameters into the formula, we have;
[tex]S.A = 2\pi (5)(6) + 2\pi (5)^2\\\\S.A =188.52+157.1 \\\\S.A = 345.62\\\\S.A=346\;in^2[/tex]
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Can someone please help me
Answers
Answer:
Hence corre ctophon is (A)
help pls
ty in advance
Answers
[tex]\bold{\huge{\underline{ Solution\: 2 }}}[/tex]
The name of the circle is IJKLThe name of central Angle[tex]\sf{\underline{= {\angle} IHJ }}[/tex]The name of the secant = KL[tex]{\bigstar}[/tex]Circle :- It is a round figures, which has no end points.
[tex]{\bigstar}[/tex] Central angle :- It the angle ,which lie in the middle of the circle.
Here, H is the mid point of the circle .So, Angle IHJ is the central angle.[tex]{\bigstar}[/tex] Secant :- A line drawn in circle in such a way that it intersect the circle from two distinct points. Then, It is called secant .
Here, KL is the line which acts as a secant because it intersect the circle from point K and point L.[tex]\bold{\huge{\underline{ Solution\: 3 }}}[/tex]
Semicircle = FGH and FIH Minor Arc :- FG or GH Major Arc :- FHG or GFH[tex]{\bigstar}[/tex] Semicircle :- Semicircle is nothing but the half of the circle.
Here, In second diagram
FGH and FIH are acting as two semicircles which simulatineously forming one circle.[tex]{\bigstar}[/tex] Minor Arc :- Minor Arc is nothing but the smaller arc of the circle and it is always smaller than the half of the circle that is semicircle.
Here,
FG or GH are the minor arc of the given circle.[tex]{\bigstar}[/tex] Major Arc :- Major Arc is nothing but the largest arc of the circle and it is always larger than the half of the circle that is semicircle.
Here,
FHG or GFH is the major arc as it is larger than the semicircle of the given circle .One of the logo meets the building requirements. Explain which logo meets the biulding requirements and why.
Answers
The logo that meets the building requirement must be:
Aesthetically appealingVisually accurate at all sizesMust be memorableRelated to the value being delivered.What are logos in art?A Logo in art is a visual symbol, that an organization selects as one of the primary visual identifiers of its brand.
They are first conceptualized, then built or created after much consultation with graphic and marketing professionals.
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Mar 31, 2:56:59 PM
Ryan needed to get his computer fixed. He took it to the repair store. The technician
at the store worked on the computer for 3.75 hours and charged him $192 for parts.
The total was $398.25. Which equation could be used to represent
the context if x represents the cost of labor per hour?
Answers
The area of the squared garden is 625 sq. m, what is its perimeter ? (Ans: 100 m)
Answers
Answer: Area of square = a*a(where a is length of one side) Putting value a x a=625 cm2 a= 25 Perimeter will be 4 x a 4 x 25 = 100 cm
Step-by-step explanation:
[tex]\sf\huge\underline{Given:-}[/tex]
Area of the square field [tex]\sf{= 625 m^2}[/tex]
[tex]\sf\huge\underline{To\: Find:-}[/tex]
[tex]\rightarrow[/tex] Perimeter of the square garden.
[tex]\sf\huge\underline{Formula \:Used:-}[/tex]
Area of square [tex]\sf{= side^2}[/tex]
Perimeter of square [tex]\sf{= 4×side}[/tex]
[tex]\sf\huge\underline{Solution:-}[/tex]
As we know,
[tex]\rightarrow[/tex] Area of square [tex]\sf{= side^2}[/tex](putting the given value of area)
[tex]\rightarrow[/tex] [tex]\sf{Side^2}[/tex] [tex]\sf{= 625}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{Side}[/tex][tex]\sf{= \sqrt{625}}[/tex]
[tex]\rightarrow[/tex][tex]\sf{Side}[/tex][tex]\sf{= 25cm}[/tex]
So, From here we got the side of the square garden that is, 25cm.
Now,
[tex]\rightarrow[/tex]Perimeter of square [tex]\sf{= 4×side}[/tex](Putting the value of side)
[tex]\rightarrow[/tex] Perimeter of square [tex]\sf{= 4×25}[/tex]
[tex]\rightarrow[/tex]Perimeter of square [tex]\sf{= 100cm}[/tex]
Therefore, perimeter of the square garden = 100cm.
There are 8 fluid ounces in 1 cup...
Answers
Answer: 4 cups
Step-by-step explanation:
First, convert the 6 cups of water to fluid ounces:
6 cups (8 fluid ounces / 1 cup) = 48 fluid ounces.
Then, since each bowl took 4 fluid ounces, and there are 4 bowls, the total fluid ounces used must be 16.
Thus, if there was 48, and 16 were used, 32 fluid ounces must be left. Convert this to cups by dividing by 8 and getting 4 cups.
Please help 10 POINTS!!!
Answers
Would be ur answer!!
Hope u have a great day beautifulll
Step-by-step explanation:
[tex]y = 5x \\ y = 9x + 4 \\substitute \:y = 5x \: to \: the \: other \: equation \\ y = 9x + 4 \\5x = 9x + 4 \\ 5x - 9x = 4 \\ - 4x = 4 \\ x = \frac{4}{ - 4} \\ x = - 1[/tex]
A cylinder has a base diameter of 16cm and a height of 20cm. What is its volume in cubic cm, to the nearest tenths place?
Answers
Answer:
4021.76
Step-by-step explanation:
v= πr^2h
3.142x8×8×20
A bag contains 30 cookies: 9 vanilla, 9 chocolate, and 12 oatmeal. What is the probability that a chocolate is randomly selected
Answers
Answer:
30% for chocolate
Step-by-step explanation:
9÷30= 30% 0.3 vanilla
9÷30=30% 0.3 chocolate
12÷30=40% 0.4 oatmeal
The probability of choosing chocolate is 0.30.
What is the probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
Number of total cookies = 30
Number of vanilla = 9
Number of chocolate = 9
Number of oatmeal = 12
The probability that chocolate is randomly selected is;
Probability of choosing a chocolate = Number of chocolate / Number of total cookies
Probability of chosen a chocolate = 9 / 30
Probability of chosen a chocolate = 3 / 10
Probability of chosen a chocolate = 0.30
Hence, the probability of choosing chocolate is 0.30.
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Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. Its current value is $2,000. The equation mc025-1. Jpg represents the situation, where t is the age of the car in years and r is the rate of depreciation. About how old is Devon’s car? Use a calculator and round your answer to the nearest whole number. 1 year 2 years 5 years 8 years.
Answers
The age of the car that Devon purchased is given by: Option C: 5 years
How to calculate compound interest's amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
[tex]CI = P(1 +\dfrac{R}{100})^T - P[/tex]
The final amount becomes:
[tex]A = CI + P\\A = P(1 +\dfrac{R}{100})^T[/tex]
We can use compound interest's formula (with a bit modification if necessary) whenever there is compounding on a base amount on some fixed rate for some time.
For this case, there is decrement happening, so rate can be taken negative. Thus, we take:
R = -35%
Let the car is T years old.
Then, as we have: Initial price of the car = P = $16000, and the final price of the car = A = $2000, thus, we get:
[tex]A = P(1 +\dfrac{R}{100})^T\\\\2000 = 16000(1 + (-35/100) )^T\\1/8 = (1-0.35)^T\\0.125 = 0.65^T\\\\T = log_{0.65}(0.125)\\T \approx 4.827 \approx 5 \text{ (in years) }[/tex]
Thus, the age of the car that Devon purchased is given by: Option C: 5 years
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Answer:
C 5 years
Step-by-step explanation:
Write your answers using set notation.
Answers
Answer:
domain = {-8, -6, 8}
range = {-4, -1, 0, 8}
Step-by-step explanation:
The domain is the set of first numbers of the ordered pairs. The range is the set of second numbers. We generally like to have the elements of a set arranged in order, with duplicates eliminated.
domain = {-8, -6, 8}
range = {-4, -1, 0, 8}
a kite is 50 m high when 200 m of sting is let out. what angle does the kite string make with the ground to the nearest tenth of a degree?
the angle between the kite string and the ground is ?
Answers
Check the picture below.
Make sure your calculator is in Degree mode.
Im deseperate. Find x, y, and z such that x³+y³+z³=k, for each k from one to 100
Answers
Answer:
x = 1, y = -1, and z = 2
HELPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
(-3,8)
step by step explanation:
y=-4/3 +4
x=-3
put in x value in first Problem
y=-4/3(-3) +4
solve
y= 12/3+4
y=4+4
y=8
we already know what x is so
x= -3, y=8
(-3,8)
hope this helps
which equation is equivalent to the expression (-2x to the power of two) (3x to the power of 5)?
A. 6x to the power of 7
B. -6x to the power of 10
C. 6x to the power of 10
D. -6x to the power of 7
Answers
Answer: pretty sure the answer is D
Step-by-step explanation:
Giving Brainliest
A spy realizes his cover is blown and flees toward his secret evacuation spot at a speed of 60 mph. Two hours later, a special agent in a helicopter starts chasing the spy. The special agent travels the same route at a speed of 90 mph.
A What distance does the spy cover in t hours?
B What distance does the special agent cover in t hours?
C How fast is the distance between them reducing
D How far apart are the spy and special agent when the chase begins?
E How long does it take the special agent to catch the spy?
F At what speed should the special agent chase the spy if the evacuation spot is 240 miles from the setting point
Answers
The distance covered by the spy in t hours will be 60t while the special agent's distance is 90t.
How to calculate the distance?The distance covered by the spy in t hours will be calculated thus:
= 60 × t
= 60t
The distance covered by the special agent in t hours will be:
= 90 × t
= 90t
The difference in the distance between them every hour will be:
= 90t - 60t
= 30t
The distance between the spy and special agent when the chase begins will be:
= (2 × 60mph) - 0
= 120m - 0
= 120m
The time taken to catch the spy will be:
120 + 60t = 90t
90t - 60t = 120
30t = 120
t = 120/30 = 4
The special agent will catch the spy in 4 hours.
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Answer:
A: 60t
B: 90t
C: 30 mph
D: 120 miles away
E: 4 hours
F: 120 mph
Step-by-step explanation:
What is the volume of the square pyramid?
Answers
Answer:
you can solve by using the formula
volume = length x width x height
(I'm also bad at math so sorry if this isn't very helpful)
Step-by-step explanation:
1 all the bases are the same which means your length and width should be 5m
2 just multiply 5 x 5 x 14.2 and that should give you the awnser
Now suppose you buy a stock for $3,500. It decreases in value by 3% and then rises 8%. To the nearest cent, what is the new value of the stock now?
Answers
The new value of the stock after the percentage decrease and increase is $3666.60.
What is the new value of the stock?Percentage is the fraction of an amount expressed as a number out of hundred. Percentage is a measure of frequency.
Value of the stock after the decrease = (100 - 3) x $3500 = $3395
alue of the stock after the increase = (100 + 8) x 3395 = $3666.60
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Math homework pls help!!!
Answers
Answer:
17.8
Step-by-step explanation:
The power ands the square root cancel out.
Bill went on a very long run, so he ran kind of slowly. He ran 2 miles in 30 minutes. How many miles would he run in three hours?
Answers
Answer:
12 miles
Step-by-step explanation:
There are 3 hours = 180 minutes
180÷30=6
6×2=12
Hope that helps!
Answer:
12 miles
Step-by-step explanation:
Ashley ate Mexican food 4 out of 7 days on her vacation. If her vacation was 35 days, how many days did she eat Mexican food?
31
21
20
28
Answers
The number of days Ashley ate Mexican food while on vacation is 20 days.
How many days did Ashley eat mexican food?
The first step is to determine the fraction of the number of days Ashley atae Mexican food. In order to do this, divide 4 by 7
4/7.
The second step is to multiply 4/7 by 35
4/7 x 35= 20 days
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8. Harper, Elie, and Raina are having a skateboard race. Harper began at the starting line and rode at a
constant rate of 3 feet per second. Elie got a five-foot head start and rode two feet every 3 seconds. Raina
rode 3 feet every five seconds and had a two-foot head start.
Answers
Answer:
Step-by-step explanation:
How much does it cost to buy 3 watering cans if each watering can costs $7.48?
Answers
Answer:
$22.44
Step-by-step explanation:
We can multiply the total number of watering cans being bought by the total cost of one watering can.
3 * 7.48 = 22.44
It will cost $22.44 to buy three watering cans.
if f(x)=4x^2-3 and g9x)=x+1, find (f-g)(x)
Answers
Step-by-step explanation:
(f-g)(x) = f(x) - g(x)
the same applies to all other basic operations (like addition, multiplication, ...).
so,
(f-g)(x) = 4x² - 3 - (x + 1) = 4x² - 3 - x - 1 = 4x² - x - 4
A school needs to buy new notebook and desktop computers for its computer lab. The notebook computers cost $300 each, and the laptop computers cost $350 each. How much would it cost to buy 18 notebooks and 12 desktop computers? How much would it cost to buy nn notebooks and dd desktop computers?
Answers
Answer:
$9,600
Step-by-step explanation:
notebook computer : $300
laptop computer : $350
18 x 300 = 5,400
12 x 350 = 4,200
4,200 + 5,400 = 9,600
Find the measure of the missing angle in this isosceles triangle.
Answers
The measure of the missing angle(a) in the isosceles triangle(two sides and angle equal) is 70 degrees.
What is an Isosceles triangle?
An Isosceles triangle is a triangle that has two of it sides equal to each other and two of it angles equal to each other.
The base angle of an isosceles triangle are equal. Therefore, let's find angle a in the triangle.
55 + 55 + a = 180
Recall the sum of angle in a triangle is 180 degrees.
110 + a = 180
subtract 110 from both sides
110 - 110 + a = 180 - 110
a = 70 degrees
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